Bayesian hierarchical model for large-scale covariance matrix estimation.

Science.gov (United States)

Zhu, Dongxiao; Hero, Alfred O

2007-12-01

Many bioinformatics problems implicitly depend on estimating large-scale covariance matrix. The traditional approaches tend to give rise to high variance and low accuracy due to "overfitting." We cast the large-scale covariance matrix estimation problem into the Bayesian hierarchical model framework, and introduce dependency between covariance parameters. We demonstrate the advantages of our approaches over the traditional approaches using simulations and OMICS data analysis.

Introduction to Hierarchical Bayesian Modeling for Ecological Data

CERN Document Server

Parent, Eric

2012-01-01

Making statistical modeling and inference more accessible to ecologists and related scientists, Introduction to Hierarchical Bayesian Modeling for Ecological Data gives readers a flexible and effective framework to learn about complex ecological processes from various sources of data. It also helps readers get started on building their own statistical models. The text begins with simple models that progressively become more complex and realistic through explanatory covariates and intermediate hidden states variables. When fitting the models to data, the authors gradually present the concepts a

Hierarchical Bayesian spatial models for multispecies conservation planning and monitoring.

Science.gov (United States)

Carroll, Carlos; Johnson, Devin S; Dunk, Jeffrey R; Zielinski, William J

2010-12-01

Biologists who develop and apply habitat models are often familiar with the statistical challenges posed by their data's spatial structure but are unsure of whether the use of complex spatial models will increase the utility of model results in planning. We compared the relative performance of nonspatial and hierarchical Bayesian spatial models for three vertebrate and invertebrate taxa of conservation concern (Church's sideband snails [Monadenia churchi], red tree voles [Arborimus longicaudus], and Pacific fishers [Martes pennanti pacifica]) that provide examples of a range of distributional extents and dispersal abilities. We used presence-absence data derived from regional monitoring programs to develop models with both landscape and site-level environmental covariates. We used Markov chain Monte Carlo algorithms and a conditional autoregressive or intrinsic conditional autoregressive model framework to fit spatial models. The fit of Bayesian spatial models was between 35 and 55% better than the fit of nonspatial analogue models. Bayesian spatial models outperformed analogous models developed with maximum entropy (Maxent) methods. Although the best spatial and nonspatial models included similar environmental variables, spatial models provided estimates of residual spatial effects that suggested how ecological processes might structure distribution patterns. Spatial models built from presence-absence data improved fit most for localized endemic species with ranges constrained by poorly known biogeographic factors and for widely distributed species suspected to be strongly affected by unmeasured environmental variables or population processes. By treating spatial effects as a variable of interest rather than a nuisance, hierarchical Bayesian spatial models, especially when they are based on a common broad-scale spatial lattice (here the national Forest Inventory and Analysis grid of 24 km(2) hexagons), can increase the relevance of habitat models to multispecies

DUST SPECTRAL ENERGY DISTRIBUTIONS IN THE ERA OF HERSCHEL AND PLANCK: A HIERARCHICAL BAYESIAN-FITTING TECHNIQUE

International Nuclear Information System (INIS)

Kelly, Brandon C.; Goodman, Alyssa A.; Shetty, Rahul; Stutz, Amelia M.; Launhardt, Ralf; Kauffmann, Jens

2012-01-01

We present a hierarchical Bayesian method for fitting infrared spectral energy distributions (SEDs) of dust emission to observed fluxes. Under the standard assumption of optically thin single temperature (T) sources, the dust SED as represented by a power-law-modified blackbody is subject to a strong degeneracy between T and the spectral index β. The traditional non-hierarchical approaches, typically based on χ 2 minimization, are severely limited by this degeneracy, as it produces an artificial anti-correlation between T and β even with modest levels of observational noise. The hierarchical Bayesian method rigorously and self-consistently treats measurement uncertainties, including calibration and noise, resulting in more precise SED fits. As a result, the Bayesian fits do not produce any spurious anti-correlations between the SED parameters due to measurement uncertainty. We demonstrate that the Bayesian method is substantially more accurate than the χ 2 fit in recovering the SED parameters, as well as the correlations between them. As an illustration, we apply our method to Herschel and submillimeter ground-based observations of the star-forming Bok globule CB244. This source is a small, nearby molecular cloud containing a single low-mass protostar and a starless core. We find that T and β are weakly positively correlated—in contradiction with the χ 2 fits, which indicate a T-β anti-correlation from the same data set. Additionally, in comparison to the χ 2 fits the Bayesian SED parameter estimates exhibit a reduced range in values.

A Fast Iterative Bayesian Inference Algorithm for Sparse Channel Estimation

DEFF Research Database (Denmark)

Pedersen, Niels Lovmand; Manchón, Carles Navarro; Fleury, Bernard Henri

2013-01-01

representation of the Bessel K probability density function; a highly efficient, fast iterative Bayesian inference method is then applied to the proposed model. The resulting estimator outperforms other state-of-the-art Bayesian and non-Bayesian estimators, either by yielding lower mean squared estimation error...

Fast Bayesian Non-Negative Matrix Factorisation and Tri-Factorisation

DEFF Research Database (Denmark)

Brouwer, Thomas; Frellsen, Jes; Liò, Pietro

We present a fast variational Bayesian algorithm for performing non-negative matrix factorisation and tri-factorisation. We show that our approach achieves faster convergence per iteration and timestep (wall-clock) than Gibbs sampling and non-probabilistic approaches, and do not require additional...... samples to estimate the posterior. We show that in particular for matrix tri-factorisation convergence is difficult, but our variational Bayesian approach offers a fast solution, allowing the tri-factorisation approach to be used more effectively....

Fast and accurate Bayesian model criticism and conflict diagnostics using R-INLA

KAUST Repository

Ferkingstad, Egil

2017-10-16

Bayesian hierarchical models are increasingly popular for realistic modelling and analysis of complex data. This trend is accompanied by the need for flexible, general and computationally efficient methods for model criticism and conflict detection. Usually, a Bayesian hierarchical model incorporates a grouping of the individual data points, as, for example, with individuals in repeated measurement data. In such cases, the following question arises: Are any of the groups “outliers,” or in conflict with the remaining groups? Existing general approaches aiming to answer such questions tend to be extremely computationally demanding when model fitting is based on Markov chain Monte Carlo. We show how group-level model criticism and conflict detection can be carried out quickly and accurately through integrated nested Laplace approximations (INLA). The new method is implemented as a part of the open-source R-INLA package for Bayesian computing (http://r-inla.org).

Hierarchical Bayesian inference for ion channel screening dose-response data [version 2; referees: 2 approved

Directory of Open Access Journals (Sweden)

Ross H Johnstone

2017-03-01

Full Text Available Dose-response (or ‘concentration-effect’ relationships commonly occur in biological and pharmacological systems and are well characterised by Hill curves. These curves are described by an equation with two parameters: the inhibitory concentration 50% (IC50; and the Hill coefficient. Typically just the ‘best fit’ parameter values are reported in the literature. Here we introduce a Python-based software tool, PyHillFit , and describe the underlying Bayesian inference methods that it uses, to infer probability distributions for these parameters as well as the level of experimental observation noise. The tool also allows for hierarchical fitting, characterising the effect of inter-experiment variability. We demonstrate the use of the tool on a recently published dataset on multiple ion channel inhibition by multiple drug compounds. We compare the maximum likelihood, Bayesian and hierarchical Bayesian approaches. We then show how uncertainty in dose-response inputs can be characterised and propagated into a cardiac action potential simulation to give a probability distribution on model outputs.

Topics in Computational Bayesian Statistics With Applications to Hierarchical Models in Astronomy and Sociology

Science.gov (United States)

Sahai, Swupnil

This thesis includes three parts. The overarching theme is how to analyze structured hierarchical data, with applications to astronomy and sociology. The first part discusses how expectation propagation can be used to parallelize the computation when fitting big hierarchical bayesian models. This methodology is then used to fit a novel, nonlinear mixture model to ultraviolet radiation from various regions of the observable universe. The second part discusses how the Stan probabilistic programming language can be used to numerically integrate terms in a hierarchical bayesian model. This technique is demonstrated on supernovae data to significantly speed up convergence to the posterior distribution compared to a previous study that used a Gibbs-type sampler. The third part builds a formal latent kernel representation for aggregate relational data as a way to more robustly estimate the mixing characteristics of agents in a network. In particular, the framework is applied to sociology surveys to estimate, as a function of ego age, the age and sex composition of the personal networks of individuals in the United States.

Road network safety evaluation using Bayesian hierarchical joint model.

Science.gov (United States)

Wang, Jie; Huang, Helai

2016-05-01

Safety and efficiency are commonly regarded as two significant performance indicators of transportation systems. In practice, road network planning has focused on road capacity and transport efficiency whereas the safety level of a road network has received little attention in the planning stage. This study develops a Bayesian hierarchical joint model for road network safety evaluation to help planners take traffic safety into account when planning a road network. The proposed model establishes relationships between road network risk and micro-level variables related to road entities and traffic volume, as well as socioeconomic, trip generation and network density variables at macro level which are generally used for long term transportation plans. In addition, network spatial correlation between intersections and their connected road segments is also considered in the model. A road network is elaborately selected in order to compare the proposed hierarchical joint model with a previous joint model and a negative binomial model. According to the results of the model comparison, the hierarchical joint model outperforms the joint model and negative binomial model in terms of the goodness-of-fit and predictive performance, which indicates the reasonableness of considering the hierarchical data structure in crash prediction and analysis. Moreover, both random effects at the TAZ level and the spatial correlation between intersections and their adjacent segments are found to be significant, supporting the employment of the hierarchical joint model as an alternative in road-network-level safety modeling as well. Copyright © 2016 Elsevier Ltd. All rights reserved.

Bayesian inference with ecological applications

CERN Document Server

Link, William A

2009-01-01

This text is written to provide a mathematically sound but accessible and engaging introduction to Bayesian inference specifically for environmental scientists, ecologists and wildlife biologists. It emphasizes the power and usefulness of Bayesian methods in an ecological context. The advent of fast personal computers and easily available software has simplified the use of Bayesian and hierarchical models . One obstacle remains for ecologists and wildlife biologists, namely the near absence of Bayesian texts written specifically for them. The book includes many relevant examples, is supported by software and examples on a companion website and will become an essential grounding in this approach for students and research ecologists. Engagingly written text specifically designed to demystify a complex subject Examples drawn from ecology and wildlife research An essential grounding for graduate and research ecologists in the increasingly prevalent Bayesian approach to inference Companion website with analyt...

Bayesian Uncertainty Quantification for Subsurface Inversion Using a Multiscale Hierarchical Model

KAUST Repository

Mondal, Anirban

2014-07-03

We consider a Bayesian approach to nonlinear inverse problems in which the unknown quantity is a random field (spatial or temporal). The Bayesian approach contains a natural mechanism for regularization in the form of prior information, can incorporate information from heterogeneous sources and provide a quantitative assessment of uncertainty in the inverse solution. The Bayesian setting casts the inverse solution as a posterior probability distribution over the model parameters. The Karhunen-Loeve expansion is used for dimension reduction of the random field. Furthermore, we use a hierarchical Bayes model to inject multiscale data in the modeling framework. In this Bayesian framework, we show that this inverse problem is well-posed by proving that the posterior measure is Lipschitz continuous with respect to the data in total variation norm. Computational challenges in this construction arise from the need for repeated evaluations of the forward model (e.g., in the context of MCMC) and are compounded by high dimensionality of the posterior. We develop two-stage reversible jump MCMC that has the ability to screen the bad proposals in the first inexpensive stage. Numerical results are presented by analyzing simulated as well as real data from hydrocarbon reservoir. This article has supplementary material available online. © 2014 American Statistical Association and the American Society for Quality.

Parameterization of aquatic ecosystem functioning and its natural variation: Hierarchical Bayesian modelling of plankton food web dynamics

Science.gov (United States)

Norros, Veera; Laine, Marko; Lignell, Risto; Thingstad, Frede

2017-10-01

Methods for extracting empirically and theoretically sound parameter values are urgently needed in aquatic ecosystem modelling to describe key flows and their variation in the system. Here, we compare three Bayesian formulations for mechanistic model parameterization that differ in their assumptions about the variation in parameter values between various datasets: 1) global analysis - no variation, 2) separate analysis - independent variation and 3) hierarchical analysis - variation arising from a shared distribution defined by hyperparameters. We tested these methods, using computer-generated and empirical data, coupled with simplified and reasonably realistic plankton food web models, respectively. While all methods were adequate, the simulated example demonstrated that a well-designed hierarchical analysis can result in the most accurate and precise parameter estimates and predictions, due to its ability to combine information across datasets. However, our results also highlighted sensitivity to hyperparameter prior distributions as an important caveat of hierarchical analysis. In the more complex empirical example, hierarchical analysis was able to combine precise identification of parameter values with reasonably good predictive performance, although the ranking of the methods was less straightforward. We conclude that hierarchical Bayesian analysis is a promising tool for identifying key ecosystem-functioning parameters and their variation from empirical datasets.

Probabilistic daily ILI syndromic surveillance with a spatio-temporal Bayesian hierarchical model.

Directory of Open Access Journals (Sweden)

Ta-Chien Chan

Full Text Available BACKGROUND: For daily syndromic surveillance to be effective, an efficient and sensible algorithm would be expected to detect aberrations in influenza illness, and alert public health workers prior to any impending epidemic. This detection or alert surely contains uncertainty, and thus should be evaluated with a proper probabilistic measure. However, traditional monitoring mechanisms simply provide a binary alert, failing to adequately address this uncertainty. METHODS AND FINDINGS: Based on the Bayesian posterior probability of influenza-like illness (ILI visits, the intensity of outbreak can be directly assessed. The numbers of daily emergency room ILI visits at five community hospitals in Taipei City during 2006-2007 were collected and fitted with a Bayesian hierarchical model containing meteorological factors such as temperature and vapor pressure, spatial interaction with conditional autoregressive structure, weekend and holiday effects, seasonality factors, and previous ILI visits. The proposed algorithm recommends an alert for action if the posterior probability is larger than 70%. External data from January to February of 2008 were retained for validation. The decision rule detects successfully the peak in the validation period. When comparing the posterior probability evaluation with the modified Cusum method, results show that the proposed method is able to detect the signals 1-2 days prior to the rise of ILI visits. CONCLUSIONS: This Bayesian hierarchical model not only constitutes a dynamic surveillance system but also constructs a stochastic evaluation of the need to call for alert. The monitoring mechanism provides earlier detection as well as a complementary tool for current surveillance programs.

Hierarchical Bayesian nonparametric mixture models for clustering with variable relevance determination.

Science.gov (United States)

Yau, Christopher; Holmes, Chris

2011-07-01

We propose a hierarchical Bayesian nonparametric mixture model for clustering when some of the covariates are assumed to be of varying relevance to the clustering problem. This can be thought of as an issue in variable selection for unsupervised learning. We demonstrate that by defining a hierarchical population based nonparametric prior on the cluster locations scaled by the inverse covariance matrices of the likelihood we arrive at a 'sparsity prior' representation which admits a conditionally conjugate prior. This allows us to perform full Gibbs sampling to obtain posterior distributions over parameters of interest including an explicit measure of each covariate's relevance and a distribution over the number of potential clusters present in the data. This also allows for individual cluster specific variable selection. We demonstrate improved inference on a number of canonical problems.

Prion Amplification and Hierarchical Bayesian Modeling Refine Detection of Prion Infection

Science.gov (United States)

Wyckoff, A. Christy; Galloway, Nathan; Meyerett-Reid, Crystal; Powers, Jenny; Spraker, Terry; Monello, Ryan J.; Pulford, Bruce; Wild, Margaret; Antolin, Michael; Vercauteren, Kurt; Zabel, Mark

2015-02-01

Prions are unique infectious agents that replicate without a genome and cause neurodegenerative diseases that include chronic wasting disease (CWD) of cervids. Immunohistochemistry (IHC) is currently considered the gold standard for diagnosis of a prion infection but may be insensitive to early or sub-clinical CWD that are important to understanding CWD transmission and ecology. We assessed the potential of serial protein misfolding cyclic amplification (sPMCA) to improve detection of CWD prior to the onset of clinical signs. We analyzed tissue samples from free-ranging Rocky Mountain elk (Cervus elaphus nelsoni) and used hierarchical Bayesian analysis to estimate the specificity and sensitivity of IHC and sPMCA conditional on simultaneously estimated disease states. Sensitivity estimates were higher for sPMCA (99.51%, credible interval (CI) 97.15-100%) than IHC of obex (brain stem, 76.56%, CI 57.00-91.46%) or retropharyngeal lymph node (90.06%, CI 74.13-98.70%) tissues, or both (98.99%, CI 90.01-100%). Our hierarchical Bayesian model predicts the prevalence of prion infection in this elk population to be 18.90% (CI 15.50-32.72%), compared to previous estimates of 12.90%. Our data reveal a previously unidentified sub-clinical prion-positive portion of the elk population that could represent silent carriers capable of significantly impacting CWD ecology.

Prion amplification and hierarchical Bayesian modeling refine detection of prion infection.

Science.gov (United States)

Wyckoff, A Christy; Galloway, Nathan; Meyerett-Reid, Crystal; Powers, Jenny; Spraker, Terry; Monello, Ryan J; Pulford, Bruce; Wild, Margaret; Antolin, Michael; VerCauteren, Kurt; Zabel, Mark

2015-02-10

Prions are unique infectious agents that replicate without a genome and cause neurodegenerative diseases that include chronic wasting disease (CWD) of cervids. Immunohistochemistry (IHC) is currently considered the gold standard for diagnosis of a prion infection but may be insensitive to early or sub-clinical CWD that are important to understanding CWD transmission and ecology. We assessed the potential of serial protein misfolding cyclic amplification (sPMCA) to improve detection of CWD prior to the onset of clinical signs. We analyzed tissue samples from free-ranging Rocky Mountain elk (Cervus elaphus nelsoni) and used hierarchical Bayesian analysis to estimate the specificity and sensitivity of IHC and sPMCA conditional on simultaneously estimated disease states. Sensitivity estimates were higher for sPMCA (99.51%, credible interval (CI) 97.15-100%) than IHC of obex (brain stem, 76.56%, CI 57.00-91.46%) or retropharyngeal lymph node (90.06%, CI 74.13-98.70%) tissues, or both (98.99%, CI 90.01-100%). Our hierarchical Bayesian model predicts the prevalence of prion infection in this elk population to be 18.90% (CI 15.50-32.72%), compared to previous estimates of 12.90%. Our data reveal a previously unidentified sub-clinical prion-positive portion of the elk population that could represent silent carriers capable of significantly impacting CWD ecology.

Fast and accurate Bayesian model criticism and conflict diagnostics using R-INLA

KAUST Repository

Ferkingstad, Egil; Held, Leonhard; Rue, Haavard

2017-01-01

. Usually, a Bayesian hierarchical model incorporates a grouping of the individual data points, as, for example, with individuals in repeated measurement data. In such cases, the following question arises: Are any of the groups “outliers,” or in conflict

Hierarchical Bayesian modeling of the space - time diffusion patterns of cholera epidemic in Kumasi, Ghana

NARCIS (Netherlands)

Osei, Frank B.; Osei, F.B.; Duker, Alfred A.; Stein, A.

2011-01-01

This study analyses the joint effects of the two transmission routes of cholera on the space-time diffusion dynamics. Statistical models are developed and presented to investigate the transmission network routes of cholera diffusion. A hierarchical Bayesian modelling approach is employed for a joint

A Bayesian Hierarchical Model for Glacial Dynamics Based on the Shallow Ice Approximation and its Evaluation Using Analytical Solutions

Science.gov (United States)

Gopalan, Giri; Hrafnkelsson, Birgir; Aðalgeirsdóttir, Guðfinna; Jarosch, Alexander H.; Pálsson, Finnur

2018-03-01

Bayesian hierarchical modeling can assist the study of glacial dynamics and ice flow properties. This approach will allow glaciologists to make fully probabilistic predictions for the thickness of a glacier at unobserved spatio-temporal coordinates, and it will also allow for the derivation of posterior probability distributions for key physical parameters such as ice viscosity and basal sliding. The goal of this paper is to develop a proof of concept for a Bayesian hierarchical model constructed, which uses exact analytical solutions for the shallow ice approximation (SIA) introduced by Bueler et al. (2005). A suite of test simulations utilizing these exact solutions suggests that this approach is able to adequately model numerical errors and produce useful physical parameter posterior distributions and predictions. A byproduct of the development of the Bayesian hierarchical model is the derivation of a novel finite difference method for solving the SIA partial differential equation (PDE). An additional novelty of this work is the correction of numerical errors induced through a numerical solution using a statistical model. This error correcting process models numerical errors that accumulate forward in time and spatial variation of numerical errors between the dome, interior, and margin of a glacier.

An economic growth model based on financial credits distribution to the government economy priority sectors of each regency in Indonesia using hierarchical Bayesian method

Science.gov (United States)

Yasmirullah, Septia Devi Prihastuti; Iriawan, Nur; Sipayung, Feronika Rosalinda

2017-11-01

The success of regional economic establishment could be measured by economic growth. Since the Act No. 32 of 2004 has been implemented, unbalance economic among the regency in Indonesia is increasing. This condition is contrary different with the government goal to build society welfare through the economic activity development in each region. This research aims to examine economic growth through the distribution of bank credits to each Indonesia's regency. The data analyzed in this research is hierarchically structured data which follow normal distribution in first level. Two modeling approaches are employed in this research, a global-one level Bayesian approach and two-level hierarchical Bayesian approach. The result shows that hierarchical Bayesian has succeeded to demonstrate a better estimation than a global-one level Bayesian. It proves that the different economic growth in each province is significantly influenced by the variations of micro level characteristics in each province. These variations are significantly affected by cities and province characteristics in second level.

Bayesian site selection for fast Gaussian process regression

KAUST Repository

Pourhabib, Arash; Liang, Faming; Ding, Yu

2014-01-01

Gaussian Process (GP) regression is a popular method in the field of machine learning and computer experiment designs; however, its ability to handle large data sets is hindered by the computational difficulty in inverting a large covariance matrix. Likelihood approximation methods were developed as a fast GP approximation, thereby reducing the computation cost of GP regression by utilizing a much smaller set of unobserved latent variables called pseudo points. This article reports a further improvement to the likelihood approximation methods by simultaneously deciding both the number and locations of the pseudo points. The proposed approach is a Bayesian site selection method where both the number and locations of the pseudo inputs are parameters in the model, and the Bayesian model is solved using a reversible jump Markov chain Monte Carlo technique. Through a number of simulated and real data sets, it is demonstrated that with appropriate priors chosen, the Bayesian site selection method can produce a good balance between computation time and prediction accuracy: it is fast enough to handle large data sets that a full GP is unable to handle, and it improves, quite often remarkably, the prediction accuracy, compared with the existing likelihood approximations. © 2014 Taylor and Francis Group, LLC.

Bayesian site selection for fast Gaussian process regression

KAUST Repository

Pourhabib, Arash

2014-02-05

Gaussian Process (GP) regression is a popular method in the field of machine learning and computer experiment designs; however, its ability to handle large data sets is hindered by the computational difficulty in inverting a large covariance matrix. Likelihood approximation methods were developed as a fast GP approximation, thereby reducing the computation cost of GP regression by utilizing a much smaller set of unobserved latent variables called pseudo points. This article reports a further improvement to the likelihood approximation methods by simultaneously deciding both the number and locations of the pseudo points. The proposed approach is a Bayesian site selection method where both the number and locations of the pseudo inputs are parameters in the model, and the Bayesian model is solved using a reversible jump Markov chain Monte Carlo technique. Through a number of simulated and real data sets, it is demonstrated that with appropriate priors chosen, the Bayesian site selection method can produce a good balance between computation time and prediction accuracy: it is fast enough to handle large data sets that a full GP is unable to handle, and it improves, quite often remarkably, the prediction accuracy, compared with the existing likelihood approximations. © 2014 Taylor and Francis Group, LLC.

A sow replacement model using Bayesian updating in a three-level hierarchic Markov process. II. Optimization model

DEFF Research Database (Denmark)

Kristensen, Anders Ringgaard; Søllested, Thomas Algot

2004-01-01

improvements. The biological model of the replacement model is described in a previous paper and in this paper the optimization model is described. The model is developed as a prototype for use under practical conditions. The application of the model is demonstrated using data from two commercial Danish sow......Recent methodological improvements in replacement models comprising multi-level hierarchical Markov processes and Bayesian updating have hardly been implemented in any replacement model and the aim of this study is to present a sow replacement model that really uses these methodological...... herds. It is concluded that the Bayesian updating technique and the hierarchical structure decrease the size of the state space dramatically. Since parameter estimates vary considerably among herds it is concluded that decision support concerning sow replacement only makes sense with parameters...

Use of a Bayesian hierarchical model to study the allometric scaling of the fetoplacental weight ratio

Directory of Open Access Journals (Sweden)

Fidel Ernesto Castro Morales

2016-03-01

Full Text Available Abstract Objectives: to propose the use of a Bayesian hierarchical model to study the allometric scaling of the fetoplacental weight ratio, including possible confounders. Methods: data from 26 singleton pregnancies with gestational age at birth between 37 and 42 weeks were analyzed. The placentas were collected immediately after delivery and stored under refrigeration until the time of analysis, which occurred within up to 12 hours. Maternal data were collected from medical records. A Bayesian hierarchical model was proposed and Markov chain Monte Carlo simulation methods were used to obtain samples from distribution a posteriori. Results: the model developed showed a reasonable fit, even allowing for the incorporation of variables and a priori information on the parameters used. Conclusions: new variables can be added to the modelfrom the available code, allowing many possibilities for data analysis and indicating the potential for use in research on the subject.

Inferring on the Intentions of Others by Hierarchical Bayesian Learning

Science.gov (United States)

Diaconescu, Andreea O.; Mathys, Christoph; Weber, Lilian A. E.; Daunizeau, Jean; Kasper, Lars; Lomakina, Ekaterina I.; Fehr, Ernst; Stephan, Klaas E.

2014-01-01

Inferring on others' (potentially time-varying) intentions is a fundamental problem during many social transactions. To investigate the underlying mechanisms, we applied computational modeling to behavioral data from an economic game in which 16 pairs of volunteers (randomly assigned to “player” or “adviser” roles) interacted. The player performed a probabilistic reinforcement learning task, receiving information about a binary lottery from a visual pie chart. The adviser, who received more predictive information, issued an additional recommendation. Critically, the game was structured such that the adviser's incentives to provide helpful or misleading information varied in time. Using a meta-Bayesian modeling framework, we found that the players' behavior was best explained by the deployment of hierarchical learning: they inferred upon the volatility of the advisers' intentions in order to optimize their predictions about the validity of their advice. Beyond learning, volatility estimates also affected the trial-by-trial variability of decisions: participants were more likely to rely on their estimates of advice accuracy for making choices when they believed that the adviser's intentions were presently stable. Finally, our model of the players' inference predicted the players' interpersonal reactivity index (IRI) scores, explicit ratings of the advisers' helpfulness and the advisers' self-reports on their chosen strategy. Overall, our results suggest that humans (i) employ hierarchical generative models to infer on the changing intentions of others, (ii) use volatility estimates to inform decision-making in social interactions, and (iii) integrate estimates of advice accuracy with non-social sources of information. The Bayesian framework presented here can quantify individual differences in these mechanisms from simple behavioral readouts and may prove useful in future clinical studies of maladaptive social cognition. PMID:25187943

A hierarchical Bayesian spatio-temporal model to forecast trapped particle fluxes over the SAA region

Czech Academy of Sciences Publication Activity Database

Suparta, W.; Gusrizal, G.; Kudela, Karel; Isa, Z.

2017-01-01

Roč. 28, č. 3 (2017), s. 357-370 ISSN 1017-0839 R&D Projects: GA MŠk EF15_003/0000481 Institutional support: RVO:61389005 Keywords : trapped particle * spatio-temporal * hierarchical Bayesian * forecasting Subject RIV: DG - Athmosphere Sciences, Meteorology OBOR OECD: Meteorology and atmospheric sciences Impact factor: 0.752, year: 2016

Assimilating irregularly spaced sparsely observed turbulent signals with hierarchical Bayesian reduced stochastic filters

International Nuclear Information System (INIS)

Brown, Kristen A.; Harlim, John

2013-01-01

In this paper, we consider a practical filtering approach for assimilating irregularly spaced, sparsely observed turbulent signals through a hierarchical Bayesian reduced stochastic filtering framework. The proposed hierarchical Bayesian approach consists of two steps, blending a data-driven interpolation scheme and the Mean Stochastic Model (MSM) filter. We examine the potential of using the deterministic piecewise linear interpolation scheme and the ordinary kriging scheme in interpolating irregularly spaced raw data to regularly spaced processed data and the importance of dynamical constraint (through MSM) in filtering the processed data on a numerically stiff state estimation problem. In particular, we test this approach on a two-layer quasi-geostrophic model in a two-dimensional domain with a small radius of deformation to mimic ocean turbulence. Our numerical results suggest that the dynamical constraint becomes important when the observation noise variance is large. Second, we find that the filtered estimates with ordinary kriging are superior to those with linear interpolation when observation networks are not too sparse; such robust results are found from numerical simulations with many randomly simulated irregularly spaced observation networks, various observation time intervals, and observation error variances. Third, when the observation network is very sparse, we find that both the kriging and linear interpolations are comparable

Bayesian Hierarchical Distributed Lag Models for Summer Ozone Exposure and Cardio-Respiratory Mortality

OpenAIRE

Yi Huang; Francesca Dominici; Michelle Bell

2004-01-01

In this paper, we develop Bayesian hierarchical distributed lag models for estimating associations between daily variations in summer ozone levels and daily variations in cardiovascular and respiratory (CVDRESP) mortality counts for 19 U.S. large cities included in the National Morbidity Mortality Air Pollution Study (NMMAPS) for the period 1987 - 1994. At the first stage, we define a semi-parametric distributed lag Poisson regression model to estimate city-specific relative rates of CVDRESP ...

Correlation Between Hierarchical Bayesian and Aerosol Optical Depth PM2.5 Data and Respiratory-Cardiovascular Chronic Diseases

Science.gov (United States)

Tools to estimate PM2.5 mass have expanded in recent years, and now include: 1) stationary monitor readings, 2) Community Multi-Scale Air Quality (CMAQ) model estimates, 3) Hierarchical Bayesian (HB) estimates from combined stationary monitor readings and CMAQ model output; and, ...

Efficient Bayesian hierarchical functional data analysis with basis function approximations using Gaussian-Wishart processes.

Science.gov (United States)

Yang, Jingjing; Cox, Dennis D; Lee, Jong Soo; Ren, Peng; Choi, Taeryon

2017-12-01

Functional data are defined as realizations of random functions (mostly smooth functions) varying over a continuum, which are usually collected on discretized grids with measurement errors. In order to accurately smooth noisy functional observations and deal with the issue of high-dimensional observation grids, we propose a novel Bayesian method based on the Bayesian hierarchical model with a Gaussian-Wishart process prior and basis function representations. We first derive an induced model for the basis-function coefficients of the functional data, and then use this model to conduct posterior inference through Markov chain Monte Carlo methods. Compared to the standard Bayesian inference that suffers serious computational burden and instability in analyzing high-dimensional functional data, our method greatly improves the computational scalability and stability, while inheriting the advantage of simultaneously smoothing raw observations and estimating the mean-covariance functions in a nonparametric way. In addition, our method can naturally handle functional data observed on random or uncommon grids. Simulation and real studies demonstrate that our method produces similar results to those obtainable by the standard Bayesian inference with low-dimensional common grids, while efficiently smoothing and estimating functional data with random and high-dimensional observation grids when the standard Bayesian inference fails. In conclusion, our method can efficiently smooth and estimate high-dimensional functional data, providing one way to resolve the curse of dimensionality for Bayesian functional data analysis with Gaussian-Wishart processes. © 2017, The International Biometric Society.

Bayesian Hierarchical Scale Mixtures of Log-Normal Models for Inference in Reliability with Stochastic Constraint

Directory of Open Access Journals (Sweden)

Hea-Jung Kim

2017-06-01

Full Text Available This paper develops Bayesian inference in reliability of a class of scale mixtures of log-normal failure time (SMLNFT models with stochastic (or uncertain constraint in their reliability measures. The class is comprehensive and includes existing failure time (FT models (such as log-normal, log-Cauchy, and log-logistic FT models as well as new models that are robust in terms of heavy-tailed FT observations. Since classical frequency approaches to reliability analysis based on the SMLNFT model with stochastic constraint are intractable, the Bayesian method is pursued utilizing a Markov chain Monte Carlo (MCMC sampling based approach. This paper introduces a two-stage maximum entropy (MaxEnt prior, which elicits a priori uncertain constraint and develops Bayesian hierarchical SMLNFT model by using the prior. The paper also proposes an MCMC method for Bayesian inference in the SMLNFT model reliability and calls attention to properties of the MaxEnt prior that are useful for method development. Finally, two data sets are used to illustrate how the proposed methodology works.

Prediction of road accidents: A Bayesian hierarchical approach.

Science.gov (United States)

Deublein, Markus; Schubert, Matthias; Adey, Bryan T; Köhler, Jochen; Faber, Michael H

2013-03-01

In this paper a novel methodology for the prediction of the occurrence of road accidents is presented. The methodology utilizes a combination of three statistical methods: (1) gamma-updating of the occurrence rates of injury accidents and injured road users, (2) hierarchical multivariate Poisson-lognormal regression analysis taking into account correlations amongst multiple dependent model response variables and effects of discrete accident count data e.g. over-dispersion, and (3) Bayesian inference algorithms, which are applied by means of data mining techniques supported by Bayesian Probabilistic Networks in order to represent non-linearity between risk indicating and model response variables, as well as different types of uncertainties which might be present in the development of the specific models. Prior Bayesian Probabilistic Networks are first established by means of multivariate regression analysis of the observed frequencies of the model response variables, e.g. the occurrence of an accident, and observed values of the risk indicating variables, e.g. degree of road curvature. Subsequently, parameter learning is done using updating algorithms, to determine the posterior predictive probability distributions of the model response variables, conditional on the values of the risk indicating variables. The methodology is illustrated through a case study using data of the Austrian rural motorway network. In the case study, on randomly selected road segments the methodology is used to produce a model to predict the expected number of accidents in which an injury has occurred and the expected number of light, severe and fatally injured road users. Additionally, the methodology is used for geo-referenced identification of road sections with increased occurrence probabilities of injury accident events on a road link between two Austrian cities. It is shown that the proposed methodology can be used to develop models to estimate the occurrence of road accidents for any

An approach based on Hierarchical Bayesian Graphical Models for measurement interpretation under uncertainty

Science.gov (United States)

Skataric, Maja; Bose, Sandip; Zeroug, Smaine; Tilke, Peter

2017-02-01

It is not uncommon in the field of non-destructive evaluation that multiple measurements encompassing a variety of modalities are available for analysis and interpretation for determining the underlying states of nature of the materials or parts being tested. Despite and sometimes due to the richness of data, significant challenges arise in the interpretation manifested as ambiguities and inconsistencies due to various uncertain factors in the physical properties (inputs), environment, measurement device properties, human errors, and the measurement data (outputs). Most of these uncertainties cannot be described by any rigorous mathematical means, and modeling of all possibilities is usually infeasible for many real time applications. In this work, we will discuss an approach based on Hierarchical Bayesian Graphical Models (HBGM) for the improved interpretation of complex (multi-dimensional) problems with parametric uncertainties that lack usable physical models. In this setting, the input space of the physical properties is specified through prior distributions based on domain knowledge and expertise, which are represented as Gaussian mixtures to model the various possible scenarios of interest for non-destructive testing applications. Forward models are then used offline to generate the expected distribution of the proposed measurements which are used to train a hierarchical Bayesian network. In Bayesian analysis, all model parameters are treated as random variables, and inference of the parameters is made on the basis of posterior distribution given the observed data. Learned parameters of the posterior distribution obtained after the training can therefore be used to build an efficient classifier for differentiating new observed data in real time on the basis of pre-trained models. We will illustrate the implementation of the HBGM approach to ultrasonic measurements used for cement evaluation of cased wells in the oil industry.

Bayesian hierarchical model for variations in earthquake peak ground acceleration within small-aperture arrays

KAUST Repository

Rahpeyma, Sahar

2018-04-17

Knowledge of the characteristics of earthquake ground motion is fundamental for earthquake hazard assessments. Over small distances, relative to the source–site distance, where uniform site conditions are expected, the ground motion variability is also expected to be insignificant. However, despite being located on what has been characterized as a uniform lava‐rock site condition, considerable peak ground acceleration (PGA) variations were observed on stations of a small‐aperture array (covering approximately 1 km2) of accelerographs in Southwest Iceland during the Ölfus earthquake of magnitude 6.3 on May 29, 2008 and its sequence of aftershocks. We propose a novel Bayesian hierarchical model for the PGA variations accounting separately for earthquake event effects, station effects, and event‐station effects. An efficient posterior inference scheme based on Markov chain Monte Carlo (MCMC) simulations is proposed for the new model. The variance of the station effect is certainly different from zero according to the posterior density, indicating that individual station effects are different from one another. The Bayesian hierarchical model thus captures the observed PGA variations and quantifies to what extent the source and recording sites contribute to the overall variation in ground motions over relatively small distances on the lava‐rock site condition.

Bayesian hierarchical model for variations in earthquake peak ground acceleration within small-aperture arrays

KAUST Repository

Rahpeyma, Sahar; Halldorsson, Benedikt; Hrafnkelsson, Birgir; Jonsson, Sigurjon

2018-01-01

Knowledge of the characteristics of earthquake ground motion is fundamental for earthquake hazard assessments. Over small distances, relative to the source–site distance, where uniform site conditions are expected, the ground motion variability is also expected to be insignificant. However, despite being located on what has been characterized as a uniform lava‐rock site condition, considerable peak ground acceleration (PGA) variations were observed on stations of a small‐aperture array (covering approximately 1 km2) of accelerographs in Southwest Iceland during the Ölfus earthquake of magnitude 6.3 on May 29, 2008 and its sequence of aftershocks. We propose a novel Bayesian hierarchical model for the PGA variations accounting separately for earthquake event effects, station effects, and event‐station effects. An efficient posterior inference scheme based on Markov chain Monte Carlo (MCMC) simulations is proposed for the new model. The variance of the station effect is certainly different from zero according to the posterior density, indicating that individual station effects are different from one another. The Bayesian hierarchical model thus captures the observed PGA variations and quantifies to what extent the source and recording sites contribute to the overall variation in ground motions over relatively small distances on the lava‐rock site condition.

Bayesian Hierarchical Structure for Quantifying Population Variability to Inform Probabilistic Health Risk Assessments.

Science.gov (United States)

Shao, Kan; Allen, Bruce C; Wheeler, Matthew W

2017-10-01

Human variability is a very important factor considered in human health risk assessment for protecting sensitive populations from chemical exposure. Traditionally, to account for this variability, an interhuman uncertainty factor is applied to lower the exposure limit. However, using a fixed uncertainty factor rather than probabilistically accounting for human variability can hardly support probabilistic risk assessment advocated by a number of researchers; new methods are needed to probabilistically quantify human population variability. We propose a Bayesian hierarchical model to quantify variability among different populations. This approach jointly characterizes the distribution of risk at background exposure and the sensitivity of response to exposure, which are commonly represented by model parameters. We demonstrate, through both an application to real data and a simulation study, that using the proposed hierarchical structure adequately characterizes variability across different populations. © 2016 Society for Risk Analysis.

A hierarchical bayesian model to quantify uncertainty of stream water temperature forecasts.

Directory of Open Access Journals (Sweden)

Guillaume Bal

Full Text Available Providing generic and cost effective modelling approaches to reconstruct and forecast freshwater temperature using predictors as air temperature and water discharge is a prerequisite to understanding ecological processes underlying the impact of water temperature and of global warming on continental aquatic ecosystems. Using air temperature as a simple linear predictor of water temperature can lead to significant bias in forecasts as it does not disentangle seasonality and long term trends in the signal. Here, we develop an alternative approach based on hierarchical Bayesian statistical time series modelling of water temperature, air temperature and water discharge using seasonal sinusoidal periodic signals and time varying means and amplitudes. Fitting and forecasting performances of this approach are compared with that of simple linear regression between water and air temperatures using i an emotive simulated example, ii application to three French coastal streams with contrasting bio-geographical conditions and sizes. The time series modelling approach better fit data and does not exhibit forecasting bias in long term trends contrary to the linear regression. This new model also allows for more accurate forecasts of water temperature than linear regression together with a fair assessment of the uncertainty around forecasting. Warming of water temperature forecast by our hierarchical Bayesian model was slower and more uncertain than that expected with the classical regression approach. These new forecasts are in a form that is readily usable in further ecological analyses and will allow weighting of outcomes from different scenarios to manage climate change impacts on freshwater wildlife.

Sampling-free Bayesian inversion with adaptive hierarchical tensor representations

Science.gov (United States)

Eigel, Martin; Marschall, Manuel; Schneider, Reinhold

2018-03-01

A sampling-free approach to Bayesian inversion with an explicit polynomial representation of the parameter densities is developed, based on an affine-parametric representation of a linear forward model. This becomes feasible due to the complete treatment in function spaces, which requires an efficient model reduction technique for numerical computations. The advocated perspective yields the crucial benefit that error bounds can be derived for all occuring approximations, leading to provable convergence subject to the discretization parameters. Moreover, it enables a fully adaptive a posteriori control with automatic problem-dependent adjustments of the employed discretizations. The method is discussed in the context of modern hierarchical tensor representations, which are used for the evaluation of a random PDE (the forward model) and the subsequent high-dimensional quadrature of the log-likelihood, alleviating the ‘curse of dimensionality’. Numerical experiments demonstrate the performance and confirm the theoretical results.

Top-down feedback in an HMAX-like cortical model of object perception based on hierarchical Bayesian networks and belief propagation.

Directory of Open Access Journals (Sweden)

Salvador Dura-Bernal

Full Text Available Hierarchical generative models, such as Bayesian networks, and belief propagation have been shown to provide a theoretical framework that can account for perceptual processes, including feedforward recognition and feedback modulation. The framework explains both psychophysical and physiological experimental data and maps well onto the hierarchical distributed cortical anatomy. However, the complexity required to model cortical processes makes inference, even using approximate methods, very computationally expensive. Thus, existing object perception models based on this approach are typically limited to tree-structured networks with no loops, use small toy examples or fail to account for certain perceptual aspects such as invariance to transformations or feedback reconstruction. In this study we develop a Bayesian network with an architecture similar to that of HMAX, a biologically-inspired hierarchical model of object recognition, and use loopy belief propagation to approximate the model operations (selectivity and invariance. Crucially, the resulting Bayesian network extends the functionality of HMAX by including top-down recursive feedback. Thus, the proposed model not only achieves successful feedforward recognition invariant to noise, occlusions, and changes in position and size, but is also able to reproduce modulatory effects such as illusory contour completion and attention. Our novel and rigorous methodology covers key aspects such as learning using a layerwise greedy algorithm, combining feedback information from multiple parents and reducing the number of operations required. Overall, this work extends an established model of object recognition to include high-level feedback modulation, based on state-of-the-art probabilistic approaches. The methodology employed, consistent with evidence from the visual cortex, can be potentially generalized to build models of hierarchical perceptual organization that include top-down and bottom

Constraining mass anomalies in the interior of spherical bodies using Trans-dimensional Bayesian Hierarchical inference.

Science.gov (United States)

Izquierdo, K.; Lekic, V.; Montesi, L.

2017-12-01

Gravity inversions are especially important for planetary applications since measurements of the variations in gravitational acceleration are often the only constraint available to map out lateral density variations in the interiors of planets and other Solar system objects. Currently, global gravity data is available for the terrestrial planets and the Moon. Although several methods for inverting these data have been developed and applied, the non-uniqueness of global density models that fit the data has not yet been fully characterized. We make use of Bayesian inference and a Reversible Jump Markov Chain Monte Carlo (RJMCMC) approach to develop a Trans-dimensional Hierarchical Bayesian (THB) inversion algorithm that yields a large sample of models that fit a gravity field. From this group of models, we can determine the most likely value of parameters of a global density model and a measure of the non-uniqueness of each parameter when the number of anomalies describing the gravity field is not fixed a priori. We explore the use of a parallel tempering algorithm and fast multipole method to reduce the number of iterations and computing time needed. We applied this method to a synthetic gravity field of the Moon and a long wavelength synthetic model of density anomalies in the Earth's lower mantle. We obtained a good match between the given gravity field and the gravity field produced by the most likely model in each inversion. The number of anomalies of the models showed parsimony of the algorithm, the value of the noise variance of the input data was retrieved, and the non-uniqueness of the models was quantified. Our results show that the ability to constrain the latitude and longitude of density anomalies, which is excellent at shallow locations (information about the overall density distribution of celestial bodies even when there is no other geophysical data available.

UNSUPERVISED TRANSIENT LIGHT CURVE ANALYSIS VIA HIERARCHICAL BAYESIAN INFERENCE

International Nuclear Information System (INIS)

Sanders, N. E.; Soderberg, A. M.; Betancourt, M.

2015-01-01

Historically, light curve studies of supernovae (SNe) and other transient classes have focused on individual objects with copious and high signal-to-noise observations. In the nascent era of wide field transient searches, objects with detailed observations are decreasing as a fraction of the overall known SN population, and this strategy sacrifices the majority of the information contained in the data about the underlying population of transients. A population level modeling approach, simultaneously fitting all available observations of objects in a transient sub-class of interest, fully mines the data to infer the properties of the population and avoids certain systematic biases. We present a novel hierarchical Bayesian statistical model for population level modeling of transient light curves, and discuss its implementation using an efficient Hamiltonian Monte Carlo technique. As a test case, we apply this model to the Type IIP SN sample from the Pan-STARRS1 Medium Deep Survey, consisting of 18,837 photometric observations of 76 SNe, corresponding to a joint posterior distribution with 9176 parameters under our model. Our hierarchical model fits provide improved constraints on light curve parameters relevant to the physical properties of their progenitor stars relative to modeling individual light curves alone. Moreover, we directly evaluate the probability for occurrence rates of unseen light curve characteristics from the model hyperparameters, addressing observational biases in survey methodology. We view this modeling framework as an unsupervised machine learning technique with the ability to maximize scientific returns from data to be collected by future wide field transient searches like LSST

UNSUPERVISED TRANSIENT LIGHT CURVE ANALYSIS VIA HIERARCHICAL BAYESIAN INFERENCE

Energy Technology Data Exchange (ETDEWEB)

Sanders, N. E.; Soderberg, A. M. [Harvard-Smithsonian Center for Astrophysics, 60 Garden Street, Cambridge, MA 02138 (United States); Betancourt, M., E-mail: nsanders@cfa.harvard.edu [Department of Statistics, University of Warwick, Coventry CV4 7AL (United Kingdom)

2015-02-10

Historically, light curve studies of supernovae (SNe) and other transient classes have focused on individual objects with copious and high signal-to-noise observations. In the nascent era of wide field transient searches, objects with detailed observations are decreasing as a fraction of the overall known SN population, and this strategy sacrifices the majority of the information contained in the data about the underlying population of transients. A population level modeling approach, simultaneously fitting all available observations of objects in a transient sub-class of interest, fully mines the data to infer the properties of the population and avoids certain systematic biases. We present a novel hierarchical Bayesian statistical model for population level modeling of transient light curves, and discuss its implementation using an efficient Hamiltonian Monte Carlo technique. As a test case, we apply this model to the Type IIP SN sample from the Pan-STARRS1 Medium Deep Survey, consisting of 18,837 photometric observations of 76 SNe, corresponding to a joint posterior distribution with 9176 parameters under our model. Our hierarchical model fits provide improved constraints on light curve parameters relevant to the physical properties of their progenitor stars relative to modeling individual light curves alone. Moreover, we directly evaluate the probability for occurrence rates of unseen light curve characteristics from the model hyperparameters, addressing observational biases in survey methodology. We view this modeling framework as an unsupervised machine learning technique with the ability to maximize scientific returns from data to be collected by future wide field transient searches like LSST.

A Bayesian Hierarchical Model for Relating Multiple SNPs within Multiple Genes to Disease Risk

Directory of Open Access Journals (Sweden)

Lewei Duan

2013-01-01

Full Text Available A variety of methods have been proposed for studying the association of multiple genes thought to be involved in a common pathway for a particular disease. Here, we present an extension of a Bayesian hierarchical modeling strategy that allows for multiple SNPs within each gene, with external prior information at either the SNP or gene level. The model involves variable selection at the SNP level through latent indicator variables and Bayesian shrinkage at the gene level towards a prior mean vector and covariance matrix that depend on external information. The entire model is fitted using Markov chain Monte Carlo methods. Simulation studies show that the approach is capable of recovering many of the truly causal SNPs and genes, depending upon their frequency and size of their effects. The method is applied to data on 504 SNPs in 38 candidate genes involved in DNA damage response in the WECARE study of second breast cancers in relation to radiotherapy exposure.

Bayesian methods for data analysis

CERN Document Server

Carlin, Bradley P.

2009-01-01

Approaches for statistical inference Introduction Motivating Vignettes Defining the Approaches The Bayes-Frequentist Controversy Some Basic Bayesian Models The Bayes approach Introduction Prior Distributions Bayesian Inference Hierarchical Modeling Model Assessment Nonparametric Methods Bayesian computation Introduction Asymptotic Methods Noniterative Monte Carlo Methods Markov Chain Monte Carlo Methods Model criticism and selection Bayesian Modeling Bayesian Robustness Model Assessment Bayes Factors via Marginal Density Estimation Bayes Factors

An Approach to Structure Determination and Estimation of Hierarchical Archimedean Copulas and its Application to Bayesian Classification

Czech Academy of Sciences Publication Activity Database

Górecki, J.; Hofert, M.; Holeňa, Martin

2016-01-01

Roč. 46, č. 1 (2016), s. 21-59 ISSN 0925-9902 R&D Projects: GA ČR GA13-17187S Grant - others:Slezská univerzita v Opavě(CZ) SGS/21/2014 Institutional support: RVO:67985807 Keywords : Copula * Hierarchical archimedean copula * Copula estimation * Structure determination * Kendall’s tau * Bayesian classification Subject RIV: IN - Informatics, Computer Science Impact factor: 1.294, year: 2016

Technique for fast and efficient hierarchical clustering

Science.gov (United States)

Stork, Christopher

2013-10-08

A fast and efficient technique for hierarchical clustering of samples in a dataset includes compressing the dataset to reduce a number of variables within each of the samples of the dataset. A nearest neighbor matrix is generated to identify nearest neighbor pairs between the samples based on differences between the variables of the samples. The samples are arranged into a hierarchy that groups the samples based on the nearest neighbor matrix. The hierarchy is rendered to a display to graphically illustrate similarities or differences between the samples.

A sow replacement model using Bayesian updating in a three-level hierarchic Markov process. I. Biological model

DEFF Research Database (Denmark)

Kristensen, Anders Ringgaard; Søllested, Thomas Algot

2004-01-01

that really uses all these methodological improvements. In this paper, the biological model describing the performance and feed intake of sows is presented. In particular, estimation of herd specific parameters is emphasized. The optimization model is described in a subsequent paper......Several replacement models have been presented in literature. In other applicational areas like dairy cow replacement, various methodological improvements like hierarchical Markov processes and Bayesian updating have been implemented, but not in sow models. Furthermore, there are methodological...... improvements like multi-level hierarchical Markov processes with decisions on multiple time scales, efficient methods for parameter estimations at herd level and standard software that has been hardly implemented at all in any replacement model. The aim of this study is to present a sow replacement model...

TYPE Ia SUPERNOVA LIGHT-CURVE INFERENCE: HIERARCHICAL BAYESIAN ANALYSIS IN THE NEAR-INFRARED

International Nuclear Information System (INIS)

Mandel, Kaisey S.; Friedman, Andrew S.; Kirshner, Robert P.; Wood-Vasey, W. Michael

2009-01-01

We present a comprehensive statistical analysis of the properties of Type Ia supernova (SN Ia) light curves in the near-infrared using recent data from Peters Automated InfraRed Imaging TELescope and the literature. We construct a hierarchical Bayesian framework, incorporating several uncertainties including photometric error, peculiar velocities, dust extinction, and intrinsic variations, for principled and coherent statistical inference. SN Ia light-curve inferences are drawn from the global posterior probability of parameters describing both individual supernovae and the population conditioned on the entire SN Ia NIR data set. The logical structure of the hierarchical model is represented by a directed acyclic graph. Fully Bayesian analysis of the model and data is enabled by an efficient Markov Chain Monte Carlo algorithm exploiting the conditional probabilistic structure using Gibbs sampling. We apply this framework to the JHK s SN Ia light-curve data. A new light-curve model captures the observed J-band light-curve shape variations. The marginal intrinsic variances in peak absolute magnitudes are σ(M J ) = 0.17 ± 0.03, σ(M H ) = 0.11 ± 0.03, and σ(M Ks ) = 0.19 ± 0.04. We describe the first quantitative evidence for correlations between the NIR absolute magnitudes and J-band light-curve shapes, and demonstrate their utility for distance estimation. The average residual in the Hubble diagram for the training set SNe at cz > 2000kms -1 is 0.10 mag. The new application of bootstrap cross-validation to SN Ia light-curve inference tests the sensitivity of the statistical model fit to the finite sample and estimates the prediction error at 0.15 mag. These results demonstrate that SN Ia NIR light curves are as effective as corrected optical light curves, and, because they are less vulnerable to dust absorption, they have great potential as precise and accurate cosmological distance indicators.

Analyzing Korean consumers’ latent preferences for electricity generation sources with a hierarchical Bayesian logit model in a discrete choice experiment

International Nuclear Information System (INIS)

Byun, Hyunsuk; Lee, Chul-Yong

2017-01-01

Generally, consumers use electricity without considering the source the electricity was generated from. Since different energy sources exert varying effects on society, it is necessary to analyze consumers’ latent preference for electricity generation sources. The present study estimates Korean consumers’ marginal utility and an appropriate generation mix is derived using the hierarchical Bayesian logit model in a discrete choice experiment. The results show that consumers consider the danger posed by the source of electricity as the most important factor among the effects of electricity generation sources. Additionally, Korean consumers wish to reduce the contribution of nuclear power from the existing 32–11%, and increase that of renewable energy from the existing 4–32%. - Highlights: • We derive an electricity mix reflecting Korean consumers’ latent preferences. • We use the discrete choice experiment and hierarchical Bayesian logit model. • The danger posed by the generation source is the most important attribute. • The consumers wish to increase the renewable energy proportion from 4.3% to 32.8%. • Korea's cost-oriented energy supply policy and consumers’ preference differ markedly.

Sparse Event Modeling with Hierarchical Bayesian Kernel Methods

Science.gov (United States)

2016-01-05

SECURITY CLASSIFICATION OF: The research objective of this proposal was to develop a predictive Bayesian kernel approach to model count data based on...several predictive variables. Such an approach, which we refer to as the Poisson Bayesian kernel model, is able to model the rate of occurrence of... kernel methods made use of: (i) the Bayesian property of improving predictive accuracy as data are dynamically obtained, and (ii) the kernel function

Analyzing thresholds and efficiency with hierarchical Bayesian logistic regression.

Science.gov (United States)

Houpt, Joseph W; Bittner, Jennifer L

2018-05-10

Ideal observer analysis is a fundamental tool used widely in vision science for analyzing the efficiency with which a cognitive or perceptual system uses available information. The performance of an ideal observer provides a formal measure of the amount of information in a given experiment. The ratio of human to ideal performance is then used to compute efficiency, a construct that can be directly compared across experimental conditions while controlling for the differences due to the stimuli and/or task specific demands. In previous research using ideal observer analysis, the effects of varying experimental conditions on efficiency have been tested using ANOVAs and pairwise comparisons. In this work, we present a model that combines Bayesian estimates of psychometric functions with hierarchical logistic regression for inference about both unadjusted human performance metrics and efficiencies. Our approach improves upon the existing methods by constraining the statistical analysis using a standard model connecting stimulus intensity to human observer accuracy and by accounting for variability in the estimates of human and ideal observer performance scores. This allows for both individual and group level inferences. Copyright © 2018 Elsevier Ltd. All rights reserved.

Bayesian models: A statistical primer for ecologists

Science.gov (United States)

Hobbs, N. Thompson; Hooten, Mevin B.

2015-01-01

Bayesian modeling has become an indispensable tool for ecological research because it is uniquely suited to deal with complexity in a statistically coherent way. This textbook provides a comprehensive and accessible introduction to the latest Bayesian methods—in language ecologists can understand. Unlike other books on the subject, this one emphasizes the principles behind the computations, giving ecologists a big-picture understanding of how to implement this powerful statistical approach.Bayesian Models is an essential primer for non-statisticians. It begins with a definition of probability and develops a step-by-step sequence of connected ideas, including basic distribution theory, network diagrams, hierarchical models, Markov chain Monte Carlo, and inference from single and multiple models. This unique book places less emphasis on computer coding, favoring instead a concise presentation of the mathematical statistics needed to understand how and why Bayesian analysis works. It also explains how to write out properly formulated hierarchical Bayesian models and use them in computing, research papers, and proposals.This primer enables ecologists to understand the statistical principles behind Bayesian modeling and apply them to research, teaching, policy, and management.Presents the mathematical and statistical foundations of Bayesian modeling in language accessible to non-statisticiansCovers basic distribution theory, network diagrams, hierarchical models, Markov chain Monte Carlo, and moreDeemphasizes computer coding in favor of basic principlesExplains how to write out properly factored statistical expressions representing Bayesian models

When mechanism matters: Bayesian forecasting using models of ecological diffusion

Science.gov (United States)

Hefley, Trevor J.; Hooten, Mevin B.; Russell, Robin E.; Walsh, Daniel P.; Powell, James A.

2017-01-01

Ecological diffusion is a theory that can be used to understand and forecast spatio-temporal processes such as dispersal, invasion, and the spread of disease. Hierarchical Bayesian modelling provides a framework to make statistical inference and probabilistic forecasts, using mechanistic ecological models. To illustrate, we show how hierarchical Bayesian models of ecological diffusion can be implemented for large data sets that are distributed densely across space and time. The hierarchical Bayesian approach is used to understand and forecast the growth and geographic spread in the prevalence of chronic wasting disease in white-tailed deer (Odocoileus virginianus). We compare statistical inference and forecasts from our hierarchical Bayesian model to phenomenological regression-based methods that are commonly used to analyse spatial occurrence data. The mechanistic statistical model based on ecological diffusion led to important ecological insights, obviated a commonly ignored type of collinearity, and was the most accurate method for forecasting.

Modelling the dynamics of an experimental host-pathogen microcosm within a hierarchical Bayesian framework.

Directory of Open Access Journals (Sweden)

David Lunn

Full Text Available The advantages of Bayesian statistical approaches, such as flexibility and the ability to acknowledge uncertainty in all parameters, have made them the prevailing method for analysing the spread of infectious diseases in human or animal populations. We introduce a Bayesian approach to experimental host-pathogen systems that shares these attractive features. Since uncertainty in all parameters is acknowledged, existing information can be accounted for through prior distributions, rather than through fixing some parameter values. The non-linear dynamics, multi-factorial design, multiple measurements of responses over time and sampling error that are typical features of experimental host-pathogen systems can also be naturally incorporated. We analyse the dynamics of the free-living protozoan Paramecium caudatum and its specialist bacterial parasite Holospora undulata. Our analysis provides strong evidence for a saturable infection function, and we were able to reproduce the two waves of infection apparent in the data by separating the initial inoculum from the parasites released after the first cycle of infection. In addition, the parameter estimates from the hierarchical model can be combined to infer variations in the parasite's basic reproductive ratio across experimental groups, enabling us to make predictions about the effect of resources and host genotype on the ability of the parasite to spread. Even though the high level of variability between replicates limited the resolution of the results, this Bayesian framework has strong potential to be used more widely in experimental ecology.

Approximate Bayesian Computation by Subset Simulation using hierarchical state-space models

Science.gov (United States)

Vakilzadeh, Majid K.; Huang, Yong; Beck, James L.; Abrahamsson, Thomas

2017-02-01

A new multi-level Markov Chain Monte Carlo algorithm for Approximate Bayesian Computation, ABC-SubSim, has recently appeared that exploits the Subset Simulation method for efficient rare-event simulation. ABC-SubSim adaptively creates a nested decreasing sequence of data-approximating regions in the output space that correspond to increasingly closer approximations of the observed output vector in this output space. At each level, multiple samples of the model parameter vector are generated by a component-wise Metropolis algorithm so that the predicted output corresponding to each parameter value falls in the current data-approximating region. Theoretically, if continued to the limit, the sequence of data-approximating regions would converge on to the observed output vector and the approximate posterior distributions, which are conditional on the data-approximation region, would become exact, but this is not practically feasible. In this paper we study the performance of the ABC-SubSim algorithm for Bayesian updating of the parameters of dynamical systems using a general hierarchical state-space model. We note that the ABC methodology gives an approximate posterior distribution that actually corresponds to an exact posterior where a uniformly distributed combined measurement and modeling error is added. We also note that ABC algorithms have a problem with learning the uncertain error variances in a stochastic state-space model and so we treat them as nuisance parameters and analytically integrate them out of the posterior distribution. In addition, the statistical efficiency of the original ABC-SubSim algorithm is improved by developing a novel strategy to regulate the proposal variance for the component-wise Metropolis algorithm at each level. We demonstrate that Self-regulated ABC-SubSim is well suited for Bayesian system identification by first applying it successfully to model updating of a two degree-of-freedom linear structure for three cases: globally

Fully probabilistic design of hierarchical Bayesian models

Czech Academy of Sciences Publication Activity Database

Quinn, A.; Kárný, Miroslav; Guy, Tatiana Valentine

2016-01-01

Roč. 369, č. 1 (2016), s. 532-547 ISSN 0020-0255 R&D Projects: GA ČR GA13-13502S Institutional support: RVO:67985556 Keywords : Fully probabilistic design * Ideal distribution * Minimum cross-entropy principle * Bayesian conditioning * Kullback-Leibler divergence * Bayesian nonparametric modelling Subject RIV: BB - Applied Statistics, Operational Research Impact factor: 4.832, year: 2016 http://library.utia.cas.cz/separaty/2016/AS/karny-0463052.pdf

Fast Bayesian Inference in Dirichlet Process Mixture Models.

Science.gov (United States)

Wang, Lianming; Dunson, David B

2011-01-01

There has been increasing interest in applying Bayesian nonparametric methods in large samples and high dimensions. As Markov chain Monte Carlo (MCMC) algorithms are often infeasible, there is a pressing need for much faster algorithms. This article proposes a fast approach for inference in Dirichlet process mixture (DPM) models. Viewing the partitioning of subjects into clusters as a model selection problem, we propose a sequential greedy search algorithm for selecting the partition. Then, when conjugate priors are chosen, the resulting posterior conditionally on the selected partition is available in closed form. This approach allows testing of parametric models versus nonparametric alternatives based on Bayes factors. We evaluate the approach using simulation studies and compare it with four other fast nonparametric methods in the literature. We apply the proposed approach to three datasets including one from a large epidemiologic study. Matlab codes for the simulation and data analyses using the proposed approach are available online in the supplemental materials.

Bayesian Hierarchical Random Effects Models in Forensic Science

Directory of Open Access Journals (Sweden)

Colin G. G. Aitken

2018-04-01

Full Text Available Statistical modeling of the evaluation of evidence with the use of the likelihood ratio has a long history. It dates from the Dreyfus case at the end of the nineteenth century through the work at Bletchley Park in the Second World War to the present day. The development received a significant boost in 1977 with a seminal work by Dennis Lindley which introduced a Bayesian hierarchical random effects model for the evaluation of evidence with an example of refractive index measurements on fragments of glass. Many models have been developed since then. The methods have now been sufficiently well-developed and have become so widespread that it is timely to try and provide a software package to assist in their implementation. With that in mind, a project (SAILR: Software for the Analysis and Implementation of Likelihood Ratios was funded by the European Network of Forensic Science Institutes through their Monopoly programme to develop a software package for use by forensic scientists world-wide that would assist in the statistical analysis and implementation of the approach based on likelihood ratios. It is the purpose of this document to provide a short review of a small part of this history. The review also provides a background, or landscape, for the development of some of the models within the SAILR package and references to SAILR as made as appropriate.

Bayesian Hierarchical Random Effects Models in Forensic Science.

Science.gov (United States)

Aitken, Colin G G

2018-01-01

Statistical modeling of the evaluation of evidence with the use of the likelihood ratio has a long history. It dates from the Dreyfus case at the end of the nineteenth century through the work at Bletchley Park in the Second World War to the present day. The development received a significant boost in 1977 with a seminal work by Dennis Lindley which introduced a Bayesian hierarchical random effects model for the evaluation of evidence with an example of refractive index measurements on fragments of glass. Many models have been developed since then. The methods have now been sufficiently well-developed and have become so widespread that it is timely to try and provide a software package to assist in their implementation. With that in mind, a project (SAILR: Software for the Analysis and Implementation of Likelihood Ratios) was funded by the European Network of Forensic Science Institutes through their Monopoly programme to develop a software package for use by forensic scientists world-wide that would assist in the statistical analysis and implementation of the approach based on likelihood ratios. It is the purpose of this document to provide a short review of a small part of this history. The review also provides a background, or landscape, for the development of some of the models within the SAILR package and references to SAILR as made as appropriate.

A hierarchical method for Bayesian inference of rate parameters from shock tube data: Application to the study of the reaction of hydroxyl with 2-methylfuran

KAUST Repository

Kim, Daesang; El Gharamti, Iman; Hantouche, Mireille; Elwardani, Ahmed Elsaid; Farooq, Aamir; Bisetti, Fabrizio; Knio, Omar

2017-01-01

We developed a novel two-step hierarchical method for the Bayesian inference of the rate parameters of a target reaction from time-resolved concentration measurements in shock tubes. The method was applied to the calibration of the parameters

A hierarchical bayesian approach to ecological count data: a flexible tool for ecologists.

Directory of Open Access Journals (Sweden)

James A Fordyce

Full Text Available Many ecological studies use the analysis of count data to arrive at biologically meaningful inferences. Here, we introduce a hierarchical bayesian approach to count data. This approach has the advantage over traditional approaches in that it directly estimates the parameters of interest at both the individual-level and population-level, appropriately models uncertainty, and allows for comparisons among models, including those that exceed the complexity of many traditional approaches, such as ANOVA or non-parametric analogs. As an example, we apply this method to oviposition preference data for butterflies in the genus Lycaeides. Using this method, we estimate the parameters that describe preference for each population, compare the preference hierarchies among populations, and explore various models that group populations that share the same preference hierarchy.

Hierarchical Bayesian Markov switching models with application to predicting spawning success of shovelnose sturgeon

Science.gov (United States)

Holan, S.H.; Davis, G.M.; Wildhaber, M.L.; DeLonay, A.J.; Papoulias, D.M.

2009-01-01

The timing of spawning in fish is tightly linked to environmental factors; however, these factors are not very well understood for many species. Specifically, little information is available to guide recruitment efforts for endangered species such as the sturgeon. Therefore, we propose a Bayesian hierarchical model for predicting the success of spawning of the shovelnose sturgeon which uses both biological and behavioural (longitudinal) data. In particular, we use data that were produced from a tracking study that was conducted in the Lower Missouri River. The data that were produced from this study consist of biological variables associated with readiness to spawn along with longitudinal behavioural data collected by using telemetry and archival data storage tags. These high frequency data are complex both biologically and in the underlying behavioural process. To accommodate such complexity we developed a hierarchical linear regression model that uses an eigenvalue predictor, derived from the transition probability matrix of a two-state Markov switching model with generalized auto-regressive conditional heteroscedastic dynamics. Finally, to minimize the computational burden that is associated with estimation of this model, a parallel computing approach is proposed. ?? Journal compilation 2009 Royal Statistical Society.

Improving satellite-based PM2.5 estimates in China using Gaussian processes modeling in a Bayesian hierarchical setting.

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Yu, Wenxi; Liu, Yang; Ma, Zongwei; Bi, Jun

2017-08-01

Using satellite-based aerosol optical depth (AOD) measurements and statistical models to estimate ground-level PM 2.5 is a promising way to fill the areas that are not covered by ground PM 2.5 monitors. The statistical models used in previous studies are primarily Linear Mixed Effects (LME) and Geographically Weighted Regression (GWR) models. In this study, we developed a new regression model between PM 2.5 and AOD using Gaussian processes in a Bayesian hierarchical setting. Gaussian processes model the stochastic nature of the spatial random effects, where the mean surface and the covariance function is specified. The spatial stochastic process is incorporated under the Bayesian hierarchical framework to explain the variation of PM 2.5 concentrations together with other factors, such as AOD, spatial and non-spatial random effects. We evaluate the results of our model and compare them with those of other, conventional statistical models (GWR and LME) by within-sample model fitting and out-of-sample validation (cross validation, CV). The results show that our model possesses a CV result (R 2  = 0.81) that reflects higher accuracy than that of GWR and LME (0.74 and 0.48, respectively). Our results indicate that Gaussian process models have the potential to improve the accuracy of satellite-based PM 2.5 estimates.

ESS-FH: Enhanced Security Scheme for Fast Handover in Hierarchical Mobile IPv6

Science.gov (United States)

You, Ilsun; Lee, Jong-Hyouk; Sakurai, Kouichi; Hori, Yoshiaki

Fast Handover for Hierarchical Mobile IPv6 (F-HMIPv6) that combines advantages of Fast Handover for Mobile IPv6 (FMIPv6) and Hierarchical Mobile IPv6 (HMIPv6) achieves the superior performance in terms of handover latency and signaling overhead compared with previously developed mobility protocols. However, without being secured, F-HMIPv6 is vulnerable to various security threats. In 2007, Kang and Park proposed a security scheme, which is seamlessly integrated into F-HMIPv6. In this paper, we reveal that Kang-Park's scheme cannot defend against the Denial of Service (DoS) and redirect attacks while largely relying on the group key. Then, we propose an Enhanced Security Scheme for F-HMIPv6 (ESS-FH) that achieves the strong key exchange and the key independence as well as addresses the weaknesses of Kang-Park's scheme. More importantly, it enables fast handover between different MAP domains. The proposed scheme is formally verified based on BAN-logic, and its handover latency is analyzed and compared with that of Kang-Park's scheme.

Catalytic Fast Pyrolysis of Kraft Lignin over Hierarchical HZSM-5 and Hβ Zeolites

Directory of Open Access Journals (Sweden)

Yadong Bi

2018-02-01

Full Text Available The hierarchical HZSM-5 and Hβ zeolites were prepared by alkaline post-treatment methods adopting Na2CO3, TMAOH/NaOH mixture, and NaOH as desilication sources, respectively. More mesopores are produced over two kinds of zeolites, while the micropores portion is well preserved. The mesopores formed in hierarchical Hβ zeolites were directly related to the basicity of the alkaline solution, indicating that Hβ zeolite is more sensitive to the alkaline post-treatment. The hierarchical HZSM-5 and Hβ zeolites are more active than the parent one for catalytic fast pyrolysis (CFP of Kraft lignin. Hierarchical zeolites retained the function of acid catalysis, while additionally creating larger mesopores to ensure the entry of bulkier reactant molecules. The increase of the condensable volatiles yield can be attributed to the improvement of the mass transfer performance, which correlates well with the change of mesoporous surface area. In particular, the condensable volatiles yield for the optimized hierarchical Hβ reached approximately two times that of the parent Hβ zeolites. In contrast to the parent HZSM-5, the optimized hierarchical HZSM-5 zeolite significantly reduced the selectivity of oxygenates from 27.2% to 3.3%.

A bayesian hierarchical model for classification with selection of functional predictors.

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Zhu, Hongxiao; Vannucci, Marina; Cox, Dennis D

2010-06-01

In functional data classification, functional observations are often contaminated by various systematic effects, such as random batch effects caused by device artifacts, or fixed effects caused by sample-related factors. These effects may lead to classification bias and thus should not be neglected. Another issue of concern is the selection of functions when predictors consist of multiple functions, some of which may be redundant. The above issues arise in a real data application where we use fluorescence spectroscopy to detect cervical precancer. In this article, we propose a Bayesian hierarchical model that takes into account random batch effects and selects effective functions among multiple functional predictors. Fixed effects or predictors in nonfunctional form are also included in the model. The dimension of the functional data is reduced through orthonormal basis expansion or functional principal components. For posterior sampling, we use a hybrid Metropolis-Hastings/Gibbs sampler, which suffers slow mixing. An evolutionary Monte Carlo algorithm is applied to improve the mixing. Simulation and real data application show that the proposed model provides accurate selection of functional predictors as well as good classification.

Hierarchical Bayesian inference of the initial mass function in composite stellar populations

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Dries, M.; Trager, S. C.; Koopmans, L. V. E.; Popping, G.; Somerville, R. S.

2018-03-01

The initial mass function (IMF) is a key ingredient in many studies of galaxy formation and evolution. Although the IMF is often assumed to be universal, there is continuing evidence that it is not universal. Spectroscopic studies that derive the IMF of the unresolved stellar populations of a galaxy often assume that this spectrum can be described by a single stellar population (SSP). To alleviate these limitations, in this paper we have developed a unique hierarchical Bayesian framework for modelling composite stellar populations (CSPs). Within this framework, we use a parametrized IMF prior to regulate a direct inference of the IMF. We use this new framework to determine the number of SSPs that is required to fit a set of realistic CSP mock spectra. The CSP mock spectra that we use are based on semi-analytic models and have an IMF that varies as a function of stellar velocity dispersion of the galaxy. Our results suggest that using a single SSP biases the determination of the IMF slope to a higher value than the true slope, although the trend with stellar velocity dispersion is overall recovered. If we include more SSPs in the fit, the Bayesian evidence increases significantly and the inferred IMF slopes of our mock spectra converge, within the errors, to their true values. Most of the bias is already removed by using two SSPs instead of one. We show that we can reconstruct the variable IMF of our mock spectra for signal-to-noise ratios exceeding ˜75.

Bayesian hierarchical modelling of North Atlantic windiness

Directory of Open Access Journals (Sweden)

E. Vanem

2013-03-01

Full Text Available Extreme weather conditions represent serious natural hazards to ship operations and may be the direct cause or contributing factor to maritime accidents. Such severe environmental conditions can be taken into account in ship design and operational windows can be defined that limits hazardous operations to less extreme conditions. Nevertheless, possible changes in the statistics of extreme weather conditions, possibly due to anthropogenic climate change, represent an additional hazard to ship operations that is less straightforward to account for in a consistent way. Obviously, there are large uncertainties as to how future climate change will affect the extreme weather conditions at sea and there is a need for stochastic models that can describe the variability in both space and time at various scales of the environmental conditions. Previously, Bayesian hierarchical space-time models have been developed to describe the variability and complex dependence structures of significant wave height in space and time. These models were found to perform reasonably well and provided some interesting results, in particular, pertaining to long-term trends in the wave climate. In this paper, a similar framework is applied to oceanic windiness and the spatial and temporal variability of the 10-m wind speed over an area in the North Atlantic ocean is investigated. When the results from the model for North Atlantic windiness is compared to the results for significant wave height over the same area, it is interesting to observe that whereas an increasing trend in significant wave height was identified, no statistically significant long-term trend was estimated in windiness. This may indicate that the increase in significant wave height is not due to an increase in locally generated wind waves, but rather to increased swell. This observation is also consistent with studies that have suggested a poleward shift of the main storm tracks.

Bayesian hierarchical modelling of North Atlantic windiness

Science.gov (United States)

Vanem, E.; Breivik, O. N.

2013-03-01

Extreme weather conditions represent serious natural hazards to ship operations and may be the direct cause or contributing factor to maritime accidents. Such severe environmental conditions can be taken into account in ship design and operational windows can be defined that limits hazardous operations to less extreme conditions. Nevertheless, possible changes in the statistics of extreme weather conditions, possibly due to anthropogenic climate change, represent an additional hazard to ship operations that is less straightforward to account for in a consistent way. Obviously, there are large uncertainties as to how future climate change will affect the extreme weather conditions at sea and there is a need for stochastic models that can describe the variability in both space and time at various scales of the environmental conditions. Previously, Bayesian hierarchical space-time models have been developed to describe the variability and complex dependence structures of significant wave height in space and time. These models were found to perform reasonably well and provided some interesting results, in particular, pertaining to long-term trends in the wave climate. In this paper, a similar framework is applied to oceanic windiness and the spatial and temporal variability of the 10-m wind speed over an area in the North Atlantic ocean is investigated. When the results from the model for North Atlantic windiness is compared to the results for significant wave height over the same area, it is interesting to observe that whereas an increasing trend in significant wave height was identified, no statistically significant long-term trend was estimated in windiness. This may indicate that the increase in significant wave height is not due to an increase in locally generated wind waves, but rather to increased swell. This observation is also consistent with studies that have suggested a poleward shift of the main storm tracks.

Estimating effectiveness in HIV prevention trials with a Bayesian hierarchical compound Poisson frailty model

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Coley, Rebecca Yates; Browna, Elizabeth R.

2016-01-01

Inconsistent results in recent HIV prevention trials of pre-exposure prophylactic interventions may be due to heterogeneity in risk among study participants. Intervention effectiveness is most commonly estimated with the Cox model, which compares event times between populations. When heterogeneity is present, this population-level measure underestimates intervention effectiveness for individuals who are at risk. We propose a likelihood-based Bayesian hierarchical model that estimates the individual-level effectiveness of candidate interventions by accounting for heterogeneity in risk with a compound Poisson-distributed frailty term. This model reflects the mechanisms of HIV risk and allows that some participants are not exposed to HIV and, therefore, have no risk of seroconversion during the study. We assess model performance via simulation and apply the model to data from an HIV prevention trial. PMID:26869051

A Bayesian hierarchical model for demand curve analysis.

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Ho, Yen-Yi; Nhu Vo, Tien; Chu, Haitao; Luo, Xianghua; Le, Chap T

2018-07-01

Drug self-administration experiments are a frequently used approach to assessing the abuse liability and reinforcing property of a compound. It has been used to assess the abuse liabilities of various substances such as psychomotor stimulants and hallucinogens, food, nicotine, and alcohol. The demand curve generated from a self-administration study describes how demand of a drug or non-drug reinforcer varies as a function of price. With the approval of the 2009 Family Smoking Prevention and Tobacco Control Act, demand curve analysis provides crucial evidence to inform the US Food and Drug Administration's policy on tobacco regulation, because it produces several important quantitative measurements to assess the reinforcing strength of nicotine. The conventional approach popularly used to analyze the demand curve data is individual-specific non-linear least square regression. The non-linear least square approach sets out to minimize the residual sum of squares for each subject in the dataset; however, this one-subject-at-a-time approach does not allow for the estimation of between- and within-subject variability in a unified model framework. In this paper, we review the existing approaches to analyze the demand curve data, non-linear least square regression, and the mixed effects regression and propose a new Bayesian hierarchical model. We conduct simulation analyses to compare the performance of these three approaches and illustrate the proposed approaches in a case study of nicotine self-administration in rats. We present simulation results and discuss the benefits of using the proposed approaches.

Bayesian Integrated Data Analysis of Fast-Ion Measurements by Velocity-Space Tomography

DEFF Research Database (Denmark)

Salewski, M.; Nocente, M.; Jacobsen, A.S.

2018-01-01

Bayesian integrated data analysis combines measurements from different diagnostics to jointly measure plasma parameters of interest such as temperatures, densities, and drift velocities. Integrated data analysis of fast-ion measurements has long been hampered by the complexity of the strongly non...... framework. The implementation for different types of diagnostics as well as the uncertainties are discussed, and we highlight the importance of integrated data analysis of all available detectors....

Application of hierarchical Bayesian unmixing models in river sediment source apportionment

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Blake, Will; Smith, Hugh; Navas, Ana; Bodé, Samuel; Goddard, Rupert; Zou Kuzyk, Zou; Lennard, Amy; Lobb, David; Owens, Phil; Palazon, Leticia; Petticrew, Ellen; Gaspar, Leticia; Stock, Brian; Boeckx, Pacsal; Semmens, Brice

2016-04-01

Fingerprinting and unmixing concepts are used widely across environmental disciplines for forensic evaluation of pollutant sources. In aquatic and marine systems, this includes tracking the source of organic and inorganic pollutants in water and linking problem sediment to soil erosion and land use sources. It is, however, the particular complexity of ecological systems that has driven creation of the most sophisticated mixing models, primarily to (i) evaluate diet composition in complex ecological food webs, (ii) inform population structure and (iii) explore animal movement. In the context of the new hierarchical Bayesian unmixing model, MIXSIAR, developed to characterise intra-population niche variation in ecological systems, we evaluate the linkage between ecological 'prey' and 'consumer' concepts and river basin sediment 'source' and sediment 'mixtures' to exemplify the value of ecological modelling tools to river basin science. Recent studies have outlined advantages presented by Bayesian unmixing approaches in handling complex source and mixture datasets while dealing appropriately with uncertainty in parameter probability distributions. MixSIAR is unique in that it allows individual fixed and random effects associated with mixture hierarchy, i.e. factors that might exert an influence on model outcome for mixture groups, to be explored within the source-receptor framework. This offers new and powerful ways of interpreting river basin apportionment data. In this contribution, key components of the model are evaluated in the context of common experimental designs for sediment fingerprinting studies namely simple, nested and distributed catchment sampling programmes. Illustrative examples using geochemical and compound specific stable isotope datasets are presented and used to discuss best practice with specific attention to (1) the tracer selection process, (2) incorporation of fixed effects relating to sample timeframe and sediment type in the modelling

Epigenetic change detection and pattern recognition via Bayesian hierarchical hidden Markov models.

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Wang, Xinlei; Zang, Miao; Xiao, Guanghua

2013-06-15

Epigenetics is the study of changes to the genome that can switch genes on or off and determine which proteins are transcribed without altering the DNA sequence. Recently, epigenetic changes have been linked to the development and progression of disease such as psychiatric disorders. High-throughput epigenetic experiments have enabled researchers to measure genome-wide epigenetic profiles and yield data consisting of intensity ratios of immunoprecipitation versus reference samples. The intensity ratios can provide a view of genomic regions where protein binding occur under one experimental condition and further allow us to detect epigenetic alterations through comparison between two different conditions. However, such experiments can be expensive, with only a few replicates available. Moreover, epigenetic data are often spatially correlated with high noise levels. In this paper, we develop a Bayesian hierarchical model, combined with hidden Markov processes with four states for modeling spatial dependence, to detect genomic sites with epigenetic changes from two-sample experiments with paired internal control. One attractive feature of the proposed method is that the four states of the hidden Markov process have well-defined biological meanings and allow us to directly call the change patterns based on the corresponding posterior probabilities. In contrast, none of existing methods can offer this advantage. In addition, the proposed method offers great power in statistical inference by spatial smoothing (via hidden Markov modeling) and information pooling (via hierarchical modeling). Both simulation studies and real data analysis in a cocaine addiction study illustrate the reliability and success of this method. Copyright © 2012 John Wiley & Sons, Ltd.

Hierarchical Bayesian Spatio–Temporal Analysis of Climatic and Socio–Economic Determinants of Rocky Mountain Spotted Fever

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Raghavan, Ram K.; Goodin, Douglas G.; Neises, Daniel; Anderson, Gary A.; Ganta, Roman R.

2016-01-01

This study aims to examine the spatio-temporal dynamics of Rocky Mountain spotted fever (RMSF) prevalence in four contiguous states of Midwestern United States, and to determine the impact of environmental and socio–economic factors associated with this disease. Bayesian hierarchical models were used to quantify space and time only trends and spatio–temporal interaction effect in the case reports submitted to the state health departments in the region. Various socio–economic, environmental and climatic covariates screened a priori in a bivariate procedure were added to a main–effects Bayesian model in progressive steps to evaluate important drivers of RMSF space-time patterns in the region. Our results show a steady increase in RMSF incidence over the study period to newer geographic areas, and the posterior probabilities of county-specific trends indicate clustering of high risk counties in the central and southern parts of the study region. At the spatial scale of a county, the prevalence levels of RMSF is influenced by poverty status, average relative humidity, and average land surface temperature (>35°C) in the region, and the relevance of these factors in the context of climate–change impacts on tick–borne diseases are discussed. PMID:26942604

Hierarchical Bayesian Spatio-Temporal Analysis of Climatic and Socio-Economic Determinants of Rocky Mountain Spotted Fever.

Science.gov (United States)

Raghavan, Ram K; Goodin, Douglas G; Neises, Daniel; Anderson, Gary A; Ganta, Roman R

2016-01-01

This study aims to examine the spatio-temporal dynamics of Rocky Mountain spotted fever (RMSF) prevalence in four contiguous states of Midwestern United States, and to determine the impact of environmental and socio-economic factors associated with this disease. Bayesian hierarchical models were used to quantify space and time only trends and spatio-temporal interaction effect in the case reports submitted to the state health departments in the region. Various socio-economic, environmental and climatic covariates screened a priori in a bivariate procedure were added to a main-effects Bayesian model in progressive steps to evaluate important drivers of RMSF space-time patterns in the region. Our results show a steady increase in RMSF incidence over the study period to newer geographic areas, and the posterior probabilities of county-specific trends indicate clustering of high risk counties in the central and southern parts of the study region. At the spatial scale of a county, the prevalence levels of RMSF is influenced by poverty status, average relative humidity, and average land surface temperature (>35°C) in the region, and the relevance of these factors in the context of climate-change impacts on tick-borne diseases are discussed.

Bayesian modeling using WinBUGS

CERN Document Server

Ntzoufras, Ioannis

2009-01-01

A hands-on introduction to the principles of Bayesian modeling using WinBUGS Bayesian Modeling Using WinBUGS provides an easily accessible introduction to the use of WinBUGS programming techniques in a variety of Bayesian modeling settings. The author provides an accessible treatment of the topic, offering readers a smooth introduction to the principles of Bayesian modeling with detailed guidance on the practical implementation of key principles. The book begins with a basic introduction to Bayesian inference and the WinBUGS software and goes on to cover key topics, including: Markov Chain Monte Carlo algorithms in Bayesian inference Generalized linear models Bayesian hierarchical models Predictive distribution and model checking Bayesian model and variable evaluation Computational notes and screen captures illustrate the use of both WinBUGS as well as R software to apply the discussed techniques. Exercises at the end of each chapter allow readers to test their understanding of the presented concepts and all ...

Combining information from multiple flood projections in a hierarchical Bayesian framework

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Le Vine, Nataliya

2016-04-01

This study demonstrates, in the context of flood frequency analysis, the potential of a recently proposed hierarchical Bayesian approach to combine information from multiple models. The approach explicitly accommodates shared multimodel discrepancy as well as the probabilistic nature of the flood estimates, and treats the available models as a sample from a hypothetical complete (but unobserved) set of models. The methodology is applied to flood estimates from multiple hydrological projections (the Future Flows Hydrology data set) for 135 catchments in the UK. The advantages of the approach are shown to be: (1) to ensure adequate "baseline" with which to compare future changes; (2) to reduce flood estimate uncertainty; (3) to maximize use of statistical information in circumstances where multiple weak predictions individually lack power, but collectively provide meaningful information; (4) to diminish the importance of model consistency when model biases are large; and (5) to explicitly consider the influence of the (model performance) stationarity assumption. Moreover, the analysis indicates that reducing shared model discrepancy is the key to further reduction of uncertainty in the flood frequency analysis. The findings are of value regarding how conclusions about changing exposure to flooding are drawn, and to flood frequency change attribution studies.

Bayesian hierarchical models for regional climate reconstructions of the last glacial maximum

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Weitzel, Nils; Hense, Andreas; Ohlwein, Christian

2017-04-01

Spatio-temporal reconstructions of past climate are important for the understanding of the long term behavior of the climate system and the sensitivity to forcing changes. Unfortunately, they are subject to large uncertainties, have to deal with a complex proxy-climate structure, and a physically reasonable interpolation between the sparse proxy observations is difficult. Bayesian Hierarchical Models (BHMs) are a class of statistical models that is well suited for spatio-temporal reconstructions of past climate because they permit the inclusion of multiple sources of information (e.g. records from different proxy types, uncertain age information, output from climate simulations) and quantify uncertainties in a statistically rigorous way. BHMs in paleoclimatology typically consist of three stages which are modeled individually and are combined using Bayesian inference techniques. The data stage models the proxy-climate relation (often named transfer function), the process stage models the spatio-temporal distribution of the climate variables of interest, and the prior stage consists of prior distributions of the model parameters. For our BHMs, we translate well-known proxy-climate transfer functions for pollen to a Bayesian framework. In addition, we can include Gaussian distributed local climate information from preprocessed proxy records. The process stage combines physically reasonable spatial structures from prior distributions with proxy records which leads to a multivariate posterior probability distribution for the reconstructed climate variables. The prior distributions that constrain the possible spatial structure of the climate variables are calculated from climate simulation output. We present results from pseudoproxy tests as well as new regional reconstructions of temperatures for the last glacial maximum (LGM, ˜ 21,000 years BP). These reconstructions combine proxy data syntheses with information from climate simulations for the LGM that were

Efficient hierarchical trans-dimensional Bayesian inversion of magnetotelluric data

Science.gov (United States)

Xiang, Enming; Guo, Rongwen; Dosso, Stan E.; Liu, Jianxin; Dong, Hao; Ren, Zhengyong

2018-06-01

This paper develops an efficient hierarchical trans-dimensional (trans-D) Bayesian algorithm to invert magnetotelluric (MT) data for subsurface geoelectrical structure, with unknown geophysical model parameterization (the number of conductivity-layer interfaces) and data-error models parameterized by an auto-regressive (AR) process to account for potential error correlations. The reversible-jump Markov-chain Monte Carlo algorithm, which adds/removes interfaces and AR parameters in birth/death steps, is applied to sample the trans-D posterior probability density for model parameterization, model parameters, error variance and AR parameters, accounting for the uncertainties of model dimension and data-error statistics in the uncertainty estimates of the conductivity profile. To provide efficient sampling over the multiple subspaces of different dimensions, advanced proposal schemes are applied. Parameter perturbations are carried out in principal-component space, defined by eigen-decomposition of the unit-lag model covariance matrix, to minimize the effect of inter-parameter correlations and provide effective perturbation directions and length scales. Parameters of new layers in birth steps are proposed from the prior, instead of focused distributions centred at existing values, to improve birth acceptance rates. Parallel tempering, based on a series of parallel interacting Markov chains with successively relaxed likelihoods, is applied to improve chain mixing over model dimensions. The trans-D inversion is applied in a simulation study to examine the resolution of model structure according to the data information content. The inversion is also applied to a measured MT data set from south-central Australia.

Bayesian data analysis in population ecology: motivations, methods, and benefits

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Dorazio, Robert

2016-01-01

During the 20th century ecologists largely relied on the frequentist system of inference for the analysis of their data. However, in the past few decades ecologists have become increasingly interested in the use of Bayesian methods of data analysis. In this article I provide guidance to ecologists who would like to decide whether Bayesian methods can be used to improve their conclusions and predictions. I begin by providing a concise summary of Bayesian methods of analysis, including a comparison of differences between Bayesian and frequentist approaches to inference when using hierarchical models. Next I provide a list of problems where Bayesian methods of analysis may arguably be preferred over frequentist methods. These problems are usually encountered in analyses based on hierarchical models of data. I describe the essentials required for applying modern methods of Bayesian computation, and I use real-world examples to illustrate these methods. I conclude by summarizing what I perceive to be the main strengths and weaknesses of using Bayesian methods to solve ecological inference problems.

How does aging affect recognition-based inference? A hierarchical Bayesian modeling approach.

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Horn, Sebastian S; Pachur, Thorsten; Mata, Rui

2015-01-01

The recognition heuristic (RH) is a simple strategy for probabilistic inference according to which recognized objects are judged to score higher on a criterion than unrecognized objects. In this article, a hierarchical Bayesian extension of the multinomial r-model is applied to measure use of the RH on the individual participant level and to re-evaluate differences between younger and older adults' strategy reliance across environments. Further, it is explored how individual r-model parameters relate to alternative measures of the use of recognition and other knowledge, such as adherence rates and indices from signal-detection theory (SDT). Both younger and older adults used the RH substantially more often in an environment with high than low recognition validity, reflecting adaptivity in strategy use across environments. In extension of previous analyses (based on adherence rates), hierarchical modeling revealed that in an environment with low recognition validity, (a) older adults had a stronger tendency than younger adults to rely on the RH and (b) variability in RH use between individuals was larger than in an environment with high recognition validity; variability did not differ between age groups. Further, the r-model parameters correlated moderately with an SDT measure expressing how well people can discriminate cases where the RH leads to a correct vs. incorrect inference; this suggests that the r-model and the SDT measures may offer complementary insights into the use of recognition in decision making. In conclusion, younger and older adults are largely adaptive in their application of the RH, but cognitive aging may be associated with an increased tendency to rely on this strategy. Copyright © 2014 Elsevier B.V. All rights reserved.

A dust spectral energy distribution model with hierarchical Bayesian inference - I. Formalism and benchmarking

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Galliano, Frédéric

2018-05-01

This article presents a new dust spectral energy distribution (SED) model, named HerBIE, aimed at eliminating the noise-induced correlations and large scatter obtained when performing least-squares fits. The originality of this code is to apply the hierarchical Bayesian approach to full dust models, including realistic optical properties, stochastic heating, and the mixing of physical conditions in the observed regions. We test the performances of our model by applying it to synthetic observations. We explore the impact on the recovered parameters of several effects: signal-to-noise ratio, SED shape, sample size, the presence of intrinsic correlations, the wavelength coverage, and the use of different SED model components. We show that this method is very efficient: the recovered parameters are consistently distributed around their true values. We do not find any clear bias, even for the most degenerate parameters, or with extreme signal-to-noise ratios.

Clarifying the Hubble constant tension with a Bayesian hierarchical model of the local distance ladder

Science.gov (United States)

Feeney, Stephen M.; Mortlock, Daniel J.; Dalmasso, Niccolò

2018-05-01

Estimates of the Hubble constant, H0, from the local distance ladder and from the cosmic microwave background (CMB) are discrepant at the ˜3σ level, indicating a potential issue with the standard Λ cold dark matter (ΛCDM) cosmology. A probabilistic (i.e. Bayesian) interpretation of this tension requires a model comparison calculation, which in turn depends strongly on the tails of the H0 likelihoods. Evaluating the tails of the local H0 likelihood requires the use of non-Gaussian distributions to faithfully represent anchor likelihoods and outliers, and simultaneous fitting of the complete distance-ladder data set to ensure correct uncertainty propagation. We have hence developed a Bayesian hierarchical model of the full distance ladder that does not rely on Gaussian distributions and allows outliers to be modelled without arbitrary data cuts. Marginalizing over the full ˜3000-parameter joint posterior distribution, we find H0 = (72.72 ± 1.67) km s-1 Mpc-1 when applied to the outlier-cleaned Riess et al. data, and (73.15 ± 1.78) km s-1 Mpc-1 with supernova outliers reintroduced (the pre-cut Cepheid data set is not available). Using our precise evaluation of the tails of the H0 likelihood, we apply Bayesian model comparison to assess the evidence for deviation from ΛCDM given the distance-ladder and CMB data. The odds against ΛCDM are at worst ˜10:1 when considering the Planck 2015 XIII data, regardless of outlier treatment, considerably less dramatic than naïvely implied by the 2.8σ discrepancy. These odds become ˜60:1 when an approximation to the more-discrepant Planck Intermediate XLVI likelihood is included.

ScreenBEAM: a novel meta-analysis algorithm for functional genomics screens via Bayesian hierarchical modeling.

Science.gov (United States)

Yu, Jiyang; Silva, Jose; Califano, Andrea

2016-01-15

Functional genomics (FG) screens, using RNAi or CRISPR technology, have become a standard tool for systematic, genome-wide loss-of-function studies for therapeutic target discovery. As in many large-scale assays, however, off-target effects, variable reagents' potency and experimental noise must be accounted for appropriately control for false positives. Indeed, rigorous statistical analysis of high-throughput FG screening data remains challenging, particularly when integrative analyses are used to combine multiple sh/sgRNAs targeting the same gene in the library. We use large RNAi and CRISPR repositories that are publicly available to evaluate a novel meta-analysis approach for FG screens via Bayesian hierarchical modeling, Screening Bayesian Evaluation and Analysis Method (ScreenBEAM). Results from our analysis show that the proposed strategy, which seamlessly combines all available data, robustly outperforms classical algorithms developed for microarray data sets as well as recent approaches designed for next generation sequencing technologies. Remarkably, the ScreenBEAM algorithm works well even when the quality of FG screens is relatively low, which accounts for about 80-95% of the public datasets. R package and source code are available at: https://github.com/jyyu/ScreenBEAM. ac2248@columbia.edu, jose.silva@mssm.edu, yujiyang@gmail.com Supplementary data are available at Bioinformatics online. © The Author 2015. Published by Oxford University Press. All rights reserved. For Permissions, please e-mail: journals.permissions@oup.com.

A novel Bayesian hierarchical model for road safety hotspot prediction.

Science.gov (United States)

Fawcett, Lee; Thorpe, Neil; Matthews, Joseph; Kremer, Karsten

2017-02-01

In this paper, we propose a Bayesian hierarchical model for predicting accident counts in future years at sites within a pool of potential road safety hotspots. The aim is to inform road safety practitioners of the location of likely future hotspots to enable a proactive, rather than reactive, approach to road safety scheme implementation. A feature of our model is the ability to rank sites according to their potential to exceed, in some future time period, a threshold accident count which may be used as a criterion for scheme implementation. Our model specification enables the classical empirical Bayes formulation - commonly used in before-and-after studies, wherein accident counts from a single before period are used to estimate counterfactual counts in the after period - to be extended to incorporate counts from multiple time periods. This allows site-specific variations in historical accident counts (e.g. locally-observed trends) to offset estimates of safety generated by a global accident prediction model (APM), which itself is used to help account for the effects of global trend and regression-to-mean (RTM). The Bayesian posterior predictive distribution is exploited to formulate predictions and to properly quantify our uncertainty in these predictions. The main contributions of our model include (i) the ability to allow accident counts from multiple time-points to inform predictions, with counts in more recent years lending more weight to predictions than counts from time-points further in the past; (ii) where appropriate, the ability to offset global estimates of trend by variations in accident counts observed locally, at a site-specific level; and (iii) the ability to account for unknown/unobserved site-specific factors which may affect accident counts. We illustrate our model with an application to accident counts at 734 potential hotspots in the German city of Halle; we also propose some simple diagnostics to validate the predictive capability of our

A Hierarchical Bayesian Setting for an Inverse Problem in Linear Parabolic PDEs with Noisy Boundary Conditions

KAUST Repository

Ruggeri, Fabrizio

2016-05-12

In this work we develop a Bayesian setting to infer unknown parameters in initial-boundary value problems related to linear parabolic partial differential equations. We realistically assume that the boundary data are noisy, for a given prescribed initial condition. We show how to derive the joint likelihood function for the forward problem, given some measurements of the solution field subject to Gaussian noise. Given Gaussian priors for the time-dependent Dirichlet boundary values, we analytically marginalize the joint likelihood using the linearity of the equation. Our hierarchical Bayesian approach is fully implemented in an example that involves the heat equation. In this example, the thermal diffusivity is the unknown parameter. We assume that the thermal diffusivity parameter can be modeled a priori through a lognormal random variable or by means of a space-dependent stationary lognormal random field. Synthetic data are used to test the inference. We exploit the behavior of the non-normalized log posterior distribution of the thermal diffusivity. Then, we use the Laplace method to obtain an approximated Gaussian posterior and therefore avoid costly Markov Chain Monte Carlo computations. Expected information gains and predictive posterior densities for observable quantities are numerically estimated using Laplace approximation for different experimental setups.

Hierarchical Bayesian Spatio-Temporal Analysis of Climatic and Socio-Economic Determinants of Rocky Mountain Spotted Fever.

Directory of Open Access Journals (Sweden)

Ram K Raghavan

Full Text Available This study aims to examine the spatio-temporal dynamics of Rocky Mountain spotted fever (RMSF prevalence in four contiguous states of Midwestern United States, and to determine the impact of environmental and socio-economic factors associated with this disease. Bayesian hierarchical models were used to quantify space and time only trends and spatio-temporal interaction effect in the case reports submitted to the state health departments in the region. Various socio-economic, environmental and climatic covariates screened a priori in a bivariate procedure were added to a main-effects Bayesian model in progressive steps to evaluate important drivers of RMSF space-time patterns in the region. Our results show a steady increase in RMSF incidence over the study period to newer geographic areas, and the posterior probabilities of county-specific trends indicate clustering of high risk counties in the central and southern parts of the study region. At the spatial scale of a county, the prevalence levels of RMSF is influenced by poverty status, average relative humidity, and average land surface temperature (>35°C in the region, and the relevance of these factors in the context of climate-change impacts on tick-borne diseases are discussed.

Detecting Hierarchical Structure in Networks

DEFF Research Database (Denmark)

Herlau, Tue; Mørup, Morten; Schmidt, Mikkel Nørgaard

2012-01-01

Many real-world networks exhibit hierarchical organization. Previous models of hierarchies within relational data has focused on binary trees; however, for many networks it is unknown whether there is hierarchical structure, and if there is, a binary tree might not account well for it. We propose...... a generative Bayesian model that is able to infer whether hierarchies are present or not from a hypothesis space encompassing all types of hierarchical tree structures. For efficient inference we propose a collapsed Gibbs sampling procedure that jointly infers a partition and its hierarchical structure....... On synthetic and real data we demonstrate that our model can detect hierarchical structure leading to better link-prediction than competing models. Our model can be used to detect if a network exhibits hierarchical structure, thereby leading to a better comprehension and statistical account the network....

Bayesian hierarchical models for smoothing in two-phase studies, with application to small area estimation.

Science.gov (United States)

Ross, Michelle; Wakefield, Jon

2015-10-01

Two-phase study designs are appealing since they allow for the oversampling of rare sub-populations which improves efficiency. In this paper we describe a Bayesian hierarchical model for the analysis of two-phase data. Such a model is particularly appealing in a spatial setting in which random effects are introduced to model between-area variability. In such a situation, one may be interested in estimating regression coefficients or, in the context of small area estimation, in reconstructing the population totals by strata. The efficiency gains of the two-phase sampling scheme are compared to standard approaches using 2011 birth data from the research triangle area of North Carolina. We show that the proposed method can overcome small sample difficulties and improve on existing techniques. We conclude that the two-phase design is an attractive approach for small area estimation.

A Bayesian Approach to Model Selection in Hierarchical Mixtures-of-Experts Architectures.

Science.gov (United States)

Tanner, Martin A.; Peng, Fengchun; Jacobs, Robert A.

1997-03-01

There does not exist a statistical model that shows good performance on all tasks. Consequently, the model selection problem is unavoidable; investigators must decide which model is best at summarizing the data for each task of interest. This article presents an approach to the model selection problem in hierarchical mixtures-of-experts architectures. These architectures combine aspects of generalized linear models with those of finite mixture models in order to perform tasks via a recursive "divide-and-conquer" strategy. Markov chain Monte Carlo methodology is used to estimate the distribution of the architectures' parameters. One part of our approach to model selection attempts to estimate the worth of each component of an architecture so that relatively unused components can be pruned from the architecture's structure. A second part of this approach uses a Bayesian hypothesis testing procedure in order to differentiate inputs that carry useful information from nuisance inputs. Simulation results suggest that the approach presented here adheres to the dictum of Occam's razor; simple architectures that are adequate for summarizing the data are favored over more complex structures. Copyright 1997 Elsevier Science Ltd. All Rights Reserved.

Fast Markov chain Monte Carlo sampling for sparse Bayesian inference in high-dimensional inverse problems using L1-type priors

International Nuclear Information System (INIS)

Lucka, Felix

2012-01-01

Sparsity has become a key concept for solving of high-dimensional inverse problems using variational regularization techniques. Recently, using similar sparsity-constraints in the Bayesian framework for inverse problems by encoding them in the prior distribution has attracted attention. Important questions about the relation between regularization theory and Bayesian inference still need to be addressed when using sparsity promoting inversion. A practical obstacle for these examinations is the lack of fast posterior sampling algorithms for sparse, high-dimensional Bayesian inversion. Accessing the full range of Bayesian inference methods requires being able to draw samples from the posterior probability distribution in a fast and efficient way. This is usually done using Markov chain Monte Carlo (MCMC) sampling algorithms. In this paper, we develop and examine a new implementation of a single component Gibbs MCMC sampler for sparse priors relying on L1-norms. We demonstrate that the efficiency of our Gibbs sampler increases when the level of sparsity or the dimension of the unknowns is increased. This property is contrary to the properties of the most commonly applied Metropolis–Hastings (MH) sampling schemes. We demonstrate that the efficiency of MH schemes for L1-type priors dramatically decreases when the level of sparsity or the dimension of the unknowns is increased. Practically, Bayesian inversion for L1-type priors using MH samplers is not feasible at all. As this is commonly believed to be an intrinsic feature of MCMC sampling, the performance of our Gibbs sampler also challenges common beliefs about the applicability of sample based Bayesian inference. (paper)

Clustering and Bayesian hierarchical modeling for the definition of informative prior distributions in hydrogeology

Science.gov (United States)

Cucchi, K.; Kawa, N.; Hesse, F.; Rubin, Y.

2017-12-01

In order to reduce uncertainty in the prediction of subsurface flow and transport processes, practitioners should use all data available. However, classic inverse modeling frameworks typically only make use of information contained in in-situ field measurements to provide estimates of hydrogeological parameters. Such hydrogeological information about an aquifer is difficult and costly to acquire. In this data-scarce context, the transfer of ex-situ information coming from previously investigated sites can be critical for improving predictions by better constraining the estimation procedure. Bayesian inverse modeling provides a coherent framework to represent such ex-situ information by virtue of the prior distribution and combine them with in-situ information from the target site. In this study, we present an innovative data-driven approach for defining such informative priors for hydrogeological parameters at the target site. Our approach consists in two steps, both relying on statistical and machine learning methods. The first step is data selection; it consists in selecting sites similar to the target site. We use clustering methods for selecting similar sites based on observable hydrogeological features. The second step is data assimilation; it consists in assimilating data from the selected similar sites into the informative prior. We use a Bayesian hierarchical model to account for inter-site variability and to allow for the assimilation of multiple types of site-specific data. We present the application and validation of the presented methods on an established database of hydrogeological parameters. Data and methods are implemented in the form of an open-source R-package and therefore facilitate easy use by other practitioners.

Technical Note: Probabilistically constraining proxy age–depth models within a Bayesian hierarchical reconstruction model

Directory of Open Access Journals (Sweden)

J. P. Werner

2015-03-01

Full Text Available Reconstructions of the late-Holocene climate rely heavily upon proxies that are assumed to be accurately dated by layer counting, such as measurements of tree rings, ice cores, and varved lake sediments. Considerable advances could be achieved if time-uncertain proxies were able to be included within these multiproxy reconstructions, and if time uncertainties were recognized and correctly modeled for proxies commonly treated as free of age model errors. Current approaches for accounting for time uncertainty are generally limited to repeating the reconstruction using each one of an ensemble of age models, thereby inflating the final estimated uncertainty – in effect, each possible age model is given equal weighting. Uncertainties can be reduced by exploiting the inferred space–time covariance structure of the climate to re-weight the possible age models. Here, we demonstrate how Bayesian hierarchical climate reconstruction models can be augmented to account for time-uncertain proxies. Critically, although a priori all age models are given equal probability of being correct, the probabilities associated with the age models are formally updated within the Bayesian framework, thereby reducing uncertainties. Numerical experiments show that updating the age model probabilities decreases uncertainty in the resulting reconstructions, as compared with the current de facto standard of sampling over all age models, provided there is sufficient information from other data sources in the spatial region of the time-uncertain proxy. This approach can readily be generalized to non-layer-counted proxies, such as those derived from marine sediments.

Bayesian disease mapping: hierarchical modeling in spatial epidemiology

National Research Council Canada - National Science Library

Lawson, Andrew

2013-01-01

Since the publication of the first edition, many new Bayesian tools and methods have been developed for space-time data analysis, the predictive modeling of health outcomes, and other spatial biostatistical areas...

Fast empirical Bayesian LASSO for multiple quantitative trait locus mapping

Directory of Open Access Journals (Sweden)

Xu Shizhong

2011-05-01

Full Text Available Abstract Background The Bayesian shrinkage technique has been applied to multiple quantitative trait loci (QTLs mapping to estimate the genetic effects of QTLs on quantitative traits from a very large set of possible effects including the main and epistatic effects of QTLs. Although the recently developed empirical Bayes (EB method significantly reduced computation comparing with the fully Bayesian approach, its speed and accuracy are limited by the fact that numerical optimization is required to estimate the variance components in the QTL model. Results We developed a fast empirical Bayesian LASSO (EBLASSO method for multiple QTL mapping. The fact that the EBLASSO can estimate the variance components in a closed form along with other algorithmic techniques render the EBLASSO method more efficient and accurate. Comparing with the EB method, our simulation study demonstrated that the EBLASSO method could substantially improve the computational speed and detect more QTL effects without increasing the false positive rate. Particularly, the EBLASSO algorithm running on a personal computer could easily handle a linear QTL model with more than 100,000 variables in our simulation study. Real data analysis also demonstrated that the EBLASSO method detected more reasonable effects than the EB method. Comparing with the LASSO, our simulation showed that the current version of the EBLASSO implemented in Matlab had similar speed as the LASSO implemented in Fortran, and that the EBLASSO detected the same number of true effects as the LASSO but a much smaller number of false positive effects. Conclusions The EBLASSO method can handle a large number of effects possibly including both the main and epistatic QTL effects, environmental effects and the effects of gene-environment interactions. It will be a very useful tool for multiple QTL mapping.

Estimating mental states of a depressed person with bayesian networks

NARCIS (Netherlands)

Klein, Michel C.A.; Modena, Gabriele

2013-01-01

In this work in progress paper we present an approach based on Bayesian Networks to model the relationship between mental states and empirical observations in a depressed person. We encode relationships and domain expertise as a Hierarchical Bayesian Network. Mental states are represented as latent

Hierarchical Bayesian modeling of spatio-temporal patterns of lung cancer incidence risk in Georgia, USA: 2000-2007

Science.gov (United States)

Yin, Ping; Mu, Lan; Madden, Marguerite; Vena, John E.

2014-10-01

Lung cancer is the second most commonly diagnosed cancer in both men and women in Georgia, USA. However, the spatio-temporal patterns of lung cancer risk in Georgia have not been fully studied. Hierarchical Bayesian models are used here to explore the spatio-temporal patterns of lung cancer incidence risk by race and gender in Georgia for the period of 2000-2007. With the census tract level as the spatial scale and the 2-year period aggregation as the temporal scale, we compare a total of seven Bayesian spatio-temporal models including two under a separate modeling framework and five under a joint modeling framework. One joint model outperforms others based on the deviance information criterion. Results show that the northwest region of Georgia has consistently high lung cancer incidence risk for all population groups during the study period. In addition, there are inverse relationships between the socioeconomic status and the lung cancer incidence risk among all Georgian population groups, and the relationships in males are stronger than those in females. By mapping more reliable variations in lung cancer incidence risk at a relatively fine spatio-temporal scale for different Georgian population groups, our study aims to better support healthcare performance assessment, etiological hypothesis generation, and health policy making.

Comparing hierarchical models via the marginalized deviance information criterion.

Science.gov (United States)

Quintero, Adrian; Lesaffre, Emmanuel

2018-07-20

Hierarchical models are extensively used in pharmacokinetics and longitudinal studies. When the estimation is performed from a Bayesian approach, model comparison is often based on the deviance information criterion (DIC). In hierarchical models with latent variables, there are several versions of this statistic: the conditional DIC (cDIC) that incorporates the latent variables in the focus of the analysis and the marginalized DIC (mDIC) that integrates them out. Regardless of the asymptotic and coherency difficulties of cDIC, this alternative is usually used in Markov chain Monte Carlo (MCMC) methods for hierarchical models because of practical convenience. The mDIC criterion is more appropriate in most cases but requires integration of the likelihood, which is computationally demanding and not implemented in Bayesian software. Therefore, we consider a method to compute mDIC by generating replicate samples of the latent variables that need to be integrated out. This alternative can be easily conducted from the MCMC output of Bayesian packages and is widely applicable to hierarchical models in general. Additionally, we propose some approximations in order to reduce the computational complexity for large-sample situations. The method is illustrated with simulated data sets and 2 medical studies, evidencing that cDIC may be misleading whilst mDIC appears pertinent. Copyright © 2018 John Wiley & Sons, Ltd.

Linking bovine tuberculosis on cattle farms to white-tailed deer and environmental variables using Bayesian hierarchical analysis.

Directory of Open Access Journals (Sweden)

W David Walter

Full Text Available Bovine tuberculosis is a bacterial disease caused by Mycobacterium bovis in livestock and wildlife with hosts that include Eurasian badgers (Meles meles, brushtail possum (Trichosurus vulpecula, and white-tailed deer (Odocoileus virginianus. Risk-assessment efforts in Michigan have been initiated on farms to minimize interactions of cattle with wildlife hosts but research on M. bovis on cattle farms has not investigated the spatial context of disease epidemiology. To incorporate spatially explicit data, initial likelihood of infection probabilities for cattle farms tested for M. bovis, prevalence of M. bovis in white-tailed deer, deer density, and environmental variables for each farm were modeled in a Bayesian hierarchical framework. We used geo-referenced locations of 762 cattle farms that have been tested for M. bovis, white-tailed deer prevalence, and several environmental variables that may lead to long-term survival and viability of M. bovis on farms and surrounding habitats (i.e., soil type, habitat type. Bayesian hierarchical analyses identified deer prevalence and proportion of sandy soil within our sampling grid as the most supported model. Analysis of cattle farms tested for M. bovis identified that for every 1% increase in sandy soil resulted in an increase in odds of infection by 4%. Our analysis revealed that the influence of prevalence of M. bovis in white-tailed deer was still a concern even after considerable efforts to prevent cattle interactions with white-tailed deer through on-farm mitigation and reduction in the deer population. Cattle farms test positive for M. bovis annually in our study area suggesting that the potential for an environmental source either on farms or in the surrounding landscape may contributing to new or re-infections with M. bovis. Our research provides an initial assessment of potential environmental factors that could be incorporated into additional modeling efforts as more knowledge of deer herd

Linking bovine tuberculosis on cattle farms to white-tailed deer and environmental variables using Bayesian hierarchical analysis

Science.gov (United States)

Walter, W. David; Smith, Rick; Vanderklok, Mike; VerCauterren, Kurt C.

2014-01-01

Bovine tuberculosis is a bacterial disease caused by Mycobacterium bovis in livestock and wildlife with hosts that include Eurasian badgers (Meles meles), brushtail possum (Trichosurus vulpecula), and white-tailed deer (Odocoileus virginianus). Risk-assessment efforts in Michigan have been initiated on farms to minimize interactions of cattle with wildlife hosts but research onM. bovis on cattle farms has not investigated the spatial context of disease epidemiology. To incorporate spatially explicit data, initial likelihood of infection probabilities for cattle farms tested for M. bovis, prevalence of M. bovis in white-tailed deer, deer density, and environmental variables for each farm were modeled in a Bayesian hierarchical framework. We used geo-referenced locations of 762 cattle farms that have been tested for M. bovis, white-tailed deer prevalence, and several environmental variables that may lead to long-term survival and viability of M. bovis on farms and surrounding habitats (i.e., soil type, habitat type). Bayesian hierarchical analyses identified deer prevalence and proportion of sandy soil within our sampling grid as the most supported model. Analysis of cattle farms tested for M. bovisidentified that for every 1% increase in sandy soil resulted in an increase in odds of infection by 4%. Our analysis revealed that the influence of prevalence of M. bovis in white-tailed deer was still a concern even after considerable efforts to prevent cattle interactions with white-tailed deer through on-farm mitigation and reduction in the deer population. Cattle farms test positive for M. bovis annually in our study area suggesting that the potential for an environmental source either on farms or in the surrounding landscape may contributing to new or re-infections with M. bovis. Our research provides an initial assessment of potential environmental factors that could be incorporated into additional modeling efforts as more knowledge of deer herd

Hierarchical Bayesian Spatio Temporal Model Comparison on the Earth Trapped Particle Forecast

International Nuclear Information System (INIS)

Suparta, Wayan; Gusrizal

2014-01-01

We compared two hierarchical Bayesian spatio temporal (HBST) results, Gaussian process (GP) and autoregressive (AR) models, on the Earth trapped particle forecast. Two models were employed on the South Atlantic Anomaly (SAA) region. Electron of >30 keV (mep0e1) from National Oceanic and Atmospheric Administration (NOAA) 15-18 satellites data was chosen as the particle modeled. We used two weeks data to perform the model fitting on a 5°x5° grid of longitude and latitude, and 31 August 2007 was set as the date of forecast. Three statistical validations were performed on the data, i.e. the root mean square error (RMSE), mean absolute percentage error (MAPE) and bias (BIAS). The statistical analysis showed that GP model performed better than AR with the average of RMSE = 0.38 and 0.63, MAPE = 11.98 and 17.30, and BIAS = 0.32 and 0.24, for GP and AR, respectively. Visual validation on both models with the NOAA map's also confirmed the superior of the GP than the AR. The variance of log flux minimum = 0.09 and 1.09, log flux maximum = 1.15 and 1.35, and in successively represents GP and AR

Doing bayesian data analysis a tutorial with R and BUGS

CERN Document Server

Kruschke, John K

2011-01-01

There is an explosion of interest in Bayesian statistics, primarily because recently created computational methods have finally made Bayesian analysis obtainable to a wide audience. Doing Bayesian Data Analysis, A Tutorial Introduction with R and BUGS provides an accessible approach to Bayesian data analysis, as material is explained clearly with concrete examples. The book begins with the basics, including essential concepts of probability and random sampling, and gradually progresses to advanced hierarchical modeling methods for realistic data. The text delivers comprehensive coverage of all

Modeling when people quit: Bayesian censored geometric models with hierarchical and latent-mixture extensions.

Science.gov (United States)

Okada, Kensuke; Vandekerckhove, Joachim; Lee, Michael D

2018-02-01

People often interact with environments that can provide only a finite number of items as resources. Eventually a book contains no more chapters, there are no more albums available from a band, and every Pokémon has been caught. When interacting with these sorts of environments, people either actively choose to quit collecting new items, or they are forced to quit when the items are exhausted. Modeling the distribution of how many items people collect before they quit involves untangling these two possibilities, We propose that censored geometric models are a useful basic technique for modeling the quitting distribution, and, show how, by implementing these models in a hierarchical and latent-mixture framework through Bayesian methods, they can be extended to capture the additional features of specific situations. We demonstrate this approach by developing and testing a series of models in two case studies involving real-world data. One case study deals with people choosing jokes from a recommender system, and the other deals with people completing items in a personality survey.

Bayesian state space models for dynamic genetic network construction across multiple tissues.

Science.gov (United States)

Liang, Yulan; Kelemen, Arpad

2016-08-01

Construction of gene-gene interaction networks and potential pathways is a challenging and important problem in genomic research for complex diseases while estimating the dynamic changes of the temporal correlations and non-stationarity are the keys in this process. In this paper, we develop dynamic state space models with hierarchical Bayesian settings to tackle this challenge for inferring the dynamic profiles and genetic networks associated with disease treatments. We treat both the stochastic transition matrix and the observation matrix time-variant and include temporal correlation structures in the covariance matrix estimations in the multivariate Bayesian state space models. The unevenly spaced short time courses with unseen time points are treated as hidden state variables. Hierarchical Bayesian approaches with various prior and hyper-prior models with Monte Carlo Markov Chain and Gibbs sampling algorithms are used to estimate the model parameters and the hidden state variables. We apply the proposed Hierarchical Bayesian state space models to multiple tissues (liver, skeletal muscle, and kidney) Affymetrix time course data sets following corticosteroid (CS) drug administration. Both simulation and real data analysis results show that the genomic changes over time and gene-gene interaction in response to CS treatment can be well captured by the proposed models. The proposed dynamic Hierarchical Bayesian state space modeling approaches could be expanded and applied to other large scale genomic data, such as next generation sequence (NGS) combined with real time and time varying electronic health record (EHR) for more comprehensive and robust systematic and network based analysis in order to transform big biomedical data into predictions and diagnostics for precision medicine and personalized healthcare with better decision making and patient outcomes.

Towards Bayesian Inference of the Fast-Ion Distribution Function

DEFF Research Database (Denmark)

Stagner, L.; Heidbrink, W.W.; Salewski, Mirko

2012-01-01

sensitivity of the measurements are incorporated into Bayesian likelihood probabilities, while prior probabilities enforce physical constraints. As an initial step, this poster uses Bayesian statistics to infer the DIII-D electron density profile from multiple diagnostic measurements. Likelihood functions....... However, when theory and experiment disagree (for one or more diagnostics), it is unclear how to proceed. Bayesian statistics provides a framework to infer the DF, quantify errors, and reconcile discrepant diagnostic measurements. Diagnostic errors and ``weight functions" that describe the phase space...

Sub-seasonal-to-seasonal Reservoir Inflow Forecast using Bayesian Hierarchical Hidden Markov Model

Science.gov (United States)

Mukhopadhyay, S.; Arumugam, S.

2017-12-01

Sub-seasonal-to-seasonal (S2S) (15-90 days) streamflow forecasting is an emerging area of research that provides seamless information for reservoir operation from weather time scales to seasonal time scales. From an operational perspective, sub-seasonal inflow forecasts are highly valuable as these enable water managers to decide short-term releases (15-30 days), while holding water for seasonal needs (e.g., irrigation and municipal supply) and to meet end-of-the-season target storage at a desired level. We propose a Bayesian Hierarchical Hidden Markov Model (BHHMM) to develop S2S inflow forecasts for the Tennessee Valley Area (TVA) reservoir system. Here, the hidden states are predicted by relevant indices that influence the inflows at S2S time scale. The hidden Markov model also captures the both spatial and temporal hierarchy in predictors that operate at S2S time scale with model parameters being estimated as a posterior distribution using a Bayesian framework. We present our work in two steps, namely single site model and multi-site model. For proof of concept, we consider inflows to Douglas Dam, Tennessee, in the single site model. For multisite model we consider reservoirs in the upper Tennessee valley. Streamflow forecasts are issued and updated continuously every day at S2S time scale. We considered precipitation forecasts obtained from NOAA Climate Forecast System (CFSv2) GCM as predictors for developing S2S streamflow forecasts along with relevant indices for predicting hidden states. Spatial dependence of the inflow series of reservoirs are also preserved in the multi-site model. To circumvent the non-normality of the data, we consider the HMM in a Generalized Linear Model setting. Skill of the proposed approach is tested using split sample validation against a traditional multi-site canonical correlation model developed using the same set of predictors. From the posterior distribution of the inflow forecasts, we also highlight different system behavior

Multimethod, multistate Bayesian hierarchical modeling approach for use in regional monitoring of wolves.

Science.gov (United States)

Jiménez, José; García, Emilio J; Llaneza, Luis; Palacios, Vicente; González, Luis Mariano; García-Domínguez, Francisco; Múñoz-Igualada, Jaime; López-Bao, José Vicente

2016-08-01

In many cases, the first step in large-carnivore management is to obtain objective, reliable, and cost-effective estimates of population parameters through procedures that are reproducible over time. However, monitoring predators over large areas is difficult, and the data have a high level of uncertainty. We devised a practical multimethod and multistate modeling approach based on Bayesian hierarchical-site-occupancy models that combined multiple survey methods to estimate different population states for use in monitoring large predators at a regional scale. We used wolves (Canis lupus) as our model species and generated reliable estimates of the number of sites with wolf reproduction (presence of pups). We used 2 wolf data sets from Spain (Western Galicia in 2013 and Asturias in 2004) to test the approach. Based on howling surveys, the naïve estimation (i.e., estimate based only on observations) of the number of sites with reproduction was 9 and 25 sites in Western Galicia and Asturias, respectively. Our model showed 33.4 (SD 9.6) and 34.4 (3.9) sites with wolf reproduction, respectively. The number of occupied sites with wolf reproduction was 0.67 (SD 0.19) and 0.76 (0.11), respectively. This approach can be used to design more cost-effective monitoring programs (i.e., to define the sampling effort needed per site). Our approach should inspire well-coordinated surveys across multiple administrative borders and populations and lead to improved decision making for management of large carnivores on a landscape level. The use of this Bayesian framework provides a simple way to visualize the degree of uncertainty around population-parameter estimates and thus provides managers and stakeholders an intuitive approach to interpreting monitoring results. Our approach can be widely applied to large spatial scales in wildlife monitoring where detection probabilities differ between population states and where several methods are being used to estimate different population

Hierarchical Bayesian models to assess between- and within-batch variability of pathogen contamination in food.

Science.gov (United States)

Commeau, Natalie; Cornu, Marie; Albert, Isabelle; Denis, Jean-Baptiste; Parent, Eric

2012-03-01

Assessing within-batch and between-batch variability is of major interest for risk assessors and risk managers in the context of microbiological contamination of food. For example, the ratio between the within-batch variability and the between-batch variability has a large impact on the results of a sampling plan. Here, we designed hierarchical Bayesian models to represent such variability. Compatible priors were built mathematically to obtain sound model comparisons. A numeric criterion is proposed to assess the contamination structure comparing the ability of the models to replicate grouped data at the batch level using a posterior predictive loss approach. Models were applied to two case studies: contamination by Listeria monocytogenes of pork breast used to produce diced bacon and contamination by the same microorganism on cold smoked salmon at the end of the process. In the first case study, a contamination structure clearly exists and is located at the batch level, that is, between batches variability is relatively strong, whereas in the second a structure also exists but is less marked. © 2012 Society for Risk Analysis.

Empirical Bayesian inference and model uncertainty

International Nuclear Information System (INIS)

Poern, K.

1994-01-01

This paper presents a hierarchical or multistage empirical Bayesian approach for the estimation of uncertainty concerning the intensity of a homogeneous Poisson process. A class of contaminated gamma distributions is considered to describe the uncertainty concerning the intensity. These distributions in turn are defined through a set of secondary parameters, the knowledge of which is also described and updated via Bayes formula. This two-stage Bayesian approach is an example where the modeling uncertainty is treated in a comprehensive way. Each contaminated gamma distributions, represented by a point in the 3D space of secondary parameters, can be considered as a specific model of the uncertainty about the Poisson intensity. Then, by the empirical Bayesian method each individual model is assigned a posterior probability

Bayesian Poisson hierarchical models for crash data analysis: Investigating the impact of model choice on site-specific predictions.

Science.gov (United States)

Khazraee, S Hadi; Johnson, Valen; Lord, Dominique

2018-08-01

The Poisson-gamma (PG) and Poisson-lognormal (PLN) regression models are among the most popular means for motor vehicle crash data analysis. Both models belong to the Poisson-hierarchical family of models. While numerous studies have compared the overall performance of alternative Bayesian Poisson-hierarchical models, little research has addressed the impact of model choice on the expected crash frequency prediction at individual sites. This paper sought to examine whether there are any trends among candidate models predictions e.g., that an alternative model's prediction for sites with certain conditions tends to be higher (or lower) than that from another model. In addition to the PG and PLN models, this research formulated a new member of the Poisson-hierarchical family of models: the Poisson-inverse gamma (PIGam). Three field datasets (from Texas, Michigan and Indiana) covering a wide range of over-dispersion characteristics were selected for analysis. This study demonstrated that the model choice can be critical when the calibrated models are used for prediction at new sites, especially when the data are highly over-dispersed. For all three datasets, the PIGam model would predict higher expected crash frequencies than would the PLN and PG models, in order, indicating a clear link between the models predictions and the shape of their mixing distributions (i.e., gamma, lognormal, and inverse gamma, respectively). The thicker tail of the PIGam and PLN models (in order) may provide an advantage when the data are highly over-dispersed. The analysis results also illustrated a major deficiency of the Deviance Information Criterion (DIC) in comparing the goodness-of-fit of hierarchical models; models with drastically different set of coefficients (and thus predictions for new sites) may yield similar DIC values, because the DIC only accounts for the parameters in the lowest (observation) level of the hierarchy and ignores the higher levels (regression coefficients

Mapping brucellosis increases relative to elk density using hierarchical Bayesian models

Science.gov (United States)

Cross, Paul C.; Heisey, Dennis M.; Scurlock, Brandon M.; Edwards, William H.; Brennan, Angela; Ebinger, Michael R.

2010-01-01

The relationship between host density and parasite transmission is central to the effectiveness of many disease management strategies. Few studies, however, have empirically estimated this relationship particularly in large mammals. We applied hierarchical Bayesian methods to a 19-year dataset of over 6400 brucellosis tests of adult female elk (Cervus elaphus) in northwestern Wyoming. Management captures that occurred from January to March were over two times more likely to be seropositive than hunted elk that were killed in September to December, while accounting for site and year effects. Areas with supplemental feeding grounds for elk had higher seroprevalence in 1991 than other regions, but by 2009 many areas distant from the feeding grounds were of comparable seroprevalence. The increases in brucellosis seroprevalence were correlated with elk densities at the elk management unit, or hunt area, scale (mean 2070 km2; range = [95–10237]). The data, however, could not differentiate among linear and non-linear effects of host density. Therefore, control efforts that focus on reducing elk densities at a broad spatial scale were only weakly supported. Additional research on how a few, large groups within a region may be driving disease dynamics is needed for more targeted and effective management interventions. Brucellosis appears to be expanding its range into new regions and elk populations, which is likely to further complicate the United States brucellosis eradication program. This study is an example of how the dynamics of host populations can affect their ability to serve as disease reservoirs.

Mapping brucellosis increases relative to elk density using hierarchical Bayesian models.

Directory of Open Access Journals (Sweden)

Paul C Cross

Full Text Available The relationship between host density and parasite transmission is central to the effectiveness of many disease management strategies. Few studies, however, have empirically estimated this relationship particularly in large mammals. We applied hierarchical Bayesian methods to a 19-year dataset of over 6400 brucellosis tests of adult female elk (Cervus elaphus in northwestern Wyoming. Management captures that occurred from January to March were over two times more likely to be seropositive than hunted elk that were killed in September to December, while accounting for site and year effects. Areas with supplemental feeding grounds for elk had higher seroprevalence in 1991 than other regions, but by 2009 many areas distant from the feeding grounds were of comparable seroprevalence. The increases in brucellosis seroprevalence were correlated with elk densities at the elk management unit, or hunt area, scale (mean 2070 km(2; range = [95-10237]. The data, however, could not differentiate among linear and non-linear effects of host density. Therefore, control efforts that focus on reducing elk densities at a broad spatial scale were only weakly supported. Additional research on how a few, large groups within a region may be driving disease dynamics is needed for more targeted and effective management interventions. Brucellosis appears to be expanding its range into new regions and elk populations, which is likely to further complicate the United States brucellosis eradication program. This study is an example of how the dynamics of host populations can affect their ability to serve as disease reservoirs.

A variational Bayesian method to inverse problems with impulsive noise

KAUST Repository

Jin, Bangti

2012-01-01

We propose a novel numerical method for solving inverse problems subject to impulsive noises which possibly contain a large number of outliers. The approach is of Bayesian type, and it exploits a heavy-tailed t distribution for data noise to achieve robustness with respect to outliers. A hierarchical model with all hyper-parameters automatically determined from the given data is described. An algorithm of variational type by minimizing the Kullback-Leibler divergence between the true posteriori distribution and a separable approximation is developed. The numerical method is illustrated on several one- and two-dimensional linear and nonlinear inverse problems arising from heat conduction, including estimating boundary temperature, heat flux and heat transfer coefficient. The results show its robustness to outliers and the fast and steady convergence of the algorithm. © 2011 Elsevier Inc.

msBayes: Pipeline for testing comparative phylogeographic histories using hierarchical approximate Bayesian computation

Directory of Open Access Journals (Sweden)

Takebayashi Naoki

2007-07-01

Full Text Available Abstract Background Although testing for simultaneous divergence (vicariance across different population-pairs that span the same barrier to gene flow is of central importance to evolutionary biology, researchers often equate the gene tree and population/species tree thereby ignoring stochastic coalescent variance in their conclusions of temporal incongruence. In contrast to other available phylogeographic software packages, msBayes is the only one that analyses data from multiple species/population pairs under a hierarchical model. Results msBayes employs approximate Bayesian computation (ABC under a hierarchical coalescent model to test for simultaneous divergence (TSD in multiple co-distributed population-pairs. Simultaneous isolation is tested by estimating three hyper-parameters that characterize the degree of variability in divergence times across co-distributed population pairs while allowing for variation in various within population-pair demographic parameters (sub-parameters that can affect the coalescent. msBayes is a software package consisting of several C and R programs that are run with a Perl "front-end". Conclusion The method reasonably distinguishes simultaneous isolation from temporal incongruence in the divergence of co-distributed population pairs, even with sparse sampling of individuals. Because the estimate step is decoupled from the simulation step, one can rapidly evaluate different ABC acceptance/rejection conditions and the choice of summary statistics. Given the complex and idiosyncratic nature of testing multi-species biogeographic hypotheses, we envision msBayes as a powerful and flexible tool for tackling a wide array of difficult research questions that use population genetic data from multiple co-distributed species. The msBayes pipeline is available for download at http://msbayes.sourceforge.net/ under an open source license (GNU Public License. The msBayes pipeline is comprised of several C and R programs that

Bayesian theory and applications

CERN Document Server

Dellaportas, Petros; Polson, Nicholas G; Stephens, David A

2013-01-01

The development of hierarchical models and Markov chain Monte Carlo (MCMC) techniques forms one of the most profound advances in Bayesian analysis since the 1970s and provides the basis for advances in virtually all areas of applied and theoretical Bayesian statistics. This volume guides the reader along a statistical journey that begins with the basic structure of Bayesian theory, and then provides details on most of the past and present advances in this field. The book has a unique format. There is an explanatory chapter devoted to each conceptual advance followed by journal-style chapters that provide applications or further advances on the concept. Thus, the volume is both a textbook and a compendium of papers covering a vast range of topics. It is appropriate for a well-informed novice interested in understanding the basic approach, methods and recent applications. Because of its advanced chapters and recent work, it is also appropriate for a more mature reader interested in recent applications and devel...

Basics of Bayesian methods.

Science.gov (United States)

Ghosh, Sujit K

2010-01-01

Bayesian methods are rapidly becoming popular tools for making statistical inference in various fields of science including biology, engineering, finance, and genetics. One of the key aspects of Bayesian inferential method is its logical foundation that provides a coherent framework to utilize not only empirical but also scientific information available to a researcher. Prior knowledge arising from scientific background, expert judgment, or previously collected data is used to build a prior distribution which is then combined with current data via the likelihood function to characterize the current state of knowledge using the so-called posterior distribution. Bayesian methods allow the use of models of complex physical phenomena that were previously too difficult to estimate (e.g., using asymptotic approximations). Bayesian methods offer a means of more fully understanding issues that are central to many practical problems by allowing researchers to build integrated models based on hierarchical conditional distributions that can be estimated even with limited amounts of data. Furthermore, advances in numerical integration methods, particularly those based on Monte Carlo methods, have made it possible to compute the optimal Bayes estimators. However, there is a reasonably wide gap between the background of the empirically trained scientists and the full weight of Bayesian statistical inference. Hence, one of the goals of this chapter is to bridge the gap by offering elementary to advanced concepts that emphasize linkages between standard approaches and full probability modeling via Bayesian methods.

Merging information from multi-model flood projections in a hierarchical Bayesian framework

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Le Vine, Nataliya

2016-04-01

Multi-model ensembles are becoming widely accepted for flood frequency change analysis. The use of multiple models results in large uncertainty around estimates of flood magnitudes, due to both uncertainty in model selection and natural variability of river flow. The challenge is therefore to extract the most meaningful signal from the multi-model predictions, accounting for both model quality and uncertainties in individual model estimates. The study demonstrates the potential of a recently proposed hierarchical Bayesian approach to combine information from multiple models. The approach facilitates explicit treatment of shared multi-model discrepancy as well as the probabilistic nature of the flood estimates, by treating the available models as a sample from a hypothetical complete (but unobserved) set of models. The advantages of the approach are: 1) to insure an adequate 'baseline' conditions with which to compare future changes; 2) to reduce flood estimate uncertainty; 3) to maximize use of statistical information in circumstances where multiple weak predictions individually lack power, but collectively provide meaningful information; 4) to adjust multi-model consistency criteria when model biases are large; and 5) to explicitly consider the influence of the (model performance) stationarity assumption. Moreover, the analysis indicates that reducing shared model discrepancy is the key to further reduction of uncertainty in the flood frequency analysis. The findings are of value regarding how conclusions about changing exposure to flooding are drawn, and to flood frequency change attribution studies.

An introduction to Bayesian statistics in health psychology.

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Depaoli, Sarah; Rus, Holly M; Clifton, James P; van de Schoot, Rens; Tiemensma, Jitske

2017-09-01

The aim of the current article is to provide a brief introduction to Bayesian statistics within the field of health psychology. Bayesian methods are increasing in prevalence in applied fields, and they have been shown in simulation research to improve the estimation accuracy of structural equation models, latent growth curve (and mixture) models, and hierarchical linear models. Likewise, Bayesian methods can be used with small sample sizes since they do not rely on large sample theory. In this article, we discuss several important components of Bayesian statistics as they relate to health-based inquiries. We discuss the incorporation and impact of prior knowledge into the estimation process and the different components of the analysis that should be reported in an article. We present an example implementing Bayesian estimation in the context of blood pressure changes after participants experienced an acute stressor. We conclude with final thoughts on the implementation of Bayesian statistics in health psychology, including suggestions for reviewing Bayesian manuscripts and grant proposals. We have also included an extensive amount of online supplementary material to complement the content presented here, including Bayesian examples using many different software programmes and an extensive sensitivity analysis examining the impact of priors.

Learning with hierarchical-deep models.

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Salakhutdinov, Ruslan; Tenenbaum, Joshua B; Torralba, Antonio

2013-08-01

We introduce HD (or “Hierarchical-Deep”) models, a new compositional learning architecture that integrates deep learning models with structured hierarchical Bayesian (HB) models. Specifically, we show how we can learn a hierarchical Dirichlet process (HDP) prior over the activities of the top-level features in a deep Boltzmann machine (DBM). This compound HDP-DBM model learns to learn novel concepts from very few training example by learning low-level generic features, high-level features that capture correlations among low-level features, and a category hierarchy for sharing priors over the high-level features that are typical of different kinds of concepts. We present efficient learning and inference algorithms for the HDP-DBM model and show that it is able to learn new concepts from very few examples on CIFAR-100 object recognition, handwritten character recognition, and human motion capture datasets.

Modelling dependable systems using hybrid Bayesian networks

International Nuclear Information System (INIS)

Neil, Martin; Tailor, Manesh; Marquez, David; Fenton, Norman; Hearty, Peter

2008-01-01

A hybrid Bayesian network (BN) is one that incorporates both discrete and continuous nodes. In our extensive applications of BNs for system dependability assessment, the models are invariably hybrid and the need for efficient and accurate computation is paramount. We apply a new iterative algorithm that efficiently combines dynamic discretisation with robust propagation algorithms on junction tree structures to perform inference in hybrid BNs. We illustrate its use in the field of dependability with two example of reliability estimation. Firstly we estimate the reliability of a simple single system and next we implement a hierarchical Bayesian model. In the hierarchical model we compute the reliability of two unknown subsystems from data collected on historically similar subsystems and then input the result into a reliability block model to compute system level reliability. We conclude that dynamic discretisation can be used as an alternative to analytical or Monte Carlo methods with high precision and can be applied to a wide range of dependability problems

A Bayesian Hierarchical Modeling Approach to Predicting Flow in Ungauged Basins

Science.gov (United States)

Gronewold, A.; Alameddine, I.; Anderson, R. M.

2009-12-01

Recent innovative approaches to identifying and applying regression-based relationships between land use patterns (such as increasing impervious surface area and decreasing vegetative cover) and rainfall-runoff model parameters represent novel and promising improvements to predicting flow from ungauged basins. In particular, these approaches allow for predicting flows under uncertain and potentially variable future conditions due to rapid land cover changes, variable climate conditions, and other factors. Despite the broad range of literature on estimating rainfall-runoff model parameters, however, the absence of a robust set of modeling tools for identifying and quantifying uncertainties in (and correlation between) rainfall-runoff model parameters represents a significant gap in current hydrological modeling research. Here, we build upon a series of recent publications promoting novel Bayesian and probabilistic modeling strategies for quantifying rainfall-runoff model parameter estimation uncertainty. Our approach applies alternative measures of rainfall-runoff model parameter joint likelihood (including Nash-Sutcliffe efficiency, among others) to simulate samples from the joint parameter posterior probability density function. We then use these correlated samples as response variables in a Bayesian hierarchical model with land use coverage data as predictor variables in order to develop a robust land use-based tool for forecasting flow in ungauged basins while accounting for, and explicitly acknowledging, parameter estimation uncertainty. We apply this modeling strategy to low-relief coastal watersheds of Eastern North Carolina, an area representative of coastal resource waters throughout the world because of its sensitive embayments and because of the abundant (but currently threatened) natural resources it hosts. Consequently, this area is the subject of several ongoing studies and large-scale planning initiatives, including those conducted through the United

Estimating temporal trend in the presence of spatial complexity: a Bayesian hierarchical model for a wetland plant population undergoing restoration.

Directory of Open Access Journals (Sweden)

Thomas J Rodhouse

Full Text Available Monitoring programs that evaluate restoration and inform adaptive management are important for addressing environmental degradation. These efforts may be well served by spatially explicit hierarchical approaches to modeling because of unavoidable spatial structure inherited from past land use patterns and other factors. We developed bayesian hierarchical models to estimate trends from annual density counts observed in a spatially structured wetland forb (Camassia quamash [camas] population following the cessation of grazing and mowing on the study area, and in a separate reference population of camas. The restoration site was bisected by roads and drainage ditches, resulting in distinct subpopulations ("zones" with different land use histories. We modeled this spatial structure by fitting zone-specific intercepts and slopes. We allowed spatial covariance parameters in the model to vary by zone, as in stratified kriging, accommodating anisotropy and improving computation and biological interpretation. Trend estimates provided evidence of a positive effect of passive restoration, and the strength of evidence was influenced by the amount of spatial structure in the model. Allowing trends to vary among zones and accounting for topographic heterogeneity increased precision of trend estimates. Accounting for spatial autocorrelation shifted parameter coefficients in ways that varied among zones depending on strength of statistical shrinkage, autocorrelation and topographic heterogeneity--a phenomenon not widely described. Spatially explicit estimates of trend from hierarchical models will generally be more useful to land managers than pooled regional estimates and provide more realistic assessments of uncertainty. The ability to grapple with historical contingency is an appealing benefit of this approach.

Hierarchical Bayesian analysis of outcome- and process-based social preferences and beliefs in Dictator Games and sequential Prisoner's Dilemmas.

Science.gov (United States)

Aksoy, Ozan; Weesie, Jeroen

2014-05-01

In this paper, using a within-subjects design, we estimate the utility weights that subjects attach to the outcome of their interaction partners in four decision situations: (1) binary Dictator Games (DG), second player's role in the sequential Prisoner's Dilemma (PD) after the first player (2) cooperated and (3) defected, and (4) first player's role in the sequential Prisoner's Dilemma game. We find that the average weights in these four decision situations have the following order: (1)>(2)>(4)>(3). Moreover, the average weight is positive in (1) but negative in (2), (3), and (4). Our findings indicate the existence of strong negative and small positive reciprocity for the average subject, but there is also high interpersonal variation in the weights in these four nodes. We conclude that the PD frame makes subjects more competitive than the DG frame. Using hierarchical Bayesian modeling, we simultaneously analyze beliefs of subjects about others' utility weights in the same four decision situations. We compare several alternative theoretical models on beliefs, e.g., rational beliefs (Bayesian-Nash equilibrium) and a consensus model. Our results on beliefs strongly support the consensus effect and refute rational beliefs: there is a strong relationship between own preferences and beliefs and this relationship is relatively stable across the four decision situations. Copyright © 2014 Elsevier Inc. All rights reserved.

Hierarchical prediction errors in midbrain and basal forebrain during sensory learning.

Science.gov (United States)

Iglesias, Sandra; Mathys, Christoph; Brodersen, Kay H; Kasper, Lars; Piccirelli, Marco; den Ouden, Hanneke E M; Stephan, Klaas E

2013-10-16

In Bayesian brain theories, hierarchically related prediction errors (PEs) play a central role for predicting sensory inputs and inferring their underlying causes, e.g., the probabilistic structure of the environment and its volatility. Notably, PEs at different hierarchical levels may be encoded by different neuromodulatory transmitters. Here, we tested this possibility in computational fMRI studies of audio-visual learning. Using a hierarchical Bayesian model, we found that low-level PEs about visual stimulus outcome were reflected by widespread activity in visual and supramodal areas but also in the midbrain. In contrast, high-level PEs about stimulus probabilities were encoded by the basal forebrain. These findings were replicated in two groups of healthy volunteers. While our fMRI measures do not reveal the exact neuron types activated in midbrain and basal forebrain, they suggest a dichotomy between neuromodulatory systems, linking dopamine to low-level PEs about stimulus outcome and acetylcholine to more abstract PEs about stimulus probabilities. Copyright © 2013 Elsevier Inc. All rights reserved.

Hierarchical Bayesian modelling of mobility metrics for hazard model input calibration

Science.gov (United States)

Calder, Eliza; Ogburn, Sarah; Spiller, Elaine; Rutarindwa, Regis; Berger, Jim

2015-04-01

In this work we present a method to constrain flow mobility input parameters for pyroclastic flow models using hierarchical Bayes modeling of standard mobility metrics such as H/L and flow volume etc. The advantage of hierarchical modeling is that it can leverage the information in global dataset for a particular mobility metric in order to reduce the uncertainty in modeling of an individual volcano, especially important where individual volcanoes have only sparse datasets. We use compiled pyroclastic flow runout data from Colima, Merapi, Soufriere Hills, Unzen and Semeru volcanoes, presented in an open-source database FlowDat (https://vhub.org/groups/massflowdatabase). While the exact relationship between flow volume and friction varies somewhat between volcanoes, dome collapse flows originating from the same volcano exhibit similar mobility relationships. Instead of fitting separate regression models for each volcano dataset, we use a variation of the hierarchical linear model (Kass and Steffey, 1989). The model presents a hierarchical structure with two levels; all dome collapse flows and dome collapse flows at specific volcanoes. The hierarchical model allows us to assume that the flows at specific volcanoes share a common distribution of regression slopes, then solves for that distribution. We present comparisons of the 95% confidence intervals on the individual regression lines for the data set from each volcano as well as those obtained from the hierarchical model. The results clearly demonstrate the advantage of considering global datasets using this technique. The technique developed is demonstrated here for mobility metrics, but can be applied to many other global datasets of volcanic parameters. In particular, such methods can provide a means to better contain parameters for volcanoes for which we only have sparse data, a ubiquitous problem in volcanology.

Sparse reconstruction using distribution agnostic bayesian matching pursuit

KAUST Repository

Masood, Mudassir; Al-Naffouri, Tareq Y.

2013-01-01

A fast matching pursuit method using a Bayesian approach is introduced for sparse signal recovery. This method performs Bayesian estimates of sparse signals even when the signal prior is non-Gaussian or unknown. It is agnostic on signal statistics

Bayesian modeling of ChIP-chip data using latent variables.

KAUST Repository

Wu, Mingqi

2009-10-26

BACKGROUND: The ChIP-chip technology has been used in a wide range of biomedical studies, such as identification of human transcription factor binding sites, investigation of DNA methylation, and investigation of histone modifications in animals and plants. Various methods have been proposed in the literature for analyzing the ChIP-chip data, such as the sliding window methods, the hidden Markov model-based methods, and Bayesian methods. Although, due to the integrated consideration of uncertainty of the models and model parameters, Bayesian methods can potentially work better than the other two classes of methods, the existing Bayesian methods do not perform satisfactorily. They usually require multiple replicates or some extra experimental information to parametrize the model, and long CPU time due to involving of MCMC simulations. RESULTS: In this paper, we propose a Bayesian latent model for the ChIP-chip data. The new model mainly differs from the existing Bayesian models, such as the joint deconvolution model, the hierarchical gamma mixture model, and the Bayesian hierarchical model, in two respects. Firstly, it works on the difference between the averaged treatment and control samples. This enables the use of a simple model for the data, which avoids the probe-specific effect and the sample (control/treatment) effect. As a consequence, this enables an efficient MCMC simulation of the posterior distribution of the model, and also makes the model more robust to the outliers. Secondly, it models the neighboring dependence of probes by introducing a latent indicator vector. A truncated Poisson prior distribution is assumed for the latent indicator variable, with the rationale being justified at length. CONCLUSION: The Bayesian latent method is successfully applied to real and ten simulated datasets, with comparisons with some of the existing Bayesian methods, hidden Markov model methods, and sliding window methods. The numerical results indicate that the

Bayesian Inference Methods for Sparse Channel Estimation

DEFF Research Database (Denmark)

Pedersen, Niels Lovmand

2013-01-01

This thesis deals with sparse Bayesian learning (SBL) with application to radio channel estimation. As opposed to the classical approach for sparse signal representation, we focus on the problem of inferring complex signals. Our investigations within SBL constitute the basis for the development...... of Bayesian inference algorithms for sparse channel estimation. Sparse inference methods aim at finding the sparse representation of a signal given in some overcomplete dictionary of basis vectors. Within this context, one of our main contributions to the field of SBL is a hierarchical representation...... analysis of the complex prior representation, where we show that the ability to induce sparse estimates of a given prior heavily depends on the inference method used and, interestingly, whether real or complex variables are inferred. We also show that the Bayesian estimators derived from the proposed...

A Bayesian hierarchical model with novel prior specifications for estimating HIV testing rates.

Science.gov (United States)

An, Qian; Kang, Jian; Song, Ruiguang; Hall, H Irene

2016-04-30

Human immunodeficiency virus (HIV) infection is a severe infectious disease actively spreading globally, and acquired immunodeficiency syndrome (AIDS) is an advanced stage of HIV infection. The HIV testing rate, that is, the probability that an AIDS-free HIV infected person seeks a test for HIV during a particular time interval, given no previous positive test has been obtained prior to the start of the time, is an important parameter for public health. In this paper, we propose a Bayesian hierarchical model with two levels of hierarchy to estimate the HIV testing rate using annual AIDS and AIDS-free HIV diagnoses data. At level one, we model the latent number of HIV infections for each year using a Poisson distribution with the intensity parameter representing the HIV incidence rate. At level two, the annual numbers of AIDS and AIDS-free HIV diagnosed cases and all undiagnosed cases stratified by the HIV infections at different years are modeled using a multinomial distribution with parameters including the HIV testing rate. We propose a new class of priors for the HIV incidence rate and HIV testing rate taking into account the temporal dependence of these parameters to improve the estimation accuracy. We develop an efficient posterior computation algorithm based on the adaptive rejection metropolis sampling technique. We demonstrate our model using simulation studies and the analysis of the national HIV surveillance data in the USA. Copyright © 2015 John Wiley & Sons, Ltd.

A fast combination method in DSmT and its application to recommender system.

Directory of Open Access Journals (Sweden)

Yilin Dong

Full Text Available In many applications involving epistemic uncertainties usually modeled by belief functions, it is often necessary to approximate general (non-Bayesian basic belief assignments (BBAs to subjective probabilities (called Bayesian BBAs. This necessity occurs if one needs to embed the fusion result in a system based on the probabilistic framework and Bayesian inference (e.g. tracking systems, or if one needs to make a decision in the decision making problems. In this paper, we present a new fast combination method, called modified rigid coarsening (MRC, to obtain the final Bayesian BBAs based on hierarchical decomposition (coarsening of the frame of discernment. Regarding this method, focal elements with probabilities are coarsened efficiently to reduce computational complexity in the process of combination by using disagreement vector and a simple dichotomous approach. In order to prove the practicality of our approach, this new approach is applied to combine users' soft preferences in recommender systems (RSs. Additionally, in order to make a comprehensive performance comparison, the proportional conflict redistribution rule #6 (PCR6 is regarded as a baseline in a range of experiments. According to the results of experiments, MRC is more effective in accuracy of recommendations compared to original Rigid Coarsening (RC method and comparable in computational time.

A fast combination method in DSmT and its application to recommender system.

Science.gov (United States)

Dong, Yilin; Li, Xinde; Liu, Yihai

2018-01-01

In many applications involving epistemic uncertainties usually modeled by belief functions, it is often necessary to approximate general (non-Bayesian) basic belief assignments (BBAs) to subjective probabilities (called Bayesian BBAs). This necessity occurs if one needs to embed the fusion result in a system based on the probabilistic framework and Bayesian inference (e.g. tracking systems), or if one needs to make a decision in the decision making problems. In this paper, we present a new fast combination method, called modified rigid coarsening (MRC), to obtain the final Bayesian BBAs based on hierarchical decomposition (coarsening) of the frame of discernment. Regarding this method, focal elements with probabilities are coarsened efficiently to reduce computational complexity in the process of combination by using disagreement vector and a simple dichotomous approach. In order to prove the practicality of our approach, this new approach is applied to combine users' soft preferences in recommender systems (RSs). Additionally, in order to make a comprehensive performance comparison, the proportional conflict redistribution rule #6 (PCR6) is regarded as a baseline in a range of experiments. According to the results of experiments, MRC is more effective in accuracy of recommendations compared to original Rigid Coarsening (RC) method and comparable in computational time.

Estimating the Term Structure With a Semiparametric Bayesian Hierarchical Model: An Application to Corporate Bonds1

Science.gov (United States)

Cruz-Marcelo, Alejandro; Ensor, Katherine B.; Rosner, Gary L.

2011-01-01

The term structure of interest rates is used to price defaultable bonds and credit derivatives, as well as to infer the quality of bonds for risk management purposes. We introduce a model that jointly estimates term structures by means of a Bayesian hierarchical model with a prior probability model based on Dirichlet process mixtures. The modeling methodology borrows strength across term structures for purposes of estimation. The main advantage of our framework is its ability to produce reliable estimators at the company level even when there are only a few bonds per company. After describing the proposed model, we discuss an empirical application in which the term structure of 197 individual companies is estimated. The sample of 197 consists of 143 companies with only one or two bonds. In-sample and out-of-sample tests are used to quantify the improvement in accuracy that results from approximating the term structure of corporate bonds with estimators by company rather than by credit rating, the latter being a popular choice in the financial literature. A complete description of a Markov chain Monte Carlo (MCMC) scheme for the proposed model is available as Supplementary Material. PMID:21765566

Bayesian 3D X-ray computed tomography image reconstruction with a scaled Gaussian mixture prior model

International Nuclear Information System (INIS)

Wang, Li; Gac, Nicolas; Mohammad-Djafari, Ali

2015-01-01

In order to improve quality of 3D X-ray tomography reconstruction for Non Destructive Testing (NDT), we investigate in this paper hierarchical Bayesian methods. In NDT, useful prior information on the volume like the limited number of materials or the presence of homogeneous area can be included in the iterative reconstruction algorithms. In hierarchical Bayesian methods, not only the volume is estimated thanks to the prior model of the volume but also the hyper parameters of this prior. This additional complexity in the reconstruction methods when applied to large volumes (from 512 3 to 8192 3 voxels) results in an increasing computational cost. To reduce it, the hierarchical Bayesian methods investigated in this paper lead to an algorithm acceleration by Variational Bayesian Approximation (VBA) [1] and hardware acceleration thanks to projection and back-projection operators paralleled on many core processors like GPU [2]. In this paper, we will consider a Student-t prior on the gradient of the image implemented in a hierarchical way [3, 4, 1]. Operators H (forward or projection) and H t (adjoint or back-projection) implanted in multi-GPU [2] have been used in this study. Different methods will be evalued on synthetic volume 'Shepp and Logan' in terms of quality and time of reconstruction. We used several simple regularizations of order 1 and order 2. Other prior models also exists [5]. Sometimes for a discrete image, we can do the segmentation and reconstruction at the same time, then the reconstruction can be done with less projections

What are hierarchical models and how do we analyze them?

Science.gov (United States)

Royle, Andy

2016-01-01

In this chapter we provide a basic definition of hierarchical models and introduce the two canonical hierarchical models in this book: site occupancy and N-mixture models. The former is a hierarchical extension of logistic regression and the latter is a hierarchical extension of Poisson regression. We introduce basic concepts of probability modeling and statistical inference including likelihood and Bayesian perspectives. We go through the mechanics of maximizing the likelihood and characterizing the posterior distribution by Markov chain Monte Carlo (MCMC) methods. We give a general perspective on topics such as model selection and assessment of model fit, although we demonstrate these topics in practice in later chapters (especially Chapters 5, 6, 7, and 10 Chapter 5 Chapter 6 Chapter 7 Chapter 10)

Compromise decision support problems for hierarchical design involving uncertainty

Science.gov (United States)

Vadde, S.; Allen, J. K.; Mistree, F.

1994-08-01

In this paper an extension to the traditional compromise Decision Support Problem (DSP) formulation is presented. Bayesian statistics is used in the formulation to model uncertainties associated with the information being used. In an earlier paper a compromise DSP that accounts for uncertainty using fuzzy set theory was introduced. The Bayesian Decision Support Problem is described in this paper. The method for hierarchical design is demonstrated by using this formulation to design a portal frame. The results are discussed and comparisons are made with those obtained using the fuzzy DSP. Finally, the efficacy of incorporating Bayesian statistics into the traditional compromise DSP formulation is discussed and some pending research issues are described. Our emphasis in this paper is on the method rather than the results per se.

Noncausal Bayesian Vector Autoregression

DEFF Research Database (Denmark)

Lanne, Markku; Luoto, Jani

We propose a Bayesian inferential procedure for the noncausal vector autoregressive (VAR) model that is capable of capturing nonlinearities and incorporating effects of missing variables. In particular, we devise a fast and reliable posterior simulator that yields the predictive distribution...

A Bayesian Panel Data Approach to Explaining Market Beta Dynamics

NARCIS (Netherlands)

R. Bauer (Rob); M.M.J.E. Cosemans (Mathijs); R. Frehen (Rik); P.C. Schotman (Peter)

2008-01-01

markdownabstractWe characterize the process that drives the market betas of individual stocks by setting up a hierarchical Bayesian panel data model that allows a flexible specification for beta. We show that combining the parametric relationship between betas and conditioning variables specified by

Subjective value of risky foods for individual domestic chicks: a hierarchical Bayesian model.

Science.gov (United States)

Kawamori, Ai; Matsushima, Toshiya

2010-05-01

For animals to decide which prey to attack, the gain and delay of the food item must be integrated in a value function. However, the subjective value is not obtained by expected profitability when it is accompanied by risk. To estimate the subjective value, we examined choices in a cross-shaped maze with two colored feeders in domestic chicks. When tested by a reversal in food amount or delay, chicks changed choices similarly in both conditions (experiment 1). We therefore examined risk sensitivity for amount and delay (experiment 2) by supplying one feeder with food of fixed profitability and the alternative feeder with high- or low-profitability food at equal probability. Profitability varied in amount (groups 1 and 2 at high and low variance) or in delay (group 3). To find the equilibrium, the amount (groups 1 and 2) or delay (group 3) of the food in the fixed feeder was adjusted in a total of 18 blocks. The Markov chain Monte Carlo method was applied to a hierarchical Bayesian model to estimate the subjective value. Chicks undervalued the variable feeder in group 1 and were indifferent in group 2 but overvalued the variable feeder in group 3 at a population level. Re-examination without the titration procedure (experiment 3) suggested that the subjective value was not absolute for each option. When the delay was varied, the variable option was often given a paradoxically high value depending on fixed alternative. Therefore, the basic assumption of the uniquely determined value function might be questioned.

Fast Bayesian optimal experimental design and its applications

KAUST Repository

Long, Quan

2015-01-01

We summarize our Laplace method and multilevel method of accelerating the computation of the expected information gain in a Bayesian Optimal Experimental Design (OED). Laplace method is a widely-used method to approximate an integration

Predicting protein subcellular locations using hierarchical ensemble of Bayesian classifiers based on Markov chains

Directory of Open Access Journals (Sweden)

Eils Roland

2006-06-01

Full Text Available Abstract Background The subcellular location of a protein is closely related to its function. It would be worthwhile to develop a method to predict the subcellular location for a given protein when only the amino acid sequence of the protein is known. Although many efforts have been made to predict subcellular location from sequence information only, there is the need for further research to improve the accuracy of prediction. Results A novel method called HensBC is introduced to predict protein subcellular location. HensBC is a recursive algorithm which constructs a hierarchical ensemble of classifiers. The classifiers used are Bayesian classifiers based on Markov chain models. We tested our method on six various datasets; among them are Gram-negative bacteria dataset, data for discriminating outer membrane proteins and apoptosis proteins dataset. We observed that our method can predict the subcellular location with high accuracy. Another advantage of the proposed method is that it can improve the accuracy of the prediction of some classes with few sequences in training and is therefore useful for datasets with imbalanced distribution of classes. Conclusion This study introduces an algorithm which uses only the primary sequence of a protein to predict its subcellular location. The proposed recursive scheme represents an interesting methodology for learning and combining classifiers. The method is computationally efficient and competitive with the previously reported approaches in terms of prediction accuracies as empirical results indicate. The code for the software is available upon request.

Introduction to applied Bayesian statistics and estimation for social scientists

CERN Document Server

Lynch, Scott M

2007-01-01

""Introduction to Applied Bayesian Statistics and Estimation for Social Scientists"" covers the complete process of Bayesian statistical analysis in great detail from the development of a model through the process of making statistical inference. The key feature of this book is that it covers models that are most commonly used in social science research - including the linear regression model, generalized linear models, hierarchical models, and multivariate regression models - and it thoroughly develops each real-data example in painstaking detail.The first part of the book provides a detailed

Bayesian Modeling of ChIP-chip Data Through a High-Order Ising Model

KAUST Repository

Mo, Qianxing

2010-01-29

ChIP-chip experiments are procedures that combine chromatin immunoprecipitation (ChIP) and DNA microarray (chip) technology to study a variety of biological problems, including protein-DNA interaction, histone modification, and DNA methylation. The most important feature of ChIP-chip data is that the intensity measurements of probes are spatially correlated because the DNA fragments are hybridized to neighboring probes in the experiments. We propose a simple, but powerful Bayesian hierarchical approach to ChIP-chip data through an Ising model with high-order interactions. The proposed method naturally takes into account the intrinsic spatial structure of the data and can be used to analyze data from multiple platforms with different genomic resolutions. The model parameters are estimated using the Gibbs sampler. The proposed method is illustrated using two publicly available data sets from Affymetrix and Agilent platforms, and compared with three alternative Bayesian methods, namely, Bayesian hierarchical model, hierarchical gamma mixture model, and Tilemap hidden Markov model. The numerical results indicate that the proposed method performs as well as the other three methods for the data from Affymetrix tiling arrays, but significantly outperforms the other three methods for the data from Agilent promoter arrays. In addition, we find that the proposed method has better operating characteristics in terms of sensitivities and false discovery rates under various scenarios. © 2010, The International Biometric Society.

Application of Bayesian networks in a hierarchical structure for environmental risk assessment: a case study of the Gabric Dam, Iran.

Science.gov (United States)

Malekmohammadi, Bahram; Tayebzadeh Moghadam, Negar

2018-04-13

Environmental risk assessment (ERA) is a commonly used, effective tool applied to reduce adverse effects of environmental risk factors. In this study, ERA was investigated using the Bayesian network (BN) model based on a hierarchical structure of variables in an influence diagram (ID). ID facilitated ranking of the different alternatives under uncertainty that were then used to evaluate comparisons of the different risk factors. BN was used to present a new model for ERA applicable to complicated development projects such as dam construction. The methodology was applied to the Gabric Dam, in southern Iran. The main environmental risk factors in the region, presented by the Gabric Dam, were identified based on the Delphi technique and specific features of the study area. These included the following: flood, water pollution, earthquake, changes in land use, erosion and sedimentation, effects on the population, and ecosensitivity. These risk factors were then categorized based on results from the output decision node of the BN, including expected utility values for risk factors in the decision node. ERA was performed for the Gabric Dam using the analytical hierarchy process (AHP) method to compare results of BN modeling with those of conventional methods. Results determined that a BN-based hierarchical structure to ERA present acceptable and reasonable risk assessment prioritization in proposing suitable solutions to reduce environmental risks and can be used as a powerful decision support system for evaluating environmental risks.

Hierarchically Macroporous Graphitic Nanowebs Exhibiting Ultra-fast and Stable Charge Storage Performance

Science.gov (United States)

Yun, Young Soo

2018-02-01

The macro/microstructures of carbon-based electrode materials for supercapacitor applications play a key role in their electrochemical performance. In this study, hierarchically macroporous graphitic nanowebs (HM-GNWs) were prepared from bacterial cellulose by high-temperature heating at 2400 °C. The HM-GNWs were composed of well-developed graphitic nanobuilding blocks with a high aspect ratio, which was entangled as a nanoweb structure. The morphological and microstructural characteristics of the HM-GNWs resulted in remarkable charge storage performance. In particular, the HM-GNWs exhibited very fast charge storage behaviors at scan rates ranging from 5 to 100 V s-1, in which area capacitances ranging from 8.9 to 3.8 mF cm-2 were achieved. In addition, 97% capacitance retention was observed after long-term cycling for more than 1,000,000 cycles.

Multiview Bayesian Correlated Component Analysis

DEFF Research Database (Denmark)

Kamronn, Simon Due; Poulsen, Andreas Trier; Hansen, Lars Kai

2015-01-01

are identical. Here we propose a hierarchical probabilistic model that can infer the level of universality in such multiview data, from completely unrelated representations, corresponding to canonical correlation analysis, to identical representations as in correlated component analysis. This new model, which...... we denote Bayesian correlated component analysis, evaluates favorably against three relevant algorithms in simulated data. A well-established benchmark EEG data set is used to further validate the new model and infer the variability of spatial representations across multiple subjects....

Multinomial Bayesian learning for modeling classical and nonclassical receptive field properties.

Science.gov (United States)

Hosoya, Haruo

2012-08-01

We study the interplay of Bayesian inference and natural image learning in a hierarchical vision system, in relation to the response properties of early visual cortex. We particularly focus on a Bayesian network with multinomial variables that can represent discrete feature spaces similar to hypercolumns combining minicolumns, enforce sparsity of activation to learn efficient representations, and explain divisive normalization. We demonstrate that maximal-likelihood learning using sampling-based Bayesian inference gives rise to classical receptive field properties similar to V1 simple cells and V2 cells, while inference performed on the trained network yields nonclassical context-dependent response properties such as cross-orientation suppression and filling in. Comparison with known physiological properties reveals some qualitative and quantitative similarities.

Progress on Bayesian Inference of the Fast Ion Distribution Function

DEFF Research Database (Denmark)

Stagner, L.; Heidbrink, W.W,; Chen, X.

2013-01-01

. However, when theory and experiment disagree (for one or more diagnostics), it is unclear how to proceed. Bayesian statistics provides a framework to infer the DF, quantify errors, and reconcile discrepant diagnostic measurements. Diagnostic errors and weight functions that describe the phase space...... sensitivity of the measurements are incorporated into Bayesian likelihood probabilities. Prior probabilities describe physical constraints. This poster will show reconstructions of classically described, low-power, MHD-quiescent distribution functions from actual FIDA measurements. A description of the full...

A hierarchical method for Bayesian inference of rate parameters from shock tube data: Application to the study of the reaction of hydroxyl with 2-methylfuran

KAUST Repository

Kim, Daesang

2017-06-22

We developed a novel two-step hierarchical method for the Bayesian inference of the rate parameters of a target reaction from time-resolved concentration measurements in shock tubes. The method was applied to the calibration of the parameters of the reaction of hydroxyl with 2-methylfuran, which is studied experimentally via absorption measurements of the OH radical\\'s concentration following shock-heating. In the first step of the approach, each shock tube experiment is treated independently to infer the posterior distribution of the rate constant and error hyper-parameter that best explains the OH signal. In the second step, these posterior distributions are sampled to calibrate the parameters appearing in the Arrhenius reaction model for the rate constant. Furthermore, the second step is modified and repeated in order to explore alternative rate constant models and to assess the effect of uncertainties in the reflected shock\\'s temperature. Comparisons of the estimates obtained via the proposed methodology against the common least squares approach are presented. The relative merits of the novel Bayesian framework are highlighted, especially with respect to the opportunity to utilize the posterior distributions of the parameters in future uncertainty quantification studies.

Bayesian statistics applied to neutron activation data for reactor flux spectrum analysis

International Nuclear Information System (INIS)

Chiesa, Davide; Previtali, Ezio; Sisti, Monica

2014-01-01

Highlights: • Bayesian statistics to analyze the neutron flux spectrum from activation data. • Rigorous statistical approach for accurate evaluation of the neutron flux groups. • Cross section and activation data uncertainties included for the problem solution. • Flexible methodology applied to analyze different nuclear reactor flux spectra. • The results are in good agreement with the MCNP simulations of neutron fluxes. - Abstract: In this paper, we present a statistical method, based on Bayesian statistics, to analyze the neutron flux spectrum from the activation data of different isotopes. The experimental data were acquired during a neutron activation experiment performed at the TRIGA Mark II reactor of Pavia University (Italy) in four irradiation positions characterized by different neutron spectra. In order to evaluate the neutron flux spectrum, subdivided in energy groups, a system of linear equations, containing the group effective cross sections and the activation rate data, has to be solved. However, since the system’s coefficients are experimental data affected by uncertainties, a rigorous statistical approach is fundamental for an accurate evaluation of the neutron flux groups. For this purpose, we applied the Bayesian statistical analysis, that allows to include the uncertainties of the coefficients and the a priori information about the neutron flux. A program for the analysis of Bayesian hierarchical models, based on Markov Chain Monte Carlo (MCMC) simulations, was used to define the problem statistical model and solve it. The first analysis involved the determination of the thermal, resonance-intermediate and fast flux components and the dependence of the results on the Prior distribution choice was investigated to confirm the reliability of the Bayesian analysis. After that, the main resonances of the activation cross sections were analyzed to implement multi-group models with finer energy subdivisions that would allow to determine the

Bayesian Group Bridge for Bi-level Variable Selection.

Science.gov (United States)

Mallick, Himel; Yi, Nengjun

2017-06-01

A Bayesian bi-level variable selection method (BAGB: Bayesian Analysis of Group Bridge) is developed for regularized regression and classification. This new development is motivated by grouped data, where generic variables can be divided into multiple groups, with variables in the same group being mechanistically related or statistically correlated. As an alternative to frequentist group variable selection methods, BAGB incorporates structural information among predictors through a group-wise shrinkage prior. Posterior computation proceeds via an efficient MCMC algorithm. In addition to the usual ease-of-interpretation of hierarchical linear models, the Bayesian formulation produces valid standard errors, a feature that is notably absent in the frequentist framework. Empirical evidence of the attractiveness of the method is illustrated by extensive Monte Carlo simulations and real data analysis. Finally, several extensions of this new approach are presented, providing a unified framework for bi-level variable selection in general models with flexible penalties.

Spatial Intensity Duration Frequency Relationships Using Hierarchical Bayesian Analysis for Urban Areas

Science.gov (United States)

Rupa, Chandra; Mujumdar, Pradeep

2016-04-01

In urban areas, quantification of extreme precipitation is important in the design of storm water drains and other infrastructure. Intensity Duration Frequency (IDF) relationships are generally used to obtain design return level for a given duration and return period. Due to lack of availability of extreme precipitation data for sufficiently large number of years, estimating the probability of extreme events is difficult. Typically, a single station data is used to obtain the design return levels for various durations and return periods, which are used in the design of urban infrastructure for the entire city. In an urban setting, the spatial variation of precipitation can be high; the precipitation amounts and patterns often vary within short distances of less than 5 km. Therefore it is crucial to study the uncertainties in the spatial variation of return levels for various durations. In this work, the extreme precipitation is modeled spatially using the Bayesian hierarchical analysis and the spatial variation of return levels is studied. The analysis is carried out with Block Maxima approach for defining the extreme precipitation, using Generalized Extreme Value (GEV) distribution for Bangalore city, Karnataka state, India. Daily data for nineteen stations in and around Bangalore city is considered in the study. The analysis is carried out for summer maxima (March - May), monsoon maxima (June - September) and the annual maxima rainfall. In the hierarchical analysis, the statistical model is specified in three layers. The data layer models the block maxima, pooling the extreme precipitation from all the stations. In the process layer, the latent spatial process characterized by geographical and climatological covariates (lat-lon, elevation, mean temperature etc.) which drives the extreme precipitation is modeled and in the prior level, the prior distributions that govern the latent process are modeled. Markov Chain Monte Carlo (MCMC) algorithm (Metropolis Hastings

Fast Bayesian optimal experimental design and its applications

KAUST Repository

Long, Quan

2015-01-07

We summarize our Laplace method and multilevel method of accelerating the computation of the expected information gain in a Bayesian Optimal Experimental Design (OED). Laplace method is a widely-used method to approximate an integration in statistics. We analyze this method in the context of optimal Bayesian experimental design and extend this method from the classical scenario, where a single dominant mode of the parameters can be completely-determined by the experiment, to the scenarios where a non-informative parametric manifold exists. We show that by carrying out this approximation the estimation of the expected Kullback-Leibler divergence can be significantly accelerated. While Laplace method requires a concentration of measure, multi-level Monte Carlo method can be used to tackle the problem when there is a lack of measure concentration. We show some initial results on this approach. The developed methodologies have been applied to various sensor deployment problems, e.g., impedance tomography and seismic source inversion.

Multi-subject hierarchical inverse covariance modelling improves estimation of functional brain networks.

Science.gov (United States)

Colclough, Giles L; Woolrich, Mark W; Harrison, Samuel J; Rojas López, Pedro A; Valdes-Sosa, Pedro A; Smith, Stephen M

2018-05-07

A Bayesian model for sparse, hierarchical inverse covariance estimation is presented, and applied to multi-subject functional connectivity estimation in the human brain. It enables simultaneous inference of the strength of connectivity between brain regions at both subject and population level, and is applicable to fmri, meg and eeg data. Two versions of the model can encourage sparse connectivity, either using continuous priors to suppress irrelevant connections, or using an explicit description of the network structure to estimate the connection probability between each pair of regions. A large evaluation of this model, and thirteen methods that represent the state of the art of inverse covariance modelling, is conducted using both simulated and resting-state functional imaging datasets. Our novel Bayesian approach has similar performance to the best extant alternative, Ng et al.'s Sparse Group Gaussian Graphical Model algorithm, which also is based on a hierarchical structure. Using data from the Human Connectome Project, we show that these hierarchical models are able to reduce the measurement error in meg beta-band functional networks by 10%, producing concomitant increases in estimates of the genetic influence on functional connectivity. Copyright © 2018. Published by Elsevier Inc.

Fast Bayesian optimal experimental design for seismic source inversion

KAUST Repository

Long, Quan

2015-07-01

We develop a fast method for optimally designing experiments in the context of statistical seismic source inversion. In particular, we efficiently compute the optimal number and locations of the receivers or seismographs. The seismic source is modeled by a point moment tensor multiplied by a time-dependent function. The parameters include the source location, moment tensor components, and start time and frequency in the time function. The forward problem is modeled by elastodynamic wave equations. We show that the Hessian of the cost functional, which is usually defined as the square of the weighted L2 norm of the difference between the experimental data and the simulated data, is proportional to the measurement time and the number of receivers. Consequently, the posterior distribution of the parameters, in a Bayesian setting, concentrates around the "true" parameters, and we can employ Laplace approximation and speed up the estimation of the expected Kullback-Leibler divergence (expected information gain), the optimality criterion in the experimental design procedure. Since the source parameters span several magnitudes, we use a scaling matrix for efficient control of the condition number of the original Hessian matrix. We use a second-order accurate finite difference method to compute the Hessian matrix and either sparse quadrature or Monte Carlo sampling to carry out numerical integration. We demonstrate the efficiency, accuracy, and applicability of our method on a two-dimensional seismic source inversion problem. © 2015 Elsevier B.V.

Fast Bayesian Optimal Experimental Design for Seismic Source Inversion

KAUST Repository

Long, Quan

2016-01-06

We develop a fast method for optimally designing experiments [1] in the context of statistical seismic source inversion [2]. In particular, we efficiently compute the optimal number and locations of the receivers or seismographs. The seismic source is modeled by a point moment tensor multiplied by a time-dependent function. The parameters include the source location, moment tensor components, and start time and frequency in the time function. The forward problem is modeled by the elastic wave equations. We show that the Hessian of the cost functional, which is usually defined as the square of the weighted L2 norm of the difference between the experimental data and the simulated data, is proportional to the measurement time and the number of receivers. Consequently, the posterior distribution of the parameters, in a Bayesian setting, concentrates around the true parameters, and we can employ Laplace approximation and speed up the estimation of the expected Kullback-Leibler divergence (expected information gain), the optimality criterion in the experimental design procedure. Since the source parameters span several magnitudes, we use a scaling matrix for efficient control of the condition number of the original Hessian matrix. We use a second-order accurate finite difference method to compute the Hessian matrix and either sparse quadrature or Monte Carlo sampling to carry out numerical integration. We demonstrate the efficiency, accuracy, and applicability of our method on a two-dimensional seismic source inversion problem.

Fast Bayesian Optimal Experimental Design for Seismic Source Inversion

KAUST Repository

Long, Quan; Motamed, Mohammad; Tempone, Raul

2016-01-01

We develop a fast method for optimally designing experiments [1] in the context of statistical seismic source inversion [2]. In particular, we efficiently compute the optimal number and locations of the receivers or seismographs. The seismic source is modeled by a point moment tensor multiplied by a time-dependent function. The parameters include the source location, moment tensor components, and start time and frequency in the time function. The forward problem is modeled by the elastic wave equations. We show that the Hessian of the cost functional, which is usually defined as the square of the weighted L2 norm of the difference between the experimental data and the simulated data, is proportional to the measurement time and the number of receivers. Consequently, the posterior distribution of the parameters, in a Bayesian setting, concentrates around the true parameters, and we can employ Laplace approximation and speed up the estimation of the expected Kullback-Leibler divergence (expected information gain), the optimality criterion in the experimental design procedure. Since the source parameters span several magnitudes, we use a scaling matrix for efficient control of the condition number of the original Hessian matrix. We use a second-order accurate finite difference method to compute the Hessian matrix and either sparse quadrature or Monte Carlo sampling to carry out numerical integration. We demonstrate the efficiency, accuracy, and applicability of our method on a two-dimensional seismic source inversion problem.

Bayesian models for astrophysical data using R, JAGS, Python, and Stan

CERN Document Server

Hilbe, Joseph M; Ishida, Emille E O

2017-01-01

This comprehensive guide to Bayesian methods in astronomy enables hands-on work by supplying complete R, JAGS, Python, and Stan code, to use directly or to adapt. It begins by examining the normal model from both frequentist and Bayesian perspectives and then progresses to a full range of Bayesian generalized linear and mixed or hierarchical models, as well as additional types of models such as ABC and INLA. The book provides code that is largely unavailable elsewhere and includes details on interpreting and evaluating Bayesian models. Initial discussions offer models in synthetic form so that readers can easily adapt them to their own data; later the models are applied to real astronomical data. The consistent focus is on hands-on modeling, analysis of data, and interpretations that address scientific questions. A must-have for astronomers, its concrete approach will also be attractive to researchers in the sciences more generally.

Relative age and birthplace effect in Japanese professional sports: a quantitative evaluation using a Bayesian hierarchical Poisson model.

Science.gov (United States)

Ishigami, Hideaki

2016-01-01

Relative age effect (RAE) in sports has been well documented. Recent studies investigate the effect of birthplace in addition to the RAE. The first objective of this study was to show the magnitude of the RAE in two major professional sports in Japan, baseball and soccer. Second, we examined the birthplace effect and compared its magnitude with that of the RAE. The effect sizes were estimated using a Bayesian hierarchical Poisson model with the number of players as dependent variable. The RAEs were 9.0% and 7.7% per month for soccer and baseball, respectively. These estimates imply that children born in the first month of a school year have about three times greater chance of becoming a professional player than those born in the last month of the year. Over half of the difference in likelihoods of becoming a professional player between birthplaces was accounted for by weather conditions, with the likelihood decreasing by 1% per snow day. An effect of population size was not detected in the data. By investigating different samples, we demonstrated that using quarterly data leads to underestimation and that the age range of sampled athletes should be set carefully.

Does mortality vary between Asian subgroups in New Zealand: an application of hierarchical Bayesian modelling.

Directory of Open Access Journals (Sweden)

Santosh Jatrana

Full Text Available The aim of this paper was to see whether all-cause and cause-specific mortality rates vary between Asian ethnic subgroups, and whether overseas born Asian subgroup mortality rate ratios varied by nativity and duration of residence. We used hierarchical Bayesian methods to allow for sparse data in the analysis of linked census-mortality data for 25-75 year old New Zealanders. We found directly standardised posterior all-cause and cardiovascular mortality rates were highest for the Indian ethnic group, significantly so when compared with those of Chinese ethnicity. In contrast, cancer mortality rates were lowest for ethnic Indians. Asian overseas born subgroups have about 70% of the mortality rate of their New Zealand born Asian counterparts, a result that showed little variation by Asian subgroup or cause of death. Within the overseas born population, all-cause mortality rates for migrants living 0-9 years in New Zealand were about 60% of the mortality rate of those living more than 25 years in New Zealand regardless of ethnicity. The corresponding figure for cardiovascular mortality rates was 50%. However, while Chinese cancer mortality rates increased with duration of residence, Indian and Other Asian cancer mortality rates did not. Future research on the mechanisms of worsening of health with increased time spent in the host country is required to improve the understanding of the process, and would assist the policy-makers and health planners.

Comparison of Extreme Precipitation Return Levels using Spatial Bayesian Hierarchical Modeling versus Regional Frequency Analysis

Science.gov (United States)

Love, C. A.; Skahill, B. E.; AghaKouchak, A.; Karlovits, G. S.; England, J. F.; Duren, A. M.

2017-12-01

We compare gridded extreme precipitation return levels obtained using spatial Bayesian hierarchical modeling (BHM) with their respective counterparts from a traditional regional frequency analysis (RFA) using the same set of extreme precipitation data. Our study area is the 11,478 square mile Willamette River basin (WRB) located in northwestern Oregon, a major tributary of the Columbia River whose 187 miles long main stem, the Willamette River, flows northward between the Coastal and Cascade Ranges. The WRB contains approximately two ­thirds of Oregon's population and 20 of the 25 most populous cities in the state. The U.S. Army Corps of Engineers (USACE) Portland District operates thirteen dams and extreme precipitation estimates are required to support risk­ informed hydrologic analyses as part of the USACE Dam Safety Program. Our intent is to profile for the USACE an alternate methodology to an RFA that was developed in 2008 due to the lack of an official NOAA Atlas 14 update for the state of Oregon. We analyze 24-hour annual precipitation maxima data for the WRB utilizing the spatial BHM R package "spatial.gev.bma", which has been shown to be efficient in developing coherent maps of extreme precipitation by return level. Our BHM modeling analysis involved application of leave-one-out cross validation (LOO-CV), which not only supported model selection but also a comprehensive assessment of location specific model performance. The LOO-CV results will provide a basis for the BHM RFA comparison.

A multi-level hierarchic Markov process with Bayesian updating for herd optimization and simulation in dairy cattle.

Science.gov (United States)

Demeter, R M; Kristensen, A R; Dijkstra, J; Oude Lansink, A G J M; Meuwissen, M P M; van Arendonk, J A M

2011-12-01

Herd optimization models that determine economically optimal insemination and replacement decisions are valuable research tools to study various aspects of farming systems. The aim of this study was to develop a herd optimization and simulation model for dairy cattle. The model determines economically optimal insemination and replacement decisions for individual cows and simulates whole-herd results that follow from optimal decisions. The optimization problem was formulated as a multi-level hierarchic Markov process, and a state space model with Bayesian updating was applied to model variation in milk yield. Methodological developments were incorporated in 2 main aspects. First, we introduced an additional level to the model hierarchy to obtain a more tractable and efficient structure. Second, we included a recently developed cattle feed intake model. In addition to methodological developments, new parameters were used in the state space model and other biological functions. Results were generated for Dutch farming conditions, and outcomes were in line with actual herd performance in the Netherlands. Optimal culling decisions were sensitive to variation in milk yield but insensitive to energy requirements for maintenance and feed intake capacity. We anticipate that the model will be applied in research and extension. Copyright © 2011 American Dairy Science Association. Published by Elsevier Inc. All rights reserved.

Fast Bayesian optimal experimental design for seismic source inversion

KAUST Repository

Long, Quan; Motamed, Mohammad; Tempone, Raul

2015-01-01

of receivers. Consequently, the posterior distribution of the parameters, in a Bayesian setting, concentrates around the "true" parameters, and we can employ Laplace approximation and speed up the estimation of the expected Kullback-Leibler divergence (expected

Sparse Estimation Using Bayesian Hierarchical Prior Modeling for Real and Complex Linear Models

DEFF Research Database (Denmark)

Pedersen, Niels Lovmand; Manchón, Carles Navarro; Badiu, Mihai Alin

2015-01-01

In sparse Bayesian learning (SBL), Gaussian scale mixtures (GSMs) have been used to model sparsity-inducing priors that realize a class of concave penalty functions for the regression task in real-valued signal models. Motivated by the relative scarcity of formal tools for SBL in complex-valued m......In sparse Bayesian learning (SBL), Gaussian scale mixtures (GSMs) have been used to model sparsity-inducing priors that realize a class of concave penalty functions for the regression task in real-valued signal models. Motivated by the relative scarcity of formal tools for SBL in complex...... error, and robustness in low and medium signal-to-noise ratio regimes....

BAYESIAN INFERENCE OF CMB GRAVITATIONAL LENSING

Energy Technology Data Exchange (ETDEWEB)

Anderes, Ethan [Department of Statistics, University of California, Davis, CA 95616 (United States); Wandelt, Benjamin D.; Lavaux, Guilhem [Sorbonne Universités, UPMC Univ Paris 06 and CNRS, UMR7095, Institut d’Astrophysique de Paris, F-75014, Paris (France)

2015-08-01

The Planck satellite, along with several ground-based telescopes, has mapped the cosmic microwave background (CMB) at sufficient resolution and signal-to-noise so as to allow a detection of the subtle distortions due to the gravitational influence of the intervening matter distribution. A natural modeling approach is to write a Bayesian hierarchical model for the lensed CMB in terms of the unlensed CMB and the lensing potential. So far there has been no feasible algorithm for inferring the posterior distribution of the lensing potential from the lensed CMB map. We propose a solution that allows efficient Markov Chain Monte Carlo sampling from the joint posterior of the lensing potential and the unlensed CMB map using the Hamiltonian Monte Carlo technique. The main conceptual step in the solution is a re-parameterization of CMB lensing in terms of the lensed CMB and the “inverse lensing” potential. We demonstrate a fast implementation on simulated data, including noise and a sky cut, that uses a further acceleration based on a very mild approximation of the inverse lensing potential. We find that the resulting Markov Chain has short correlation lengths and excellent convergence properties, making it promising for applications to high-resolution CMB data sets in the future.

Multi-level Bayesian analyses for single- and multi-vehicle freeway crashes.

Science.gov (United States)

Yu, Rongjie; Abdel-Aty, Mohamed

2013-09-01

This study presents multi-level analyses for single- and multi-vehicle crashes on a mountainous freeway. Data from a 15-mile mountainous freeway section on I-70 were investigated. Both aggregate and disaggregate models for the two crash conditions were developed. Five years of crash data were used in the aggregate investigation, while the disaggregate models utilized one year of crash data along with real-time traffic and weather data. For the aggregate analyses, safety performance functions were developed for the purpose of revealing the contributing factors for each crash type. Two methodologies, a Bayesian bivariate Poisson-lognormal model and a Bayesian hierarchical Poisson model with correlated random effects, were estimated to simultaneously analyze the two crash conditions with consideration of possible correlations. Except for the factors related to geometric characteristics, two exposure parameters (annual average daily traffic and segment length) were included. Two different sets of significant explanatory and exposure variables were identified for the single-vehicle (SV) and multi-vehicle (MV) crashes. It was found that the Bayesian bivariate Poisson-lognormal model is superior to the Bayesian hierarchical Poisson model, the former with a substantially lower DIC and more significant variables. In addition to the aggregate analyses, microscopic real-time crash risk evaluation models were developed for the two crash conditions. Multi-level Bayesian logistic regression models were estimated with the random parameters accounting for seasonal variations, crash-unit-level diversity and segment-level random effects capturing unobserved heterogeneity caused by the geometric characteristics. The model results indicate that the effects of the selected variables on crash occurrence vary across seasons and crash units; and that geometric characteristic variables contribute to the segment variations: the more unobserved heterogeneity have been accounted, the better

A Bayesian Double Fusion Model for Resting-State Brain Connectivity Using Joint Functional and Structural Data

KAUST Repository

Kang, Hakmook; Ombao, Hernando; Fonnesbeck, Christopher; Ding, Zhaohua; Morgan, Victoria L.

2017-01-01

DTI that could potentially enhance estimation of resting-state functional connectivity (FC) between brain regions. To overcome this limitation, we develop a Bayesian hierarchical spatiotemporal model that incorporates structural connectivity (SC

Discriminative Bayesian Dictionary Learning for Classification.

Science.gov (United States)

Akhtar, Naveed; Shafait, Faisal; Mian, Ajmal

2016-12-01

We propose a Bayesian approach to learn discriminative dictionaries for sparse representation of data. The proposed approach infers probability distributions over the atoms of a discriminative dictionary using a finite approximation of Beta Process. It also computes sets of Bernoulli distributions that associate class labels to the learned dictionary atoms. This association signifies the selection probabilities of the dictionary atoms in the expansion of class-specific data. Furthermore, the non-parametric character of the proposed approach allows it to infer the correct size of the dictionary. We exploit the aforementioned Bernoulli distributions in separately learning a linear classifier. The classifier uses the same hierarchical Bayesian model as the dictionary, which we present along the analytical inference solution for Gibbs sampling. For classification, a test instance is first sparsely encoded over the learned dictionary and the codes are fed to the classifier. We performed experiments for face and action recognition; and object and scene-category classification using five public datasets and compared the results with state-of-the-art discriminative sparse representation approaches. Experiments show that the proposed Bayesian approach consistently outperforms the existing approaches.

An efficient Bayesian inference approach to inverse problems based on an adaptive sparse grid collocation method

International Nuclear Information System (INIS)

Ma Xiang; Zabaras, Nicholas

2009-01-01

A new approach to modeling inverse problems using a Bayesian inference method is introduced. The Bayesian approach considers the unknown parameters as random variables and seeks the probabilistic distribution of the unknowns. By introducing the concept of the stochastic prior state space to the Bayesian formulation, we reformulate the deterministic forward problem as a stochastic one. The adaptive hierarchical sparse grid collocation (ASGC) method is used for constructing an interpolant to the solution of the forward model in this prior space which is large enough to capture all the variability/uncertainty in the posterior distribution of the unknown parameters. This solution can be considered as a function of the random unknowns and serves as a stochastic surrogate model for the likelihood calculation. Hierarchical Bayesian formulation is used to derive the posterior probability density function (PPDF). The spatial model is represented as a convolution of a smooth kernel and a Markov random field. The state space of the PPDF is explored using Markov chain Monte Carlo algorithms to obtain statistics of the unknowns. The likelihood calculation is performed by directly sampling the approximate stochastic solution obtained through the ASGC method. The technique is assessed on two nonlinear inverse problems: source inversion and permeability estimation in flow through porous media

Analysis of the Spatial Variation of Network-Constrained Phenomena Represented by a Link Attribute Using a Hierarchical Bayesian Model

Directory of Open Access Journals (Sweden)

Zhensheng Wang

2017-02-01

Full Text Available The spatial variation of geographical phenomena is a classical problem in spatial data analysis and can provide insight into underlying processes. Traditional exploratory methods mostly depend on the planar distance assumption, but many spatial phenomena are constrained to a subset of Euclidean space. In this study, we apply a method based on a hierarchical Bayesian model to analyse the spatial variation of network-constrained phenomena represented by a link attribute in conjunction with two experiments based on a simplified hypothetical network and a complex road network in Shenzhen that includes 4212 urban facility points of interest (POIs for leisure activities. Then, the methods named local indicators of network-constrained clusters (LINCS are applied to explore local spatial patterns in the given network space. The proposed method is designed for phenomena that are represented by attribute values of network links and is capable of removing part of random variability resulting from small-sample estimation. The effects of spatial dependence and the base distribution are also considered in the proposed method, which could be applied in the fields of urban planning and safety research.

Optimizing an estuarine water quality monitoring program through an entropy-based hierarchical spatiotemporal Bayesian framework

Science.gov (United States)

Alameddine, Ibrahim; Karmakar, Subhankar; Qian, Song S.; Paerl, Hans W.; Reckhow, Kenneth H.

2013-10-01

The total maximum daily load program aims to monitor more than 40,000 standard violations in around 20,000 impaired water bodies across the United States. Given resource limitations, future monitoring efforts have to be hedged against the uncertainties in the monitored system, while taking into account existing knowledge. In that respect, we have developed a hierarchical spatiotemporal Bayesian model that can be used to optimize an existing monitoring network by retaining stations that provide the maximum amount of information, while identifying locations that would benefit from the addition of new stations. The model assumes the water quality parameters are adequately described by a joint matrix normal distribution. The adopted approach allows for a reduction in redundancies, while emphasizing information richness rather than data richness. The developed approach incorporates the concept of entropy to account for the associated uncertainties. Three different entropy-based criteria are adopted: total system entropy, chlorophyll-a standard violation entropy, and dissolved oxygen standard violation entropy. A multiple attribute decision making framework is adopted to integrate the competing design criteria and to generate a single optimal design. The approach is implemented on the water quality monitoring system of the Neuse River Estuary in North Carolina, USA. The model results indicate that the high priority monitoring areas identified by the total system entropy and the dissolved oxygen violation entropy criteria are largely coincident. The monitoring design based on the chlorophyll-a standard violation entropy proved to be less informative, given the low probabilities of violating the water quality standard in the estuary.

A meta-analysis accounting for sources of variability to estimate heat resistance reference parameters of bacteria using hierarchical Bayesian modeling: Estimation of D at 121.1 °C and pH 7, zT and zpH of Geobacillus stearothermophilus.

Science.gov (United States)

Rigaux, Clémence; Denis, Jean-Baptiste; Albert, Isabelle; Carlin, Frédéric

2013-02-01

Predicting microbial survival requires reference parameters for each micro-organism of concern. When data are abundant and publicly available, a meta-analysis is a useful approach for assessment of these parameters, which can be performed with hierarchical Bayesian modeling. Geobacillus stearothermophilus is a major agent of microbial spoilage of canned foods and is therefore a persistent problem in the food industry. The thermal inactivation parameters of G. stearothermophilus (D(ref), i.e.the decimal reduction time D at the reference temperature 121.1°C and pH 7.0, z(T) and z(pH)) were estimated from a large set of 430 D values mainly collected from scientific literature. Between-study variability hypotheses on the inactivation parameters D(ref), z(T) and z(pH) were explored, using three different hierarchical Bayesian models. Parameter estimations were made using Bayesian inference and the models were compared with a graphical and a Bayesian criterion. Results show the necessity to account for random effects associated with between-study variability. Assuming variability on D(ref), z(T) and z(pH), the resulting distributions for D(ref), z(T) and z(pH) led to a mean of 3.3 min for D(ref) (95% Credible Interval CI=[0.8; 9.6]), to a mean of 9.1°C for z(T) (CI=[5.4; 13.1]) and to a mean of 4.3 pH units for z(pH) (CI=[2.9; 6.3]), in the range pH 3 to pH 7.5. Results are also given separating variability and uncertainty in these distributions, as well as adjusted parametric distributions to facilitate further use of these results in aqueous canned foods such as canned vegetables. Copyright © 2012 Elsevier B.V. All rights reserved.

Estimation of Mental Disorders Prevalence in High School Students Using Small Area Methods: A Hierarchical Bayesian Approach

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Ali Reza Soltanian

2016-08-01

Full Text Available Background Adolescence is one of the most important periods in the course of human evolution and the prevalence of mental disorders among adolescence in different regions of Iran, especially in southern Iran. Objectives This study was conducted to determine the prevalence of mental disorders among high school students in Bushehr province, south of Iran. Methods In this cross-sectional study, 286 high school students were recruited by a multi-stage random sampling in Bushehr province in 2015. A general health questionnaire (GHQ-28 was used to assess mental disorders. The small area method, under the hierarchical Bayesian approach, was used to determine the prevalence of mental disorders and data analysis. Results From 286 questionnaires only 182 were completely filed and evaluated (the response rate was 70.5%. Of the students, 58.79% and 41.21% were male and female, respectively. Of all students, the prevalence of mental disorders in Bushehr, Dayyer, Deylam, Kangan, Dashtestan, Tangestan, Genaveh, and Dashty were 0.48, 0.42, 0.45, 0.52, 0.41, 0.47, 0.42, and 0.43, respectively. Conclusions Based on this study, the prevalence of mental disorders among adolescents was increasing in Bushehr Province counties. The lack of a national policy in this way is a serious obstacle to mental health and wellbeing access.

Application of hierarchical matrices for partial inverse

KAUST Repository

Litvinenko, Alexander

2013-11-26

In this work we combine hierarchical matrix techniques (Hackbusch, 1999) and domain decomposition methods to obtain fast and efficient algorithms for the solution of multiscale problems. This combination results in the hierarchical domain decomposition (HDD) method, which can be applied for solution multi-scale problems. Multiscale problems are problems that require the use of different length scales. Using only the finest scale is very expensive, if not impossible, in computational time and memory. Domain decomposition methods decompose the complete problem into smaller systems of equations corresponding to boundary value problems in subdomains. Then fast solvers can be applied to each subdomain. Subproblems in subdomains are independent, much smaller and require less computational resources as the initial problem.

Probability biases as Bayesian inference

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Andre; C. R. Martins

2006-11-01

Full Text Available In this article, I will show how several observed biases in human probabilistic reasoning can be partially explained as good heuristics for making inferences in an environment where probabilities have uncertainties associated to them. Previous results show that the weight functions and the observed violations of coalescing and stochastic dominance can be understood from a Bayesian point of view. We will review those results and see that Bayesian methods should also be used as part of the explanation behind other known biases. That means that, although the observed errors are still errors under the be understood as adaptations to the solution of real life problems. Heuristics that allow fast evaluations and mimic a Bayesian inference would be an evolutionary advantage, since they would give us an efficient way of making decisions. %XX In that sense, it should be no surprise that humans reason with % probability as it has been observed.

TYPE Ia SUPERNOVA COLORS AND EJECTA VELOCITIES: HIERARCHICAL BAYESIAN REGRESSION WITH NON-GAUSSIAN DISTRIBUTIONS

International Nuclear Information System (INIS)

Mandel, Kaisey S.; Kirshner, Robert P.; Foley, Ryan J.

2014-01-01

We investigate the statistical dependence of the peak intrinsic colors of Type Ia supernovae (SNe Ia) on their expansion velocities at maximum light, measured from the Si II λ6355 spectral feature. We construct a new hierarchical Bayesian regression model, accounting for the random effects of intrinsic scatter, measurement error, and reddening by host galaxy dust, and implement a Gibbs sampler and deviance information criteria to estimate the correlation. The method is applied to the apparent colors from BVRI light curves and Si II velocity data for 79 nearby SNe Ia. The apparent color distributions of high-velocity (HV) and normal velocity (NV) supernovae exhibit significant discrepancies for B – V and B – R, but not other colors. Hence, they are likely due to intrinsic color differences originating in the B band, rather than dust reddening. The mean intrinsic B – V and B – R color differences between HV and NV groups are 0.06 ± 0.02 and 0.09 ± 0.02 mag, respectively. A linear model finds significant slopes of –0.021 ± 0.006 and –0.030 ± 0.009 mag (10 3 km s –1 ) –1 for intrinsic B – V and B – R colors versus velocity, respectively. Because the ejecta velocity distribution is skewed toward high velocities, these effects imply non-Gaussian intrinsic color distributions with skewness up to +0.3. Accounting for the intrinsic-color-velocity correlation results in corrections to A V extinction estimates as large as –0.12 mag for HV SNe Ia and +0.06 mag for NV events. Velocity measurements from SN Ia spectra have the potential to diminish systematic errors from the confounding of intrinsic colors and dust reddening affecting supernova distances

Fast model updating coupling Bayesian inference and PGD model reduction

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Rubio, Paul-Baptiste; Louf, François; Chamoin, Ludovic

2018-04-01

The paper focuses on a coupled Bayesian-Proper Generalized Decomposition (PGD) approach for the real-time identification and updating of numerical models. The purpose is to use the most general case of Bayesian inference theory in order to address inverse problems and to deal with different sources of uncertainties (measurement and model errors, stochastic parameters). In order to do so with a reasonable CPU cost, the idea is to replace the direct model called for Monte-Carlo sampling by a PGD reduced model, and in some cases directly compute the probability density functions from the obtained analytical formulation. This procedure is first applied to a welding control example with the updating of a deterministic parameter. In the second application, the identification of a stochastic parameter is studied through a glued assembly example.

A hierarchical spatiotemporal analog forecasting model for count data.

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McDermott, Patrick L; Wikle, Christopher K; Millspaugh, Joshua

2018-01-01

Analog forecasting is a mechanism-free nonlinear method that forecasts a system forward in time by examining how past states deemed similar to the current state moved forward. Previous applications of analog forecasting has been successful at producing robust forecasts for a variety of ecological and physical processes, but it has typically been presented in an empirical or heuristic procedure, rather than as a formal statistical model. The methodology presented here extends the model-based analog method of McDermott and Wikle (Environmetrics, 27, 2016, 70) by placing analog forecasting within a fully hierarchical statistical framework that can accommodate count observations. Using a Bayesian approach, the hierarchical analog model is able to quantify rigorously the uncertainty associated with forecasts. Forecasting waterfowl settling patterns in the northwestern United States and Canada is conducted by applying the hierarchical analog model to a breeding population survey dataset. Sea surface temperature (SST) in the Pacific Ocean is used to help identify potential analogs for the waterfowl settling patterns.

Comparison of Bayesian and frequentist approaches in modelling risk of preterm birth near the Sydney Tar Ponds, Nova Scotia, Canada

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Canty Angelo

2007-09-01

Full Text Available Abstract Background This study compares the Bayesian and frequentist (non-Bayesian approaches in the modelling of the association between the risk of preterm birth and maternal proximity to hazardous waste and pollution from the Sydney Tar Pond site in Nova Scotia, Canada. Methods The data includes 1604 observed cases of preterm birth out of a total population of 17559 at risk of preterm birth from 144 enumeration districts in the Cape Breton Regional Municipality. Other covariates include the distance from the Tar Pond; the rate of unemployment to population; the proportion of persons who are separated, divorced or widowed; the proportion of persons who have no high school diploma; the proportion of persons living alone; the proportion of single parent families and average income. Bayesian hierarchical Poisson regression, quasi-likelihood Poisson regression and weighted linear regression models were fitted to the data. Results The results of the analyses were compared together with their limitations. Conclusion The results of the weighted linear regression and the quasi-likelihood Poisson regression agrees with the result from the Bayesian hierarchical modelling which incorporates the spatial effects.

Cholinergic stimulation enhances Bayesian belief updating in the deployment of spatial attention.

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Vossel, Simone; Bauer, Markus; Mathys, Christoph; Adams, Rick A; Dolan, Raymond J; Stephan, Klaas E; Friston, Karl J

2014-11-19

The exact mechanisms whereby the cholinergic neurotransmitter system contributes to attentional processing remain poorly understood. Here, we applied computational modeling to psychophysical data (obtained from a spatial attention task) under a psychopharmacological challenge with the cholinesterase inhibitor galantamine (Reminyl). This allowed us to characterize the cholinergic modulation of selective attention formally, in terms of hierarchical Bayesian inference. In a placebo-controlled, within-subject, crossover design, 16 healthy human subjects performed a modified version of Posner's location-cueing task in which the proportion of validly and invalidly cued targets (percentage of cue validity, % CV) changed over time. Saccadic response speeds were used to estimate the parameters of a hierarchical Bayesian model to test whether cholinergic stimulation affected the trial-wise updating of probabilistic beliefs that underlie the allocation of attention or whether galantamine changed the mapping from those beliefs to subsequent eye movements. Behaviorally, galantamine led to a greater influence of probabilistic context (% CV) on response speed than placebo. Crucially, computational modeling suggested this effect was due to an increase in the rate of belief updating about cue validity (as opposed to the increased sensitivity of behavioral responses to those beliefs). We discuss these findings with respect to cholinergic effects on hierarchical cortical processing and in relation to the encoding of expected uncertainty or precision. Copyright © 2014 the authors 0270-6474/14/3415735-08$15.00/0.

Improved Bayesian optimization algorithm with fast convergence%一种快速收敛的改进贝叶斯优化算法

Institute of Scientific and Technical Information of China (English)

王翔; 郑建国; 张超群; 刘荣辉

2011-01-01

针对贝叶斯优化算法(BOA)中学习贝叶斯网络结构时间复杂度较高的问题,提出了一种可以快速收敛的基于K2的贝叶斯优化算法(K2-BOA).为了提升收敛速度,在学习贝叶斯网络结构的步骤中进行了2处改进:首先,随机生成n个变量的拓扑排序,加大了算法的随机性;其次,在排序的基础上利用K2算法学习贝叶斯网络结构,减少了整个算法的时问复杂度.针对3个标准Benchmark函数的仿真实验表明:采用K2-BOA算法和BOA算法解决简单分解函数问题时,寻找到最优值的适应度函数评价次数几乎相同,但是每次迭代K2-BOA算法运行速度提升明显;当解决比较复杂的6阶双极欺骗函数问题时,K2-BOA算法无论是运行时间还是适应度函数评价次数,都远小于BOA算法.%K2-Bayesian optimization algorithm (BOA) with fast convergence was proposed to enhance the convergence rate figuring out the problem that the time complexity of learning Bayesian networks was high in the Bayesian optimization algorithm. There were two improvements in learning Bayesian network of the new algorithm: the topological sort of n variables was randomly generated for increasing the randomness of the algorithm, and on the basis of the sort K2 algorithm was used to learn Bayesian network structure to reduce the time complexity of the new algorithm. The simulation results for three benchmark functions show two conclusions. Firstly, when 3-deceptive function and trap-5 function are solved, the number of fitness function evaluation of K2-Bayesian optimization algorithm is almost the same as that of Bayesian optimization algorithm; however the running time of K2-Bayesian optimization algorithm is less than that of Bayesian optimization algorithm. Secondly, when 6-bipolar function is solved, the number of fitness function evaluation and the running time of K2-Bayesian optimization algorithm are much better than those of Bayesian optimization algorithm.

Improving Hierarchical Models Using Historical Data with Applications in High-Throughput Genomics Data Analysis.

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Li, Ben; Li, Yunxiao; Qin, Zhaohui S

2017-06-01

Modern high-throughput biotechnologies such as microarray and next generation sequencing produce a massive amount of information for each sample assayed. However, in a typical high-throughput experiment, only limited amount of data are observed for each individual feature, thus the classical 'large p , small n ' problem. Bayesian hierarchical model, capable of borrowing strength across features within the same dataset, has been recognized as an effective tool in analyzing such data. However, the shrinkage effect, the most prominent feature of hierarchical features, can lead to undesirable over-correction for some features. In this work, we discuss possible causes of the over-correction problem and propose several alternative solutions. Our strategy is rooted in the fact that in the Big Data era, large amount of historical data are available which should be taken advantage of. Our strategy presents a new framework to enhance the Bayesian hierarchical model. Through simulation and real data analysis, we demonstrated superior performance of the proposed strategy. Our new strategy also enables borrowing information across different platforms which could be extremely useful with emergence of new technologies and accumulation of data from different platforms in the Big Data era. Our method has been implemented in R package "adaptiveHM", which is freely available from https://github.com/benliemory/adaptiveHM.

A Bayesian approach to degradation-based burn-in optimization for display products exhibiting two-phase degradation patterns

International Nuclear Information System (INIS)

Yuan, Tao; Bae, Suk Joo; Zhu, Xiaoyan

2016-01-01

Motivated by the two-phase degradation phenomena observed in light displays (e.g., plasma display panels (PDPs), organic light emitting diodes (OLEDs)), this study proposes a new degradation-based burn-in testing plan for display products exhibiting two-phase degradation patterns. The primary focus of the burn-in test in this study is to eliminate the initial rapid degradation phase, while the major purpose of traditional burn-in tests is to detect and eliminate early failures from weak units. A hierarchical Bayesian bi-exponential model is used to capture two-phase degradation patterns of the burn-in population. Mission reliability and total cost are introduced as planning criteria. The proposed burn-in approach accounts for unit-to-unit variability within the burn-in population, and uncertainty concerning the model parameters, mainly in the hierarchical Bayesian framework. Available pre-burn-in data is conveniently incorporated into the burn-in decision-making procedure. A practical example of PDP degradation data is used to illustrate the proposed methodology. The proposed method is compared to other approaches such as the maximum likelihood method or the change-point regression. - Highlights: • We propose a degradation-based burn-in test for products with two-phase degradation. • Mission reliability and total cost are used as planning criteria. • The proposed burn-in approach is built within the hierarchical Bayesian framework. • A practical example was used to illustrate the proposed methodology.

Bayesian inference in processing experimental data: principles and basic applications

International Nuclear Information System (INIS)

D'Agostini, G

2003-01-01

This paper introduces general ideas and some basic methods of the Bayesian probability theory applied to physics measurements. Our aim is to make the reader familiar, through examples rather than rigorous formalism, with concepts such as the following: model comparison (including the automatic Ockham's Razor filter provided by the Bayesian approach); parametric inference; quantification of the uncertainty about the value of physical quantities, also taking into account systematic effects; role of marginalization; posterior characterization; predictive distributions; hierarchical modelling and hyperparameters; Gaussian approximation of the posterior and recovery of conventional methods, especially maximum likelihood and chi-square fits under well-defined conditions; conjugate priors, transformation invariance and maximum entropy motivated priors; and Monte Carlo (MC) estimates of expectation, including a short introduction to Markov Chain MC methods

Mobile Multicast in Hierarchical Proxy Mobile IPV6

Science.gov (United States)

Hafizah Mohd Aman, Azana; Hashim, Aisha Hassan A.; Mustafa, Amin; Abdullah, Khaizuran

2013-12-01

Mobile Internet Protocol Version 6 (MIPv6) environments have been developing very rapidly. Many challenges arise with the fast progress of MIPv6 technologies and its environment. Therefore the importance of improving the existing architecture and operations increases. One of the many challenges which need to be addressed is the need for performance improvement to support mobile multicast. Numerous approaches have been proposed to improve mobile multicast performance. This includes Context Transfer Protocol (CXTP), Hierarchical Mobile IPv6 (HMIPv6), Fast Mobile IPv6 (FMIPv6) and Proxy Mobile IPv6 (PMIPv6). This document describes multicast context transfer in hierarchical proxy mobile IPv6 (H-PMIPv6) to provide better multicasting performance in PMIPv6 domain.

OFDM receiver for fast time-varying channels using block-sparse Bayesian learning

DEFF Research Database (Denmark)

Barbu, Oana-Elena; Manchón, Carles Navarro; Rom, Christian

2016-01-01

characterized with a basis expansion model using a small number of terms. As a result, the channel estimation problem is posed as that of estimating a vector of complex coefficients that exhibits a block-sparse structure, which we solve with tools from block-sparse Bayesian learning. Using variational Bayesian...... inference, we embed the channel estimator in a receiver structure that performs iterative channel and noise precision estimation, intercarrier interference cancellation, detection and decoding. Simulation results illustrate the superior performance of the proposed receiver over state-of-art receivers....

Cortical hierarchies perform Bayesian causal inference in multisensory perception.

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Tim Rohe

2015-02-01

Full Text Available To form a veridical percept of the environment, the brain needs to integrate sensory signals from a common source but segregate those from independent sources. Thus, perception inherently relies on solving the "causal inference problem." Behaviorally, humans solve this problem optimally as predicted by Bayesian Causal Inference; yet, the underlying neural mechanisms are unexplored. Combining psychophysics, Bayesian modeling, functional magnetic resonance imaging (fMRI, and multivariate decoding in an audiovisual spatial localization task, we demonstrate that Bayesian Causal Inference is performed by a hierarchy of multisensory processes in the human brain. At the bottom of the hierarchy, in auditory and visual areas, location is represented on the basis that the two signals are generated by independent sources (= segregation. At the next stage, in posterior intraparietal sulcus, location is estimated under the assumption that the two signals are from a common source (= forced fusion. Only at the top of the hierarchy, in anterior intraparietal sulcus, the uncertainty about the causal structure of the world is taken into account and sensory signals are combined as predicted by Bayesian Causal Inference. Characterizing the computational operations of signal interactions reveals the hierarchical nature of multisensory perception in human neocortex. It unravels how the brain accomplishes Bayesian Causal Inference, a statistical computation fundamental for perception and cognition. Our results demonstrate how the brain combines information in the face of uncertainty about the underlying causal structure of the world.

Physics of ultrasonic wave propagation in bone and heart characterized using Bayesian parameter estimation

Science.gov (United States)

Anderson, Christian Carl

This Dissertation explores the physics underlying the propagation of ultrasonic waves in bone and in heart tissue through the use of Bayesian probability theory. Quantitative ultrasound is a noninvasive modality used for clinical detection, characterization, and evaluation of bone quality and cardiovascular disease. Approaches that extend the state of knowledge of the physics underpinning the interaction of ultrasound with inherently inhomogeneous and isotropic tissue have the potential to enhance its clinical utility. Simulations of fast and slow compressional wave propagation in cancellous bone were carried out to demonstrate the plausibility of a proposed explanation for the widely reported anomalous negative dispersion in cancellous bone. The results showed that negative dispersion could arise from analysis that proceeded under the assumption that the data consist of only a single ultrasonic wave, when in fact two overlapping and interfering waves are present. The confounding effect of overlapping fast and slow waves was addressed by applying Bayesian parameter estimation to simulated data, to experimental data acquired on bone-mimicking phantoms, and to data acquired in vitro on cancellous bone. The Bayesian approach successfully estimated the properties of the individual fast and slow waves even when they strongly overlapped in the acquired data. The Bayesian parameter estimation technique was further applied to an investigation of the anisotropy of ultrasonic properties in cancellous bone. The degree to which fast and slow waves overlap is partially determined by the angle of insonation of ultrasound relative to the predominant direction of trabecular orientation. In the past, studies of anisotropy have been limited by interference between fast and slow waves over a portion of the range of insonation angles. Bayesian analysis estimated attenuation, velocity, and amplitude parameters over the entire range of insonation angles, allowing a more complete

A novel approach to quantifying the sensitivity of current and future cosmological datasets to the neutrino mass ordering through Bayesian hierarchical modeling

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Gerbino, Martina; Lattanzi, Massimiliano; Mena, Olga; Freese, Katherine

2017-12-01

We present a novel approach to derive constraints on neutrino masses, as well as on other cosmological parameters, from cosmological data, while taking into account our ignorance of the neutrino mass ordering. We derive constraints from a combination of current as well as future cosmological datasets on the total neutrino mass Mν and on the mass fractions fν,i =mi /Mν (where the index i = 1 , 2 , 3 indicates the three mass eigenstates) carried by each of the mass eigenstates mi, after marginalizing over the (unknown) neutrino mass ordering, either normal ordering (NH) or inverted ordering (IH). The bounds on all the cosmological parameters, including those on the total neutrino mass, take therefore into account the uncertainty related to our ignorance of the mass hierarchy that is actually realized in nature. This novel approach is carried out in the framework of Bayesian analysis of a typical hierarchical problem, where the distribution of the parameters of the model depends on further parameters, the hyperparameters. In this context, the choice of the neutrino mass ordering is modeled via the discrete hyperparameterhtype, which we introduce in the usual Markov chain analysis. The preference from cosmological data for either the NH or the IH scenarios is then simply encoded in the posterior distribution of the hyperparameter itself. Current cosmic microwave background (CMB) measurements assign equal odds to the two hierarchies, and are thus unable to distinguish between them. However, after the addition of baryon acoustic oscillation (BAO) measurements, a weak preference for the normal hierarchical scenario appears, with odds of 4 : 3 from Planck temperature and large-scale polarization in combination with BAO (3 : 2 if small-scale polarization is also included). Concerning next-generation cosmological experiments, forecasts suggest that the combination of upcoming CMB (COrE) and BAO surveys (DESI) may determine the neutrino mass hierarchy at a high statistical

LiDAR based prediction of forest biomass using hierarchical models with spatially varying coefficients

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Chad Babcock; Andrew O. Finley; John B. Bradford; Randy Kolka; Richard Birdsey; Michael G. Ryan

2015-01-01

Many studies and production inventory systems have shown the utility of coupling covariates derived from Light Detection and Ranging (LiDAR) data with forest variables measured on georeferenced inventory plots through regression models. The objective of this study was to propose and assess the use of a Bayesian hierarchical modeling framework that accommodates both...

Spatio Temporal EEG Source Imaging with the Hierarchical Bayesian Elastic Net and Elitist Lasso Models.

Science.gov (United States)

Paz-Linares, Deirel; Vega-Hernández, Mayrim; Rojas-López, Pedro A; Valdés-Hernández, Pedro A; Martínez-Montes, Eduardo; Valdés-Sosa, Pedro A

2017-01-01

The estimation of EEG generating sources constitutes an Inverse Problem (IP) in Neuroscience. This is an ill-posed problem due to the non-uniqueness of the solution and regularization or prior information is needed to undertake Electrophysiology Source Imaging. Structured Sparsity priors can be attained through combinations of (L1 norm-based) and (L2 norm-based) constraints such as the Elastic Net (ENET) and Elitist Lasso (ELASSO) models. The former model is used to find solutions with a small number of smooth nonzero patches, while the latter imposes different degrees of sparsity simultaneously along different dimensions of the spatio-temporal matrix solutions. Both models have been addressed within the penalized regression approach, where the regularization parameters are selected heuristically, leading usually to non-optimal and computationally expensive solutions. The existing Bayesian formulation of ENET allows hyperparameter learning, but using the computationally intensive Monte Carlo/Expectation Maximization methods, which makes impractical its application to the EEG IP. While the ELASSO have not been considered before into the Bayesian context. In this work, we attempt to solve the EEG IP using a Bayesian framework for ENET and ELASSO models. We propose a Structured Sparse Bayesian Learning algorithm based on combining the Empirical Bayes and the iterative coordinate descent procedures to estimate both the parameters and hyperparameters. Using realistic simulations and avoiding the inverse crime we illustrate that our methods are able to recover complicated source setups more accurately and with a more robust estimation of the hyperparameters and behavior under different sparsity scenarios than classical LORETA, ENET and LASSO Fusion solutions. We also solve the EEG IP using data from a visual attention experiment, finding more interpretable neurophysiological patterns with our methods. The Matlab codes used in this work, including Simulations, Methods

Understanding uncertainties in non-linear population trajectories: a Bayesian semi-parametric hierarchical approach to large-scale surveys of coral cover.

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Julie Vercelloni

Full Text Available Recently, attempts to improve decision making in species management have focussed on uncertainties associated with modelling temporal fluctuations in populations. Reducing model uncertainty is challenging; while larger samples improve estimation of species trajectories and reduce statistical errors, they typically amplify variability in observed trajectories. In particular, traditional modelling approaches aimed at estimating population trajectories usually do not account well for nonlinearities and uncertainties associated with multi-scale observations characteristic of large spatio-temporal surveys. We present a Bayesian semi-parametric hierarchical model for simultaneously quantifying uncertainties associated with model structure and parameters, and scale-specific variability over time. We estimate uncertainty across a four-tiered spatial hierarchy of coral cover from the Great Barrier Reef. Coral variability is well described; however, our results show that, in the absence of additional model specifications, conclusions regarding coral trajectories become highly uncertain when considering multiple reefs, suggesting that management should focus more at the scale of individual reefs. The approach presented facilitates the description and estimation of population trajectories and associated uncertainties when variability cannot be attributed to specific causes and origins. We argue that our model can unlock value contained in large-scale datasets, provide guidance for understanding sources of uncertainty, and support better informed decision making.

Accounting for uncertainty in ecological analysis: the strengths and limitations of hierarchical statistical modeling.

Science.gov (United States)

Cressie, Noel; Calder, Catherine A; Clark, James S; Ver Hoef, Jay M; Wikle, Christopher K

2009-04-01

Analyses of ecological data should account for the uncertainty in the process(es) that generated the data. However, accounting for these uncertainties is a difficult task, since ecology is known for its complexity. Measurement and/or process errors are often the only sources of uncertainty modeled when addressing complex ecological problems, yet analyses should also account for uncertainty in sampling design, in model specification, in parameters governing the specified model, and in initial and boundary conditions. Only then can we be confident in the scientific inferences and forecasts made from an analysis. Probability and statistics provide a framework that accounts for multiple sources of uncertainty. Given the complexities of ecological studies, the hierarchical statistical model is an invaluable tool. This approach is not new in ecology, and there are many examples (both Bayesian and non-Bayesian) in the literature illustrating the benefits of this approach. In this article, we provide a baseline for concepts, notation, and methods, from which discussion on hierarchical statistical modeling in ecology can proceed. We have also planted some seeds for discussion and tried to show where the practical difficulties lie. Our thesis is that hierarchical statistical modeling is a powerful way of approaching ecological analysis in the presence of inevitable but quantifiable uncertainties, even if practical issues sometimes require pragmatic compromises.

A species-level phylogeny of all extant and late Quaternary extinct mammals using a novel heuristic-hierarchical Bayesian approach.

Science.gov (United States)

Faurby, Søren; Svenning, Jens-Christian

2015-03-01

Across large clades, two problems are generally encountered in the estimation of species-level phylogenies: (a) the number of taxa involved is generally so high that computation-intensive approaches cannot readily be utilized and (b) even for clades that have received intense study (e.g., mammals), attention has been centered on relatively few selected species, and most taxa must therefore be positioned on the basis of very limited genetic data. Here, we describe a new heuristic-hierarchical Bayesian approach and use it to construct a species-level phylogeny for all extant and late Quaternary extinct mammals. In this approach, species with large quantities of genetic data are placed nearly freely in the mammalian phylogeny according to these data, whereas the placement of species with lower quantities of data is performed with steadily stricter restrictions for decreasing data quantities. The advantages of the proposed method include (a) an improved ability to incorporate phylogenetic uncertainty in downstream analyses based on the resulting phylogeny, (b) a reduced potential for long-branch attraction or other types of errors that place low-data taxa far from their true position, while maintaining minimal restrictions for better-studied taxa, and (c) likely improved placement of low-data taxa due to the use of closer outgroups. Copyright © 2014 Elsevier Inc. All rights reserved.

Hierarchical modularity in human brain functional networks

Directory of Open Access Journals (Sweden)

David Meunier

2009-10-01

Full Text Available The idea that complex systems have a hierarchical modular organization originates in the early 1960s and has recently attracted fresh support from quantitative studies of large scale, real-life networks. Here we investigate the hierarchical modular (or “modules-within-modules” decomposition of human brain functional networks, measured using functional magnetic resonance imaging (fMRI in 18 healthy volunteers under no-task or resting conditions. We used a customized template to extract networks with more than 1800 regional nodes, and we applied a fast algorithm to identify nested modular structure at several hierarchical levels. We used mutual information, 0 < I < 1, to estimate the similarity of community structure of networks in different subjects, and to identify the individual network that is most representative of the group. Results show that human brain functional networks have a hierarchical modular organization with a fair degree of similarity between subjects, I=0.63. The largest 5 modules at the highest level of the hierarchy were medial occipital, lateral occipital, central, parieto-frontal and fronto-temporal systems; occipital modules demonstrated less sub-modular organization than modules comprising regions of multimodal association cortex. Connector nodes and hubs, with a key role in inter-modular connectivity, were also concentrated in association cortical areas. We conclude that methods are available for hierarchical modular decomposition of large numbers of high resolution brain functional networks using computationally expedient algorithms. This could enable future investigations of Simon's original hypothesis that hierarchy or near-decomposability of physical symbol systems is a critical design feature for their fast adaptivity to changing environmental conditions.

A Bayesian Approach for Summarizing and Modeling Time-Series Exposure Data with Left Censoring.

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Houseman, E Andres; Virji, M Abbas

2017-08-01

Direct reading instruments are valuable tools for measuring exposure as they provide real-time measurements for rapid decision making. However, their use is limited to general survey applications in part due to issues related to their performance. Moreover, statistical analysis of real-time data is complicated by autocorrelation among successive measurements, non-stationary time series, and the presence of left-censoring due to limit-of-detection (LOD). A Bayesian framework is proposed that accounts for non-stationary autocorrelation and LOD issues in exposure time-series data in order to model workplace factors that affect exposure and estimate summary statistics for tasks or other covariates of interest. A spline-based approach is used to model non-stationary autocorrelation with relatively few assumptions about autocorrelation structure. Left-censoring is addressed by integrating over the left tail of the distribution. The model is fit using Markov-Chain Monte Carlo within a Bayesian paradigm. The method can flexibly account for hierarchical relationships, random effects and fixed effects of covariates. The method is implemented using the rjags package in R, and is illustrated by applying it to real-time exposure data. Estimates for task means and covariates from the Bayesian model are compared to those from conventional frequentist models including linear regression, mixed-effects, and time-series models with different autocorrelation structures. Simulations studies are also conducted to evaluate method performance. Simulation studies with percent of measurements below the LOD ranging from 0 to 50% showed lowest root mean squared errors for task means and the least biased standard deviations from the Bayesian model compared to the frequentist models across all levels of LOD. In the application, task means from the Bayesian model were similar to means from the frequentist models, while the standard deviations were different. Parameter estimates for covariates

A Hierarchical Multivariate Bayesian Approach to Ensemble Model output Statistics in Atmospheric Prediction

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2017-09-01

application of statistical inference. Even when human forecasters leverage their professional experience, which is often gained through long periods of... application throughout statistics and Bayesian data analysis. The multivariate form of 2( , )  (e.g., Figure 12) is similarly analytically...data (i.e., no systematic manipulations with analytical functions), it is common in the statistical literature to apply mathematical transformations

Hierarchical Recurrent Neural Hashing for Image Retrieval With Hierarchical Convolutional Features.

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Lu, Xiaoqiang; Chen, Yaxiong; Li, Xuelong

Hashing has been an important and effective technology in image retrieval due to its computational efficiency and fast search speed. The traditional hashing methods usually learn hash functions to obtain binary codes by exploiting hand-crafted features, which cannot optimally represent the information of the sample. Recently, deep learning methods can achieve better performance, since deep learning architectures can learn more effective image representation features. However, these methods only use semantic features to generate hash codes by shallow projection but ignore texture details. In this paper, we proposed a novel hashing method, namely hierarchical recurrent neural hashing (HRNH), to exploit hierarchical recurrent neural network to generate effective hash codes. There are three contributions of this paper. First, a deep hashing method is proposed to extensively exploit both spatial details and semantic information, in which, we leverage hierarchical convolutional features to construct image pyramid representation. Second, our proposed deep network can exploit directly convolutional feature maps as input to preserve the spatial structure of convolutional feature maps. Finally, we propose a new loss function that considers the quantization error of binarizing the continuous embeddings into the discrete binary codes, and simultaneously maintains the semantic similarity and balanceable property of hash codes. Experimental results on four widely used data sets demonstrate that the proposed HRNH can achieve superior performance over other state-of-the-art hashing methods.Hashing has been an important and effective technology in image retrieval due to its computational efficiency and fast search speed. The traditional hashing methods usually learn hash functions to obtain binary codes by exploiting hand-crafted features, which cannot optimally represent the information of the sample. Recently, deep learning methods can achieve better performance, since deep

Superresolution radar imaging based on fast inverse-free sparse Bayesian learning for multiple measurement vectors

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He, Xingyu; Tong, Ningning; Hu, Xiaowei

2018-01-01

Compressive sensing has been successfully applied to inverse synthetic aperture radar (ISAR) imaging of moving targets. By exploiting the block sparse structure of the target image, sparse solution for multiple measurement vectors (MMV) can be applied in ISAR imaging and a substantial performance improvement can be achieved. As an effective sparse recovery method, sparse Bayesian learning (SBL) for MMV involves a matrix inverse at each iteration. Its associated computational complexity grows significantly with the problem size. To address this problem, we develop a fast inverse-free (IF) SBL method for MMV. A relaxed evidence lower bound (ELBO), which is computationally more amiable than the traditional ELBO used by SBL, is obtained by invoking fundamental property for smooth functions. A variational expectation-maximization scheme is then employed to maximize the relaxed ELBO, and a computationally efficient IF-MSBL algorithm is proposed. Numerical results based on simulated and real data show that the proposed method can reconstruct row sparse signal accurately and obtain clear superresolution ISAR images. Moreover, the running time and computational complexity are reduced to a great extent compared with traditional SBL methods.

Modeling visual search using three-parameter probability functions in a hierarchical Bayesian framework.

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Lin, Yi-Shin; Heinke, Dietmar; Humphreys, Glyn W

2015-04-01

In this study, we applied Bayesian-based distributional analyses to examine the shapes of response time (RT) distributions in three visual search paradigms, which varied in task difficulty. In further analyses we investigated two common observations in visual search-the effects of display size and of variations in search efficiency across different task conditions-following a design that had been used in previous studies (Palmer, Horowitz, Torralba, & Wolfe, Journal of Experimental Psychology: Human Perception and Performance, 37, 58-71, 2011; Wolfe, Palmer, & Horowitz, Vision Research, 50, 1304-1311, 2010) in which parameters of the response distributions were measured. Our study showed that the distributional parameters in an experimental condition can be reliably estimated by moderate sample sizes when Monte Carlo simulation techniques are applied. More importantly, by analyzing trial RTs, we were able to extract paradigm-dependent shape changes in the RT distributions that could be accounted for by using the EZ2 diffusion model. The study showed that Bayesian-based RT distribution analyses can provide an important means to investigate the underlying cognitive processes in search, including stimulus grouping and the bottom-up guidance of attention.

Hierarchical Spatial Concept Formation Based on Multimodal Information for Human Support Robots.

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Hagiwara, Yoshinobu; Inoue, Masakazu; Kobayashi, Hiroyoshi; Taniguchi, Tadahiro

2018-01-01

In this paper, we propose a hierarchical spatial concept formation method based on the Bayesian generative model with multimodal information e.g., vision, position and word information. Since humans have the ability to select an appropriate level of abstraction according to the situation and describe their position linguistically, e.g., "I am in my home" and "I am in front of the table," a hierarchical structure of spatial concepts is necessary in order for human support robots to communicate smoothly with users. The proposed method enables a robot to form hierarchical spatial concepts by categorizing multimodal information using hierarchical multimodal latent Dirichlet allocation (hMLDA). Object recognition results using convolutional neural network (CNN), hierarchical k-means clustering result of self-position estimated by Monte Carlo localization (MCL), and a set of location names are used, respectively, as features in vision, position, and word information. Experiments in forming hierarchical spatial concepts and evaluating how the proposed method can predict unobserved location names and position categories are performed using a robot in the real world. Results verify that, relative to comparable baseline methods, the proposed method enables a robot to predict location names and position categories closer to predictions made by humans. As an application example of the proposed method in a home environment, a demonstration in which a human support robot moves to an instructed place based on human speech instructions is achieved based on the formed hierarchical spatial concept.

Hierarchical Spatial Concept Formation Based on Multimodal Information for Human Support Robots

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Yoshinobu Hagiwara

2018-03-01

Full Text Available In this paper, we propose a hierarchical spatial concept formation method based on the Bayesian generative model with multimodal information e.g., vision, position and word information. Since humans have the ability to select an appropriate level of abstraction according to the situation and describe their position linguistically, e.g., “I am in my home” and “I am in front of the table,” a hierarchical structure of spatial concepts is necessary in order for human support robots to communicate smoothly with users. The proposed method enables a robot to form hierarchical spatial concepts by categorizing multimodal information using hierarchical multimodal latent Dirichlet allocation (hMLDA. Object recognition results using convolutional neural network (CNN, hierarchical k-means clustering result of self-position estimated by Monte Carlo localization (MCL, and a set of location names are used, respectively, as features in vision, position, and word information. Experiments in forming hierarchical spatial concepts and evaluating how the proposed method can predict unobserved location names and position categories are performed using a robot in the real world. Results verify that, relative to comparable baseline methods, the proposed method enables a robot to predict location names and position categories closer to predictions made by humans. As an application example of the proposed method in a home environment, a demonstration in which a human support robot moves to an instructed place based on human speech instructions is achieved based on the formed hierarchical spatial concept.

A Bayesian Supertree Model for Genome-Wide Species Tree Reconstruction

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De Oliveira Martins, Leonardo; Mallo, Diego; Posada, David

2016-01-01

Current phylogenomic data sets highlight the need for species tree methods able to deal with several sources of gene tree/species tree incongruence. At the same time, we need to make most use of all available data. Most species tree methods deal with single processes of phylogenetic discordance, namely, gene duplication and loss, incomplete lineage sorting (ILS) or horizontal gene transfer. In this manuscript, we address the problem of species tree inference from multilocus, genome-wide data sets regardless of the presence of gene duplication and loss and ILS therefore without the need to identify orthologs or to use a single individual per species. We do this by extending the idea of Maximum Likelihood (ML) supertrees to a hierarchical Bayesian model where several sources of gene tree/species tree disagreement can be accounted for in a modular manner. We implemented this model in a computer program called guenomu whose inputs are posterior distributions of unrooted gene tree topologies for multiple gene families, and whose output is the posterior distribution of rooted species tree topologies. We conducted extensive simulations to evaluate the performance of our approach in comparison with other species tree approaches able to deal with more than one leaf from the same species. Our method ranked best under simulated data sets, in spite of ignoring branch lengths, and performed well on empirical data, as well as being fast enough to analyze relatively large data sets. Our Bayesian supertree method was also very successful in obtaining better estimates of gene trees, by reducing the uncertainty in their distributions. In addition, our results show that under complex simulation scenarios, gene tree parsimony is also a competitive approach once we consider its speed, in contrast to more sophisticated models. PMID:25281847

A Bayesian Supertree Model for Genome-Wide Species Tree Reconstruction.

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De Oliveira Martins, Leonardo; Mallo, Diego; Posada, David

2016-05-01

Current phylogenomic data sets highlight the need for species tree methods able to deal with several sources of gene tree/species tree incongruence. At the same time, we need to make most use of all available data. Most species tree methods deal with single processes of phylogenetic discordance, namely, gene duplication and loss, incomplete lineage sorting (ILS) or horizontal gene transfer. In this manuscript, we address the problem of species tree inference from multilocus, genome-wide data sets regardless of the presence of gene duplication and loss and ILS therefore without the need to identify orthologs or to use a single individual per species. We do this by extending the idea of Maximum Likelihood (ML) supertrees to a hierarchical Bayesian model where several sources of gene tree/species tree disagreement can be accounted for in a modular manner. We implemented this model in a computer program called guenomu whose inputs are posterior distributions of unrooted gene tree topologies for multiple gene families, and whose output is the posterior distribution of rooted species tree topologies. We conducted extensive simulations to evaluate the performance of our approach in comparison with other species tree approaches able to deal with more than one leaf from the same species. Our method ranked best under simulated data sets, in spite of ignoring branch lengths, and performed well on empirical data, as well as being fast enough to analyze relatively large data sets. Our Bayesian supertree method was also very successful in obtaining better estimates of gene trees, by reducing the uncertainty in their distributions. In addition, our results show that under complex simulation scenarios, gene tree parsimony is also a competitive approach once we consider its speed, in contrast to more sophisticated models. © The Author(s) 2014. Published by Oxford University Press on behalf of the Society of Systematic Biologists.

MEG source localization of spatially extended generators of epileptic activity: comparing entropic and hierarchical bayesian approaches.

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Chowdhury, Rasheda Arman; Lina, Jean Marc; Kobayashi, Eliane; Grova, Christophe

2013-01-01

Localizing the generators of epileptic activity in the brain using Electro-EncephaloGraphy (EEG) or Magneto-EncephaloGraphy (MEG) signals is of particular interest during the pre-surgical investigation of epilepsy. Epileptic discharges can be detectable from background brain activity, provided they are associated with spatially extended generators. Using realistic simulations of epileptic activity, this study evaluates the ability of distributed source localization methods to accurately estimate the location of the generators and their sensitivity to the spatial extent of such generators when using MEG data. Source localization methods based on two types of realistic models have been investigated: (i) brain activity may be modeled using cortical parcels and (ii) brain activity is assumed to be locally smooth within each parcel. A Data Driven Parcellization (DDP) method was used to segment the cortical surface into non-overlapping parcels and diffusion-based spatial priors were used to model local spatial smoothness within parcels. These models were implemented within the Maximum Entropy on the Mean (MEM) and the Hierarchical Bayesian (HB) source localization frameworks. We proposed new methods in this context and compared them with other standard ones using Monte Carlo simulations of realistic MEG data involving sources of several spatial extents and depths. Detection accuracy of each method was quantified using Receiver Operating Characteristic (ROC) analysis and localization error metrics. Our results showed that methods implemented within the MEM framework were sensitive to all spatial extents of the sources ranging from 3 cm(2) to 30 cm(2), whatever were the number and size of the parcels defining the model. To reach a similar level of accuracy within the HB framework, a model using parcels larger than the size of the sources should be considered.

MEG source localization of spatially extended generators of epileptic activity: comparing entropic and hierarchical bayesian approaches.

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Rasheda Arman Chowdhury

Full Text Available Localizing the generators of epileptic activity in the brain using Electro-EncephaloGraphy (EEG or Magneto-EncephaloGraphy (MEG signals is of particular interest during the pre-surgical investigation of epilepsy. Epileptic discharges can be detectable from background brain activity, provided they are associated with spatially extended generators. Using realistic simulations of epileptic activity, this study evaluates the ability of distributed source localization methods to accurately estimate the location of the generators and their sensitivity to the spatial extent of such generators when using MEG data. Source localization methods based on two types of realistic models have been investigated: (i brain activity may be modeled using cortical parcels and (ii brain activity is assumed to be locally smooth within each parcel. A Data Driven Parcellization (DDP method was used to segment the cortical surface into non-overlapping parcels and diffusion-based spatial priors were used to model local spatial smoothness within parcels. These models were implemented within the Maximum Entropy on the Mean (MEM and the Hierarchical Bayesian (HB source localization frameworks. We proposed new methods in this context and compared them with other standard ones using Monte Carlo simulations of realistic MEG data involving sources of several spatial extents and depths. Detection accuracy of each method was quantified using Receiver Operating Characteristic (ROC analysis and localization error metrics. Our results showed that methods implemented within the MEM framework were sensitive to all spatial extents of the sources ranging from 3 cm(2 to 30 cm(2, whatever were the number and size of the parcels defining the model. To reach a similar level of accuracy within the HB framework, a model using parcels larger than the size of the sources should be considered.

Effects of management intervention on post-disturbance community composition: an experimental analysis using bayesian hierarchical models.

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Jack Giovanini

Full Text Available As human demand for ecosystem products increases, management intervention may become more frequent after environmental disturbances. Evaluations of ecological responses to cumulative effects of management interventions and natural disturbances provide critical decision-support tools for managers who strive to balance environmental conservation and economic development. We conducted an experiment to evaluate the effects of salvage logging on avian community composition in lodgepole pine (Pinus contorta forests affected by beetle outbreaks in Oregon, USA, 1996-1998. Treatments consisted of the removal of lodgepole pine snags only, and live trees were not harvested. We used a bayesian hierarchical model to quantify occupancy dynamics for 27 breeding species, while accounting for variation in the detection process. We examined how magnitude and precision of treatment effects varied when incorporating prior information from a separate intervention study that occurred in a similar ecological system. Regardless of which prior we evaluated, we found no evidence that the harvest treatment had a negative impact on species richness, with an estimated average of 0.2-2.2 more species in harvested stands than unharvested stands. Estimated average similarity between control and treatment stands ranged from 0.82-0.87 (1 indicating complete similarity between a pair of stands and suggested that treatment stands did not contain novel assemblies of species responding to the harvesting prescription. Estimated treatment effects were positive for twenty-four (90% of the species, although the credible intervals contained 0 in all cases. These results suggest that, unlike most post-fire salvage logging prescriptions, selective harvesting after beetle outbreaks may meet multiple management objectives, including the maintenance of avian community richness comparable to what is found in unharvested stands. Our results provide managers with prescription alternatives to

A Bayesian Model of Biases in Artificial Language Learning: The Case of a Word-Order Universal

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Culbertson, Jennifer; Smolensky, Paul

2012-01-01

In this article, we develop a hierarchical Bayesian model of learning in a general type of artificial language-learning experiment in which learners are exposed to a mixture of grammars representing the variation present in real learners' input, particularly at times of language change. The modeling goal is to formalize and quantify hypothesized…

Bayesian automated cortical segmentation for neonatal MRI

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Chou, Zane; Paquette, Natacha; Ganesh, Bhavana; Wang, Yalin; Ceschin, Rafael; Nelson, Marvin D.; Macyszyn, Luke; Gaonkar, Bilwaj; Panigrahy, Ashok; Lepore, Natasha

2017-11-01

Several attempts have been made in the past few years to develop and implement an automated segmentation of neonatal brain structural MRI. However, accurate automated MRI segmentation remains challenging in this population because of the low signal-to-noise ratio, large partial volume effects and inter-individual anatomical variability of the neonatal brain. In this paper, we propose a learning method for segmenting the whole brain cortical grey matter on neonatal T2-weighted images. We trained our algorithm using a neonatal dataset composed of 3 fullterm and 4 preterm infants scanned at term equivalent age. Our segmentation pipeline combines the FAST algorithm from the FSL library software and a Bayesian segmentation approach to create a threshold matrix that minimizes the error of mislabeling brain tissue types. Our method shows promising results with our pilot training set. In both preterm and full-term neonates, automated Bayesian segmentation generates a smoother and more consistent parcellation compared to FAST, while successfully removing the subcortical structure and cleaning the edges of the cortical grey matter. This method show promising refinement of the FAST segmentation by considerably reducing manual input and editing required from the user, and further improving reliability and processing time of neonatal MR images. Further improvement will include a larger dataset of training images acquired from different manufacturers.

A novel approach to quantifying the sensitivity of current and future cosmological datasets to the neutrino mass ordering through Bayesian hierarchical modeling

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Martina Gerbino

2017-12-01

Full Text Available We present a novel approach to derive constraints on neutrino masses, as well as on other cosmological parameters, from cosmological data, while taking into account our ignorance of the neutrino mass ordering. We derive constraints from a combination of current as well as future cosmological datasets on the total neutrino mass Mν and on the mass fractions fν,i=mi/Mν (where the index i=1,2,3 indicates the three mass eigenstates carried by each of the mass eigenstates mi, after marginalizing over the (unknown neutrino mass ordering, either normal ordering (NH or inverted ordering (IH. The bounds on all the cosmological parameters, including those on the total neutrino mass, take therefore into account the uncertainty related to our ignorance of the mass hierarchy that is actually realized in nature. This novel approach is carried out in the framework of Bayesian analysis of a typical hierarchical problem, where the distribution of the parameters of the model depends on further parameters, the hyperparameters. In this context, the choice of the neutrino mass ordering is modeled via the discrete hyperparameter htype, which we introduce in the usual Markov chain analysis. The preference from cosmological data for either the NH or the IH scenarios is then simply encoded in the posterior distribution of the hyperparameter itself. Current cosmic microwave background (CMB measurements assign equal odds to the two hierarchies, and are thus unable to distinguish between them. However, after the addition of baryon acoustic oscillation (BAO measurements, a weak preference for the normal hierarchical scenario appears, with odds of 4:3 from Planck temperature and large-scale polarization in combination with BAO (3:2 if small-scale polarization is also included. Concerning next-generation cosmological experiments, forecasts suggest that the combination of upcoming CMB (COrE and BAO surveys (DESI may determine the neutrino mass hierarchy at a high

Bayesian Modeling of Air Pollution Extremes Using Nested Multivariate Max-Stable Processes

KAUST Repository

Vettori, Sabrina; Huser, Raphaë l; Genton, Marc G.

2018-01-01

Capturing the potentially strong dependence among the peak concentrations of multiple air pollutants across a spatial region is crucial for assessing the related public health risks. In order to investigate the multivariate spatial dependence properties of air pollution extremes, we introduce a new class of multivariate max-stable processes. Our proposed model admits a hierarchical tree-based formulation, in which the data are conditionally independent given some latent nested $\\alpha$-stable random factors. The hierarchical structure facilitates Bayesian inference and offers a convenient and interpretable characterization. We fit this nested multivariate max-stable model to the maxima of air pollution concentrations and temperatures recorded at a number of sites in the Los Angeles area, showing that the proposed model succeeds in capturing their complex tail dependence structure.

Bayesian Modeling of Air Pollution Extremes Using Nested Multivariate Max-Stable Processes

KAUST Repository

Vettori, Sabrina

2018-03-18

Capturing the potentially strong dependence among the peak concentrations of multiple air pollutants across a spatial region is crucial for assessing the related public health risks. In order to investigate the multivariate spatial dependence properties of air pollution extremes, we introduce a new class of multivariate max-stable processes. Our proposed model admits a hierarchical tree-based formulation, in which the data are conditionally independent given some latent nested $\\\\alpha$-stable random factors. The hierarchical structure facilitates Bayesian inference and offers a convenient and interpretable characterization. We fit this nested multivariate max-stable model to the maxima of air pollution concentrations and temperatures recorded at a number of sites in the Los Angeles area, showing that the proposed model succeeds in capturing their complex tail dependence structure.

Sparse Bayesian Learning for DOA Estimation with Mutual Coupling

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Jisheng Dai

2015-10-01

Full Text Available Sparse Bayesian learning (SBL has given renewed interest to the problem of direction-of-arrival (DOA estimation. It is generally assumed that the measurement matrix in SBL is precisely known. Unfortunately, this assumption may be invalid in practice due to the imperfect manifold caused by unknown or misspecified mutual coupling. This paper describes a modified SBL method for joint estimation of DOAs and mutual coupling coefficients with uniform linear arrays (ULAs. Unlike the existing method that only uses stationary priors, our new approach utilizes a hierarchical form of the Student t prior to enforce the sparsity of the unknown signal more heavily. We also provide a distinct Bayesian inference for the expectation-maximization (EM algorithm, which can update the mutual coupling coefficients more efficiently. Another difference is that our method uses an additional singular value decomposition (SVD to reduce the computational complexity of the signal reconstruction process and the sensitivity to the measurement noise.

Bayesian analysis of deterministic and stochastic prisoner's dilemma games

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Howard Kunreuther

2009-08-01

Full Text Available This paper compares the behavior of individuals playing a classic two-person deterministic prisoner's dilemma (PD game with choice data obtained from repeated interdependent security prisoner's dilemma games with varying probabilities of loss and the ability to learn (or not learn about the actions of one's counterpart, an area of recent interest in experimental economics. This novel data set, from a series of controlled laboratory experiments, is analyzed using Bayesian hierarchical methods, the first application of such methods in this research domain. We find that individuals are much more likely to be cooperative when payoffs are deterministic than when the outcomes are probabilistic. A key factor explaining this difference is that subjects in a stochastic PD game respond not just to what their counterparts did but also to whether or not they suffered a loss. These findings are interpreted in the context of behavioral theories of commitment, altruism and reciprocity. The work provides a linkage between Bayesian statistics, experimental economics, and consumer psychology.

Hierarchically organized layout for visualization of biochemical pathways.

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Tsay, Jyh-Jong; Wu, Bo-Liang; Jeng, Yu-Sen

2010-01-01

Many complex pathways are described as hierarchical structures in which a pathway is recursively partitioned into several sub-pathways, and organized hierarchically as a tree. The hierarchical structure provides a natural way to visualize the global structure of a complex pathway. However, none of the previous research on pathway visualization explores the hierarchical structures provided by many complex pathways. In this paper, we aim to develop algorithms that can take advantages of hierarchical structures, and give layouts that explore the global structures as well as local structures of pathways. We present a new hierarchically organized layout algorithm to produce layouts for hierarchically organized pathways. Our algorithm first decomposes a complex pathway into sub-pathway groups along the hierarchical organization, and then partition each sub-pathway group into basic components. It then applies conventional layout algorithms, such as hierarchical layout and force-directed layout, to compute the layout of each basic component. Finally, component layouts are joined to form a final layout of the pathway. Our main contribution is the development of algorithms for decomposing pathways and joining layouts. Experiment shows that our algorithm is able to give comprehensible visualization for pathways with hierarchies, cycles as well as complex structures. It clearly renders the global component structures as well as the local structure in each component. In addition, it runs very fast, and gives better visualization for many examples from previous related research. 2009 Elsevier B.V. All rights reserved.

Dynamic relations between fast-food restaurant and body weight status: a longitudinal and multilevel analysis of Chinese adults.

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Xu, Hongwei; Short, Susan E; Liu, Tao

2013-03-01

Mixed findings have been reported on the association between Western fast-food restaurants and body weight status. Results vary across study contexts and are sensitive to the samples, measures and methods used. Most studies have failed to examine the temporally dynamic associations between community exposure to fast-food restaurants and weight changes. Bayesian hierarchical regressions are used to model changes in body mass index, waist-to-height ratio (WHtR) and waist-to-hip ratio (WHpR) as a function of changes in Western fast-food restaurants in 216 communities for more than 9000 Chinese adults followed up multiple times between 2000 and 2009. Number of Western fast-food restaurants is positively associated with subsequent increases in WHtR and WHpR among rural population. More fast-food restaurants are positively associated with a future increase in WHpR for urban women. Increased availability of fast food between two waves is related to increased WHtR for urban men over the same period. A past increase in number of fast-food restaurants is associated with subsequent increases in WHtR and WHpR for rural population. The associations between community exposure to Western fast food and weight changes are temporally dynamic rather than static. Improved measures of exposure to community environment are needed to achieve more precise estimates and better understanding of these relationships. In light of the findings in this study and China's rapid economic growth, further investigation and increased public health monitoring is warranted since Western fast food is likely to be more accessible and affordable in the near future.

From least squares to multilevel modeling: A graphical introduction to Bayesian inference

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Loredo, Thomas J.

2016-01-01

This tutorial presentation will introduce some of the key ideas and techniques involved in applying Bayesian methods to problems in astrostatistics. The focus will be on the big picture: understanding the foundations (interpreting probability, Bayes's theorem, the law of total probability and marginalization), making connections to traditional methods (propagation of errors, least squares, chi-squared, maximum likelihood, Monte Carlo simulation), and highlighting problems where a Bayesian approach can be particularly powerful (Poisson processes, density estimation and curve fitting with measurement error). The "graphical" component of the title reflects an emphasis on pictorial representations of some of the math, but also on the use of graphical models (multilevel or hierarchical models) for analyzing complex data. Code for some examples from the talk will be available to participants, in Python and in the Stan probabilistic programming language.

Robust and scalable hierarchical matrix-based fast direct solver and preconditioner for the numerical solution of elliptic partial differential equations

KAUST Repository

Chavez, Gustavo Ivan

2017-07-10

This dissertation introduces a novel fast direct solver and preconditioner for the solution of block tridiagonal linear systems that arise from the discretization of elliptic partial differential equations on a Cartesian product mesh, such as the variable-coefficient Poisson equation, the convection-diffusion equation, and the wave Helmholtz equation in heterogeneous media. The algorithm extends the traditional cyclic reduction method with hierarchical matrix techniques. The resulting method exposes substantial concurrency, and its arithmetic operations and memory consumption grow only log-linearly with problem size, assuming bounded rank of off-diagonal matrix blocks, even for problems with arbitrary coefficient structure. The method can be used as a standalone direct solver with tunable accuracy, or as a black-box preconditioner in conjunction with Krylov methods. The challenges that distinguish this work from other thrusts in this active field are the hybrid distributed-shared parallelism that can demonstrate the algorithm at large-scale, full three-dimensionality, and the three stressors of the current state-of-the-art multigrid technology: high wavenumber Helmholtz (indefiniteness), high Reynolds convection (nonsymmetry), and high contrast diffusion (inhomogeneity). Numerical experiments corroborate the robustness, accuracy, and complexity claims and provide a baseline of the performance and memory footprint by comparisons with competing approaches such as the multigrid solver hypre, and the STRUMPACK implementation of the multifrontal factorization with hierarchically semi-separable matrices. The companion implementation can utilize many thousands of cores of Shaheen, KAUST\\'s Haswell-based Cray XC-40 supercomputer, and compares favorably with other implementations of hierarchical solvers in terms of time-to-solution and memory consumption.

Sparse reconstruction using distribution agnostic bayesian matching pursuit

KAUST Repository

Masood, Mudassir

2013-11-01

A fast matching pursuit method using a Bayesian approach is introduced for sparse signal recovery. This method performs Bayesian estimates of sparse signals even when the signal prior is non-Gaussian or unknown. It is agnostic on signal statistics and utilizes a priori statistics of additive noise and the sparsity rate of the signal, which are shown to be easily estimated from data if not available. The method utilizes a greedy approach and order-recursive updates of its metrics to find the most dominant sparse supports to determine the approximate minimum mean-square error (MMSE) estimate of the sparse signal. Simulation results demonstrate the power and robustness of our proposed estimator. © 2013 IEEE.

A Direct Elliptic Solver Based on Hierarchically Low-Rank Schur Complements

KAUST Repository

Chávez, Gustavo

2017-03-17

A parallel fast direct solver for rank-compressible block tridiagonal linear systems is presented. Algorithmic synergies between Cyclic Reduction and Hierarchical matrix arithmetic operations result in a solver with O(Nlog2N) arithmetic complexity and O(NlogN) memory footprint. We provide a baseline for performance and applicability by comparing with well-known implementations of the $$\\\\mathcal{H}$$ -LU factorization and algebraic multigrid within a shared-memory parallel environment that leverages the concurrency features of the method. Numerical experiments reveal that this method is comparable with other fast direct solvers based on Hierarchical Matrices such as $$\\\\mathcal{H}$$ -LU and that it can tackle problems where algebraic multigrid fails to converge.

Hierarchical Matrices Method and Its Application in Electromagnetic Integral Equations

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Han Guo

2012-01-01

Full Text Available Hierarchical (H- matrices method is a general mathematical framework providing a highly compact representation and efficient numerical arithmetic. When applied in integral-equation- (IE- based computational electromagnetics, H-matrices can be regarded as a fast algorithm; therefore, both the CPU time and memory requirement are reduced significantly. Its kernel independent feature also makes it suitable for any kind of integral equation. To solve H-matrices system, Krylov iteration methods can be employed with appropriate preconditioners, and direct solvers based on the hierarchical structure of H-matrices are also available along with high efficiency and accuracy, which is a unique advantage compared to other fast algorithms. In this paper, a novel sparse approximate inverse (SAI preconditioner in multilevel fashion is proposed to accelerate the convergence rate of Krylov iterations for solving H-matrices system in electromagnetic applications, and a group of parallel fast direct solvers are developed for dealing with multiple right-hand-side cases. Finally, numerical experiments are given to demonstrate the advantages of the proposed multilevel preconditioner compared to conventional “single level” preconditioners and the practicability of the fast direct solvers for arbitrary complex structures.

conting : an R package for Bayesian analysis of complete and incomplete contingency tables

OpenAIRE

Overstall, Antony; King, Ruth

2014-01-01

The aim of this paper is to demonstrate the R package conting for the Bayesian analysis of complete and incomplete contingency tables using hierarchical log-linear models. This package allows a user to identify interactions between categorical factors (via complete contingency tables) and to estimate closed population sizes using capture-recapture studies (via incomplete contingency tables). The models are fitted using Markov chain Monte Carlo methods. In particular, implementations of the Me...

Bayesian techniques for fatigue life prediction and for inference in linear time dependent PDEs

KAUST Repository

Scavino, Marco

2016-01-08

In this talk we introduce first the main characteristics of a systematic statistical approach to model calibration, model selection and model ranking when stress-life data are drawn from a collection of records of fatigue experiments. Focusing on Bayesian prediction assessment, we consider fatigue-limit models and random fatigue-limit models under different a priori assumptions. In the second part of the talk, we present a hierarchical Bayesian technique for the inference of the coefficients of time dependent linear PDEs, under the assumption that noisy measurements are available in both the interior of a domain of interest and from boundary conditions. We present a computational technique based on the marginalization of the contribution of the boundary parameters and apply it to inverse heat conduction problems.

Identification of transmissivity fields using a Bayesian strategy and perturbative approach

Science.gov (United States)

Zanini, Andrea; Tanda, Maria Giovanna; Woodbury, Allan D.

2017-10-01

The paper deals with the crucial problem of the groundwater parameter estimation that is the basis for efficient modeling and reclamation activities. A hierarchical Bayesian approach is developed: it uses the Akaike's Bayesian Information Criteria in order to estimate the hyperparameters (related to the covariance model chosen) and to quantify the unknown noise variance. The transmissivity identification proceeds in two steps: the first, called empirical Bayesian interpolation, uses Y* (Y = lnT) observations to interpolate Y values on a specified grid; the second, called empirical Bayesian update, improve the previous Y estimate through the addition of hydraulic head observations. The relationship between the head and the lnT has been linearized through a perturbative solution of the flow equation. In order to test the proposed approach, synthetic aquifers from literature have been considered. The aquifers in question contain a variety of boundary conditions (both Dirichelet and Neuman type) and scales of heterogeneities (σY2 = 1.0 and σY2 = 5.3). The estimated transmissivity fields were compared to the true one. The joint use of Y* and head measurements improves the estimation of Y considering both degrees of heterogeneity. Even if the variance of the strong transmissivity field can be considered high for the application of the perturbative approach, the results show the same order of approximation of the non-linear methods proposed in literature. The procedure allows to compute the posterior probability distribution of the target quantities and to quantify the uncertainty in the model prediction. Bayesian updating has advantages related both to the Monte-Carlo (MC) and non-MC approaches. In fact, as the MC methods, Bayesian updating allows computing the direct posterior probability distribution of the target quantities and as non-MC methods it has computational times in the order of seconds.

Bayesian Age-Period-Cohort Modeling and Prediction - BAMP

Directory of Open Access Journals (Sweden)

Volker J. Schmid

2007-10-01

Full Text Available The software package BAMP provides a method of analyzing incidence or mortality data on the Lexis diagram, using a Bayesian version of an age-period-cohort model. A hierarchical model is assumed with a binomial model in the first-stage. As smoothing priors for the age, period and cohort parameters random walks of first and second order, with and without an additional unstructured component are available. Unstructured heterogeneity can also be included in the model. In order to evaluate the model fit, posterior deviance, DIC and predictive deviances are computed. By projecting the random walk prior into the future, future death rates can be predicted.

Hierarchical modeling and inference in ecology: The analysis of data from populations, metapopulations and communities

Science.gov (United States)

Royle, J. Andrew; Dorazio, Robert M.

2008-01-01

A guide to data collection, modeling and inference strategies for biological survey data using Bayesian and classical statistical methods. This book describes a general and flexible framework for modeling and inference in ecological systems based on hierarchical models, with a strict focus on the use of probability models and parametric inference. Hierarchical models represent a paradigm shift in the application of statistics to ecological inference problems because they combine explicit models of ecological system structure or dynamics with models of how ecological systems are observed. The principles of hierarchical modeling are developed and applied to problems in population, metapopulation, community, and metacommunity systems. The book provides the first synthetic treatment of many recent methodological advances in ecological modeling and unifies disparate methods and procedures. The authors apply principles of hierarchical modeling to ecological problems, including * occurrence or occupancy models for estimating species distribution * abundance models based on many sampling protocols, including distance sampling * capture-recapture models with individual effects * spatial capture-recapture models based on camera trapping and related methods * population and metapopulation dynamic models * models of biodiversity, community structure and dynamics.

On Bayesian shared component disease mapping and ecological regression with errors in covariates.

Science.gov (United States)

MacNab, Ying C

2010-05-20

Recent literature on Bayesian disease mapping presents shared component models (SCMs) for joint spatial modeling of two or more diseases with common risk factors. In this study, Bayesian hierarchical formulations of shared component disease mapping and ecological models are explored and developed in the context of ecological regression, taking into consideration errors in covariates. A review of multivariate disease mapping models (MultiVMs) such as the multivariate conditional autoregressive models that are also part of the more recent Bayesian disease mapping literature is presented. Some insights into the connections and distinctions between the SCM and MultiVM procedures are communicated. Important issues surrounding (appropriate) formulation of shared- and disease-specific components, consideration/choice of spatial or non-spatial random effects priors, and identification of model parameters in SCMs are explored and discussed in the context of spatial and ecological analysis of small area multivariate disease or health outcome rates and associated ecological risk factors. The methods are illustrated through an in-depth analysis of four-variate road traffic accident injury (RTAI) data: gender-specific fatal and non-fatal RTAI rates in 84 local health areas in British Columbia (Canada). Fully Bayesian inference via Markov chain Monte Carlo simulations is presented. Copyright 2010 John Wiley & Sons, Ltd.

Bayesian methods for hackers probabilistic programming and Bayesian inference

CERN Document Server

Davidson-Pilon, Cameron

2016-01-01

Bayesian methods of inference are deeply natural and extremely powerful. However, most discussions of Bayesian inference rely on intensely complex mathematical analyses and artificial examples, making it inaccessible to anyone without a strong mathematical background. Now, though, Cameron Davidson-Pilon introduces Bayesian inference from a computational perspective, bridging theory to practice–freeing you to get results using computing power. Bayesian Methods for Hackers illuminates Bayesian inference through probabilistic programming with the powerful PyMC language and the closely related Python tools NumPy, SciPy, and Matplotlib. Using this approach, you can reach effective solutions in small increments, without extensive mathematical intervention. Davidson-Pilon begins by introducing the concepts underlying Bayesian inference, comparing it with other techniques and guiding you through building and training your first Bayesian model. Next, he introduces PyMC through a series of detailed examples a...

Manual hierarchical clustering of regional geochemical data using a Bayesian finite mixture model

International Nuclear Information System (INIS)

Ellefsen, Karl J.; Smith, David B.

2016-01-01

Interpretation of regional scale, multivariate geochemical data is aided by a statistical technique called “clustering.” We investigate a particular clustering procedure by applying it to geochemical data collected in the State of Colorado, United States of America. The clustering procedure partitions the field samples for the entire survey area into two clusters. The field samples in each cluster are partitioned again to create two subclusters, and so on. This manual procedure generates a hierarchy of clusters, and the different levels of the hierarchy show geochemical and geological processes occurring at different spatial scales. Although there are many different clustering methods, we use Bayesian finite mixture modeling with two probability distributions, which yields two clusters. The model parameters are estimated with Hamiltonian Monte Carlo sampling of the posterior probability density function, which usually has multiple modes. Each mode has its own set of model parameters; each set is checked to ensure that it is consistent both with the data and with independent geologic knowledge. The set of model parameters that is most consistent with the independent geologic knowledge is selected for detailed interpretation and partitioning of the field samples. - Highlights: • We evaluate a clustering procedure by applying it to geochemical data. • The procedure generates a hierarchy of clusters. • Different levels of the hierarchy show geochemical processes at different spatial scales. • The clustering method is Bayesian finite mixture modeling. • Model parameters are estimated with Hamiltonian Monte Carlo sampling.

A novel hierarchical ZnO disordered/ordered bilayer nanostructured film for dye sensitized solar cells

Energy Technology Data Exchange (ETDEWEB)

Feng, Yamin, E-mail: yaminfengccnuphy@outlook.com; Wu, Fei; Jiang, Jian; Zhu, Jianhui; Fodjouong, Ghislain Joel; Meng, Gaoxiang; Xing, Yanmin; Wang, Wenwu; Huang, Xintang, E-mail: xthuang@phy.ccnu.edu.cn

2013-12-25

Graphical abstract: A novel hierarchical disordered/ordered bilayer ZnO nanostructured film in the length of 18 μm have been successfully synthesized on the FTO substrate; the hierarchical ZnO nanostructured film electrodes applied in DSSCs exhibit photoelectric conversion efficiency as high as 5.16%. Highlights: •A novel hierarchical ZnO structure film was fabricated on a FTO substrate. •Hierarchical ZnO film is applied as the electrodes for dye sensitized solar cells. •The film possess high specific surface area and fast electron transport effect. •The light-scattering effect of the hierarchical film is pronounced. •The energy conversion efficiency of hierarchical ZnO electrode reaches to 5.16%. -- Abstract: A novel hierarchical ZnO nanostructured film is synthesized via a chemical bath deposition (CBD) method followed by a treatment of thermal decomposition onto a fluorine-doped tin oxide (FTO) substrate. This hierarchical film is composed of disordered ZnO nanorods (NRs) (top layer) and ordered ZnO nanowires (NWs) (bottom layer). The products possess the following features such as high specific surface area, fast electron transport, and pronounced light-scattering effect, which are quite suitable for dye sensitized solar cells (DSSCs) applications. A light-to-electricity conversion efficiency of 5.16% is achieved when the hierarchical ZnO nanostructured film is used as the photoanode under 100 mW cm{sup −2} illumination. This efficiency is found to be much higher than that of the DSSCs with pure ordered ZnO NWs (1.45%) and disordered ZnO NRs (3.31%) photoanodes.

A novel hierarchical ZnO disordered/ordered bilayer nanostructured film for dye sensitized solar cells

International Nuclear Information System (INIS)

Feng, Yamin; Wu, Fei; Jiang, Jian; Zhu, Jianhui; Fodjouong, Ghislain Joel; Meng, Gaoxiang; Xing, Yanmin; Wang, Wenwu; Huang, Xintang

2013-01-01

Graphical abstract: A novel hierarchical disordered/ordered bilayer ZnO nanostructured film in the length of 18 μm have been successfully synthesized on the FTO substrate; the hierarchical ZnO nanostructured film electrodes applied in DSSCs exhibit photoelectric conversion efficiency as high as 5.16%. Highlights: •A novel hierarchical ZnO structure film was fabricated on a FTO substrate. •Hierarchical ZnO film is applied as the electrodes for dye sensitized solar cells. •The film possess high specific surface area and fast electron transport effect. •The light-scattering effect of the hierarchical film is pronounced. •The energy conversion efficiency of hierarchical ZnO electrode reaches to 5.16%. -- Abstract: A novel hierarchical ZnO nanostructured film is synthesized via a chemical bath deposition (CBD) method followed by a treatment of thermal decomposition onto a fluorine-doped tin oxide (FTO) substrate. This hierarchical film is composed of disordered ZnO nanorods (NRs) (top layer) and ordered ZnO nanowires (NWs) (bottom layer). The products possess the following features such as high specific surface area, fast electron transport, and pronounced light-scattering effect, which are quite suitable for dye sensitized solar cells (DSSCs) applications. A light-to-electricity conversion efficiency of 5.16% is achieved when the hierarchical ZnO nanostructured film is used as the photoanode under 100 mW cm −2 illumination. This efficiency is found to be much higher than that of the DSSCs with pure ordered ZnO NWs (1.45%) and disordered ZnO NRs (3.31%) photoanodes

Can Bayesian Theories of Autism Spectrum Disorder Help Improve Clinical Practice?

Science.gov (United States)

Haker, Helene; Schneebeli, Maya; Stephan, Klaas Enno

2016-01-01

Diagnosis and individualized treatment of autism spectrum disorder (ASD) represent major problems for contemporary psychiatry. Tackling these problems requires guidance by a pathophysiological theory. In this paper, we consider recent theories that re-conceptualize ASD from a "Bayesian brain" perspective, which posit that the core abnormality of ASD resides in perceptual aberrations due to a disbalance in the precision of prediction errors (sensory noise) relative to the precision of predictions (prior beliefs). This results in percepts that are dominated by sensory inputs and less guided by top-down regularization and shifts the perceptual focus to detailed aspects of the environment with difficulties in extracting meaning. While these Bayesian theories have inspired ongoing empirical studies, their clinical implications have not yet been carved out. Here, we consider how this Bayesian perspective on disease mechanisms in ASD might contribute to improving clinical care for affected individuals. Specifically, we describe a computational strategy, based on generative (e.g., hierarchical Bayesian) models of behavioral and functional neuroimaging data, for establishing diagnostic tests. These tests could provide estimates of specific cognitive processes underlying ASD and delineate pathophysiological mechanisms with concrete treatment targets. Written with a clinical audience in mind, this article outlines how the development of computational diagnostics applicable to behavioral and functional neuroimaging data in routine clinical practice could not only fundamentally alter our concept of ASD but eventually also transform the clinical management of this disorder.

A Bayesian foundation for individual learning under uncertainty

Directory of Open Access Journals (Sweden)

Christoph eMathys

2011-05-01

Full Text Available Computational learning models are critical for understanding mechanisms of adaptive behavior. However, the two major current frameworks, reinforcement learning (RL and Bayesian learning, both have certain limitations. For example, many Bayesian models are agnostic of inter-individual variability and involve complicated integrals, making online learning difficult. Here, we introduce a generic hierarchical Bayesian framework for individual learning under multiple forms of uncertainty (e.g., environmental volatility and perceptual uncertainty. The model assumes Gaussian random walks of states at all but the first level, with the step size determined by the next higher level. The coupling between levels is controlled by parameters that shape the influence of uncertainty on learning in a subject-specific fashion. Using variational Bayes under a mean field approximation and a novel approximation to the posterior energy function, we derive trial-by-trial update equations which (i are analytical and extremely efficient, enabling real-time learning, (ii have a natural interpretation in terms of RL, and (iii contain parameters representing processes which play a key role in current theories of learning, e.g., precision-weighting of prediction error. These parameters allow for the expression of individual differences in learning and may relate to specific neuromodulatory mechanisms in the brain. Our model is very general: it can deal with both discrete and continuous states and equally accounts for deterministic and probabilistic relations between environmental events and perceptual states (i.e., situations with and without perceptual uncertainty. These properties are illustrated by simulations and analyses of empirical time series. Overall, our framework provides a novel foundation for understanding normal and pathological learning that contextualizes RL within a generic Bayesian scheme and thus connects it to principles of optimality from probability

A bayesian foundation for individual learning under uncertainty.

Science.gov (United States)

Mathys, Christoph; Daunizeau, Jean; Friston, Karl J; Stephan, Klaas E

2011-01-01

Computational learning models are critical for understanding mechanisms of adaptive behavior. However, the two major current frameworks, reinforcement learning (RL) and Bayesian learning, both have certain limitations. For example, many Bayesian models are agnostic of inter-individual variability and involve complicated integrals, making online learning difficult. Here, we introduce a generic hierarchical Bayesian framework for individual learning under multiple forms of uncertainty (e.g., environmental volatility and perceptual uncertainty). The model assumes Gaussian random walks of states at all but the first level, with the step size determined by the next highest level. The coupling between levels is controlled by parameters that shape the influence of uncertainty on learning in a subject-specific fashion. Using variational Bayes under a mean-field approximation and a novel approximation to the posterior energy function, we derive trial-by-trial update equations which (i) are analytical and extremely efficient, enabling real-time learning, (ii) have a natural interpretation in terms of RL, and (iii) contain parameters representing processes which play a key role in current theories of learning, e.g., precision-weighting of prediction error. These parameters allow for the expression of individual differences in learning and may relate to specific neuromodulatory mechanisms in the brain. Our model is very general: it can deal with both discrete and continuous states and equally accounts for deterministic and probabilistic relations between environmental events and perceptual states (i.e., situations with and without perceptual uncertainty). These properties are illustrated by simulations and analyses of empirical time series. Overall, our framework provides a novel foundation for understanding normal and pathological learning that contextualizes RL within a generic Bayesian scheme and thus connects it to principles of optimality from probability theory.

Disentangling Complexity in Bayesian Automatic Adaptive Quadrature

Science.gov (United States)

Adam, Gheorghe; Adam, Sanda

2018-02-01

The paper describes a Bayesian automatic adaptive quadrature (BAAQ) solution for numerical integration which is simultaneously robust, reliable, and efficient. Detailed discussion is provided of three main factors which contribute to the enhancement of these features: (1) refinement of the m-panel automatic adaptive scheme through the use of integration-domain-length-scale-adapted quadrature sums; (2) fast early problem complexity assessment - enables the non-transitive choice among three execution paths: (i) immediate termination (exceptional cases); (ii) pessimistic - involves time and resource consuming Bayesian inference resulting in radical reformulation of the problem to be solved; (iii) optimistic - asks exclusively for subrange subdivision by bisection; (3) use of the weaker accuracy target from the two possible ones (the input accuracy specifications and the intrinsic integrand properties respectively) - results in maximum possible solution accuracy under minimum possible computing time.

Fast Bayesian approach for modal identification using forced vibration data considering the ambient effect

Science.gov (United States)

Ni, Yan-Chun; Zhang, Feng-Liang

2018-05-01

Modal identification based on vibration response measured from real structures is becoming more popular, especially after benefiting from the great improvement of the measurement technology. The results are reliable to estimate the dynamic performance, which fits the increasing requirement of different design configurations of the new structures. However, the high-quality vibration data collection technology calls for a more accurate modal identification method to improve the accuracy of the results. Through the whole measurement process of dynamic testing, there are many aspects that will cause the rise of uncertainty, such as measurement noise, alignment error and modeling error, since the test conditions are not directly controlled. Depending on these demands, a Bayesian statistical approach is developed in this work to estimate the modal parameters using the forced vibration response of structures, simultaneously considering the effect of the ambient vibration. This method makes use of the Fast Fourier Transform (FFT) of the data in a selected frequency band to identify the modal parameters of the mode dominating this frequency band and estimate the remaining uncertainty of the parameters correspondingly. In the existing modal identification methods for forced vibration, it is generally assumed that the forced vibration response dominates the measurement data and the influence of the ambient vibration response is ignored. However, ambient vibration will cause modeling error and affect the accuracy of the identified results. The influence is shown in the spectra as some phenomena that are difficult to explain and irrelevant to the mode to be identified. These issues all mean that careful choice of assumptions in the identification model and fundamental formulation to account for uncertainty are necessary. During the calculation, computational difficulties associated with calculating the posterior statistics are addressed. Finally, a fast computational algorithm

Bayesian artificial intelligence

CERN Document Server

Korb, Kevin B

2010-01-01

Updated and expanded, Bayesian Artificial Intelligence, Second Edition provides a practical and accessible introduction to the main concepts, foundation, and applications of Bayesian networks. It focuses on both the causal discovery of networks and Bayesian inference procedures. Adopting a causal interpretation of Bayesian networks, the authors discuss the use of Bayesian networks for causal modeling. They also draw on their own applied research to illustrate various applications of the technology.New to the Second EditionNew chapter on Bayesian network classifiersNew section on object-oriente

Bayesian spatio-temporal modeling of particulate matter concentrations in Peninsular Malaysia

Science.gov (United States)

Manga, Edna; Awang, Norhashidah

2016-06-01

This article presents an application of a Bayesian spatio-temporal Gaussian process (GP) model on particulate matter concentrations from Peninsular Malaysia. We analyze daily PM10 concentration levels from 35 monitoring sites in June and July 2011. The spatiotemporal model set in a Bayesian hierarchical framework allows for inclusion of informative covariates, meteorological variables and spatiotemporal interactions. Posterior density estimates of the model parameters are obtained by Markov chain Monte Carlo methods. Preliminary data analysis indicate information on PM10 levels at sites classified as industrial locations could explain part of the space time variations. We include the site-type indicator in our modeling efforts. Results of the parameter estimates for the fitted GP model show significant spatio-temporal structure and positive effect of the location-type explanatory variable. We also compute some validation criteria for the out of sample sites that show the adequacy of the model for predicting PM10 at unmonitored sites.

Bayesian semiparametric regression models to characterize molecular evolution

Directory of Open Access Journals (Sweden)

Datta Saheli

2012-10-01

Full Text Available Abstract Background Statistical models and methods that associate changes in the physicochemical properties of amino acids with natural selection at the molecular level typically do not take into account the correlations between such properties. We propose a Bayesian hierarchical regression model with a generalization of the Dirichlet process prior on the distribution of the regression coefficients that describes the relationship between the changes in amino acid distances and natural selection in protein-coding DNA sequence alignments. Results The Bayesian semiparametric approach is illustrated with simulated data and the abalone lysin sperm data. Our method identifies groups of properties which, for this particular dataset, have a similar effect on evolution. The model also provides nonparametric site-specific estimates for the strength of conservation of these properties. Conclusions The model described here is distinguished by its ability to handle a large number of amino acid properties simultaneously, while taking into account that such data can be correlated. The multi-level clustering ability of the model allows for appealing interpretations of the results in terms of properties that are roughly equivalent from the standpoint of molecular evolution.

An evaluation of the Bayesian approach to fitting the N-mixture model for use with pseudo-replicated count data

Science.gov (United States)

Toribo, S.G.; Gray, B.R.; Liang, S.

2011-01-01

The N-mixture model proposed by Royle in 2004 may be used to approximate the abundance and detection probability of animal species in a given region. In 2006, Royle and Dorazio discussed the advantages of using a Bayesian approach in modelling animal abundance and occurrence using a hierarchical N-mixture model. N-mixture models assume replication on sampling sites, an assumption that may be violated when the site is not closed to changes in abundance during the survey period or when nominal replicates are defined spatially. In this paper, we studied the robustness of a Bayesian approach to fitting the N-mixture model for pseudo-replicated count data. Our simulation results showed that the Bayesian estimates for abundance and detection probability are slightly biased when the actual detection probability is small and are sensitive to the presence of extra variability within local sites.

Assessing Local Model Adequacy in Bayesian Hierarchical Models Using the Partitioned Deviance Information Criterion

Science.gov (United States)

Wheeler, David C.; Hickson, DeMarc A.; Waller, Lance A.

2010-01-01

Many diagnostic tools and goodness-of-fit measures, such as the Akaike information criterion (AIC) and the Bayesian deviance information criterion (DIC), are available to evaluate the overall adequacy of linear regression models. In addition, visually assessing adequacy in models has become an essential part of any regression analysis. In this paper, we focus on a spatial consideration of the local DIC measure for model selection and goodness-of-fit evaluation. We use a partitioning of the DIC into the local DIC, leverage, and deviance residuals to assess local model fit and influence for both individual observations and groups of observations in a Bayesian framework. We use visualization of the local DIC and differences in local DIC between models to assist in model selection and to visualize the global and local impacts of adding covariates or model parameters. We demonstrate the utility of the local DIC in assessing model adequacy using HIV prevalence data from pregnant women in the Butare province of Rwanda during 1989-1993 using a range of linear model specifications, from global effects only to spatially varying coefficient models, and a set of covariates related to sexual behavior. Results of applying the diagnostic visualization approach include more refined model selection and greater understanding of the models as applied to the data. PMID:21243121

BUMPER: the Bayesian User-friendly Model for Palaeo-Environmental Reconstruction

Science.gov (United States)

Holden, Phil; Birks, John; Brooks, Steve; Bush, Mark; Hwang, Grace; Matthews-Bird, Frazer; Valencia, Bryan; van Woesik, Robert

2017-04-01

We describe the Bayesian User-friendly Model for Palaeo-Environmental Reconstruction (BUMPER), a Bayesian transfer function for inferring past climate and other environmental variables from microfossil assemblages. The principal motivation for a Bayesian approach is that the palaeoenvironment is treated probabilistically, and can be updated as additional data become available. Bayesian approaches therefore provide a reconstruction-specific quantification of the uncertainty in the data and in the model parameters. BUMPER is fully self-calibrating, straightforward to apply, and computationally fast, requiring 2 seconds to build a 100-taxon model from a 100-site training-set on a standard personal computer. We apply the model's probabilistic framework to generate thousands of artificial training-sets under ideal assumptions. We then use these to demonstrate both the general applicability of the model and the sensitivity of reconstructions to the characteristics of the training-set, considering assemblage richness, taxon tolerances, and the number of training sites. We demonstrate general applicability to real data, considering three different organism types (chironomids, diatoms, pollen) and different reconstructed variables. In all of these applications an identically configured model is used, the only change being the input files that provide the training-set environment and taxon-count data.

Bayesian Graphical Models

DEFF Research Database (Denmark)

Jensen, Finn Verner; Nielsen, Thomas Dyhre

2016-01-01

Mathematically, a Bayesian graphical model is a compact representation of the joint probability distribution for a set of variables. The most frequently used type of Bayesian graphical models are Bayesian networks. The structural part of a Bayesian graphical model is a graph consisting of nodes...

Structure-based bayesian sparse reconstruction

KAUST Repository

Quadeer, Ahmed Abdul

2012-12-01

Sparse signal reconstruction algorithms have attracted research attention due to their wide applications in various fields. In this paper, we present a simple Bayesian approach that utilizes the sparsity constraint and a priori statistical information (Gaussian or otherwise) to obtain near optimal estimates. In addition, we make use of the rich structure of the sensing matrix encountered in many signal processing applications to develop a fast sparse recovery algorithm. The computational complexity of the proposed algorithm is very low compared with the widely used convex relaxation methods as well as greedy matching pursuit techniques, especially at high sparsity. © 1991-2012 IEEE.

Disease Mapping and Regression with Count Data in the Presence of Overdispersion and Spatial Autocorrelation: A Bayesian Model Averaging Approach

Science.gov (United States)

Mohebbi, Mohammadreza; Wolfe, Rory; Forbes, Andrew

2014-01-01

This paper applies the generalised linear model for modelling geographical variation to esophageal cancer incidence data in the Caspian region of Iran. The data have a complex and hierarchical structure that makes them suitable for hierarchical analysis using Bayesian techniques, but with care required to deal with problems arising from counts of events observed in small geographical areas when overdispersion and residual spatial autocorrelation are present. These considerations lead to nine regression models derived from using three probability distributions for count data: Poisson, generalised Poisson and negative binomial, and three different autocorrelation structures. We employ the framework of Bayesian variable selection and a Gibbs sampling based technique to identify significant cancer risk factors. The framework deals with situations where the number of possible models based on different combinations of candidate explanatory variables is large enough such that calculation of posterior probabilities for all models is difficult or infeasible. The evidence from applying the modelling methodology suggests that modelling strategies based on the use of generalised Poisson and negative binomial with spatial autocorrelation work well and provide a robust basis for inference. PMID:24413702

Bayesian soft X-ray tomography using non-stationary Gaussian Processes

International Nuclear Information System (INIS)

Li, Dong; Svensson, J.; Thomsen, H.; Werner, A.; Wolf, R.; Medina, F.

2013-01-01

In this study, a Bayesian based non-stationary Gaussian Process (GP) method for the inference of soft X-ray emissivity distribution along with its associated uncertainties has been developed. For the investigation of equilibrium condition and fast magnetohydrodynamic behaviors in nuclear fusion plasmas, it is of importance to infer, especially in the plasma center, spatially resolved soft X-ray profiles from a limited number of noisy line integral measurements. For this ill-posed inversion problem, Bayesian probability theory can provide a posterior probability distribution over all possible solutions under given model assumptions. Specifically, the use of a non-stationary GP to model the emission allows the model to adapt to the varying length scales of the underlying diffusion process. In contrast to other conventional methods, the prior regularization is realized in a probability form which enhances the capability of uncertainty analysis, in consequence, scientists who concern the reliability of their results will benefit from it. Under the assumption of normally distributed noise, the posterior distribution evaluated at a discrete number of points becomes a multivariate normal distribution whose mean and covariance are analytically available, making inversions and calculation of uncertainty fast. Additionally, the hyper-parameters embedded in the model assumption can be optimized through a Bayesian Occam's Razor formalism and thereby automatically adjust the model complexity. This method is shown to produce convincing reconstructions and good agreements with independently calculated results from the Maximum Entropy and Equilibrium-Based Iterative Tomography Algorithm methods

Bayesian soft X-ray tomography using non-stationary Gaussian Processes

Science.gov (United States)

Li, Dong; Svensson, J.; Thomsen, H.; Medina, F.; Werner, A.; Wolf, R.

2013-08-01

In this study, a Bayesian based non-stationary Gaussian Process (GP) method for the inference of soft X-ray emissivity distribution along with its associated uncertainties has been developed. For the investigation of equilibrium condition and fast magnetohydrodynamic behaviors in nuclear fusion plasmas, it is of importance to infer, especially in the plasma center, spatially resolved soft X-ray profiles from a limited number of noisy line integral measurements. For this ill-posed inversion problem, Bayesian probability theory can provide a posterior probability distribution over all possible solutions under given model assumptions. Specifically, the use of a non-stationary GP to model the emission allows the model to adapt to the varying length scales of the underlying diffusion process. In contrast to other conventional methods, the prior regularization is realized in a probability form which enhances the capability of uncertainty analysis, in consequence, scientists who concern the reliability of their results will benefit from it. Under the assumption of normally distributed noise, the posterior distribution evaluated at a discrete number of points becomes a multivariate normal distribution whose mean and covariance are analytically available, making inversions and calculation of uncertainty fast. Additionally, the hyper-parameters embedded in the model assumption can be optimized through a Bayesian Occam's Razor formalism and thereby automatically adjust the model complexity. This method is shown to produce convincing reconstructions and good agreements with independently calculated results from the Maximum Entropy and Equilibrium-Based Iterative Tomography Algorithm methods.

Bayesian artificial intelligence

CERN Document Server

Korb, Kevin B

2003-01-01

As the power of Bayesian techniques has become more fully realized, the field of artificial intelligence has embraced Bayesian methodology and integrated it to the point where an introduction to Bayesian techniques is now a core course in many computer science programs. Unlike other books on the subject, Bayesian Artificial Intelligence keeps mathematical detail to a minimum and covers a broad range of topics. The authors integrate all of Bayesian net technology and learning Bayesian net technology and apply them both to knowledge engineering. They emphasize understanding and intuition but also provide the algorithms and technical background needed for applications. Software, exercises, and solutions are available on the authors' website.

Bayesian inference on genetic merit under uncertain paternity

Directory of Open Access Journals (Sweden)

Tempelman Robert J

2003-09-01

Full Text Available Abstract A hierarchical animal model was developed for inference on genetic merit of livestock with uncertain paternity. Fully conditional posterior distributions for fixed and genetic effects, variance components, sire assignments and their probabilities are derived to facilitate a Bayesian inference strategy using MCMC methods. We compared this model to a model based on the Henderson average numerator relationship (ANRM in a simulation study with 10 replicated datasets generated for each of two traits. Trait 1 had a medium heritability (h2 for each of direct and maternal genetic effects whereas Trait 2 had a high h2 attributable only to direct effects. The average posterior probabilities inferred on the true sire were between 1 and 10% larger than the corresponding priors (the inverse of the number of candidate sires in a mating pasture for Trait 1 and between 4 and 13% larger than the corresponding priors for Trait 2. The predicted additive and maternal genetic effects were very similar using both models; however, model choice criteria (Pseudo Bayes Factor and Deviance Information Criterion decisively favored the proposed hierarchical model over the ANRM model.

Inferring cetacean population densities from the absolute dynamic topography of the ocean in a hierarchical Bayesian framework.

Directory of Open Access Journals (Sweden)

Mario A Pardo

Full Text Available We inferred the population densities of blue whales (Balaenoptera musculus and short-beaked common dolphins (Delphinus delphis in the Northeast Pacific Ocean as functions of the water-column's physical structure by implementing hierarchical models in a Bayesian framework. This approach allowed us to propagate the uncertainty of the field observations into the inference of species-habitat relationships and to generate spatially explicit population density predictions with reduced effects of sampling heterogeneity. Our hypothesis was that the large-scale spatial distributions of these two cetacean species respond primarily to ecological processes resulting from shoaling and outcropping of the pycnocline in regions of wind-forced upwelling and eddy-like circulation. Physically, these processes affect the thermodynamic balance of the water column, decreasing its volume and thus the height of the absolute dynamic topography (ADT. Biologically, they lead to elevated primary productivity and persistent aggregation of low-trophic-level prey. Unlike other remotely sensed variables, ADT provides information about the structure of the entire water column and it is also routinely measured at high spatial-temporal resolution by satellite altimeters with uniform global coverage. Our models provide spatially explicit population density predictions for both species, even in areas where the pycnocline shoals but does not outcrop (e.g. the Costa Rica Dome and the North Equatorial Countercurrent thermocline ridge. Interannual variations in distribution during El Niño anomalies suggest that the population density of both species decreases dramatically in the Equatorial Cold Tongue and the Costa Rica Dome, and that their distributions retract to particular areas that remain productive, such as the more oceanic waters in the central California Current System, the northern Gulf of California, the North Equatorial Countercurrent thermocline ridge, and the more

A Bayesian, generalized frailty model for comet assays.

Science.gov (United States)

Ghebretinsae, Aklilu Habteab; Faes, Christel; Molenberghs, Geert; De Boeck, Marlies; Geys, Helena

2013-05-01

This paper proposes a flexible modeling approach for so-called comet assay data regularly encountered in preclinical research. While such data consist of non-Gaussian outcomes in a multilevel hierarchical structure, traditional analyses typically completely or partly ignore this hierarchical nature by summarizing measurements within a cluster. Non-Gaussian outcomes are often modeled using exponential family models. This is true not only for binary and count data, but also for, example, time-to-event outcomes. Two important reasons for extending this family are for (1) the possible occurrence of overdispersion, meaning that the variability in the data may not be adequately described by the models, which often exhibit a prescribed mean-variance link, and (2) the accommodation of a hierarchical structure in the data, owing to clustering in the data. The first issue is dealt with through so-called overdispersion models. Clustering is often accommodated through the inclusion of random subject-specific effects. Though not always, one conventionally assumes such random effects to be normally distributed. In the case of time-to-event data, one encounters, for example, the gamma frailty model (Duchateau and Janssen, 2007 ). While both of these issues may occur simultaneously, models combining both are uncommon. Molenberghs et al. ( 2010 ) proposed a broad class of generalized linear models accommodating overdispersion and clustering through two separate sets of random effects. Here, we use this method to model data from a comet assay with a three-level hierarchical structure. Although a conjugate gamma random effect is used for the overdispersion random effect, both gamma and normal random effects are considered for the hierarchical random effect. Apart from model formulation, we place emphasis on Bayesian estimation. Our proposed method has an upper hand over the traditional analysis in that it (1) uses the appropriate distribution stipulated in the literature; (2) deals

Bayesian inferences of generation and growth of corrosion defects on energy pipelines based on imperfect inspection data

International Nuclear Information System (INIS)

Qin, H.; Zhou, W.; Zhang, S.

2015-01-01

Stochastic process-based models are developed to characterize the generation and growth of metal-loss corrosion defects on oil and gas steel pipelines. The generation of corrosion defects over time is characterized by the non-homogenous Poisson process, and the growth of depths of individual defects is modeled by the non-homogenous gamma process (NHGP). The defect generation and growth models are formulated in a hierarchical Bayesian framework, whereby the parameters of the models are evaluated from the in-line inspection (ILI) data through the Bayesian updating by accounting for the probability of detection (POD) and measurement errors associated with the ILI data. The Markov Chain Monte Carlo (MCMC) simulation in conjunction with the data augmentation (DA) technique is employed to carry out the Bayesian updating. Numerical examples that involve simulated ILI data are used to illustrate and validate the proposed methodology. - Highlights: • Bayesian updating of growth and generation models of defects on energy pipelines. • Non-homogeneous Poisson process for defect generation. • Non-homogeneous gamma process for defect growth. • Updating based on inspection data with detecting and sizing uncertainties. • MCMC in conjunction with data augmentation technique employed for the updating.

Fast gradient-based methods for Bayesian reconstruction of transmission and emission PET images

International Nuclear Information System (INIS)

Mumcuglu, E.U.; Leahy, R.; Zhou, Z.; Cherry, S.R.

1994-01-01

The authors describe conjugate gradient algorithms for reconstruction of transmission and emission PET images. The reconstructions are based on a Bayesian formulation, where the data are modeled as a collection of independent Poisson random variables and the image is modeled using a Markov random field. A conjugate gradient algorithm is used to compute a maximum a posteriori (MAP) estimate of the image by maximizing over the posterior density. To ensure nonnegativity of the solution, a penalty function is used to convert the problem to one of unconstrained optimization. Preconditioners are used to enhance convergence rates. These methods generally achieve effective convergence in 15--25 iterations. Reconstructions are presented of an 18 FDG whole body scan from data collected using a Siemens/CTI ECAT931 whole body system. These results indicate significant improvements in emission image quality using the Bayesian approach, in comparison to filtered backprojection, particularly when reprojections of the MAP transmission image are used in place of the standard attenuation correction factors

Bayesian geostatistical modeling of leishmaniasis incidence in Brazil.

Directory of Open Access Journals (Sweden)

Dimitrios-Alexios Karagiannis-Voules

Full Text Available BACKGROUND: Leishmaniasis is endemic in 98 countries with an estimated 350 million people at risk and approximately 2 million cases annually. Brazil is one of the most severely affected countries. METHODOLOGY: We applied Bayesian geostatistical negative binomial models to analyze reported incidence data of cutaneous and visceral leishmaniasis in Brazil covering a 10-year period (2001-2010. Particular emphasis was placed on spatial and temporal patterns. The models were fitted using integrated nested Laplace approximations to perform fast approximate Bayesian inference. Bayesian variable selection was employed to determine the most important climatic, environmental, and socioeconomic predictors of cutaneous and visceral leishmaniasis. PRINCIPAL FINDINGS: For both types of leishmaniasis, precipitation and socioeconomic proxies were identified as important risk factors. The predicted number of cases in 2010 were 30,189 (standard deviation [SD]: 7,676 for cutaneous leishmaniasis and 4,889 (SD: 288 for visceral leishmaniasis. Our risk maps predicted the highest numbers of infected people in the states of Minas Gerais and Pará for visceral and cutaneous leishmaniasis, respectively. CONCLUSIONS/SIGNIFICANCE: Our spatially explicit, high-resolution incidence maps identified priority areas where leishmaniasis control efforts should be targeted with the ultimate goal to reduce disease incidence.

Discriminative Hierarchical K-Means Tree for Large-Scale Image Classification.

Science.gov (United States)

Chen, Shizhi; Yang, Xiaodong; Tian, Yingli

2015-09-01

A key challenge in large-scale image classification is how to achieve efficiency in terms of both computation and memory without compromising classification accuracy. The learning-based classifiers achieve the state-of-the-art accuracies, but have been criticized for the computational complexity that grows linearly with the number of classes. The nonparametric nearest neighbor (NN)-based classifiers naturally handle large numbers of categories, but incur prohibitively expensive computation and memory costs. In this brief, we present a novel classification scheme, i.e., discriminative hierarchical K-means tree (D-HKTree), which combines the advantages of both learning-based and NN-based classifiers. The complexity of the D-HKTree only grows sublinearly with the number of categories, which is much better than the recent hierarchical support vector machines-based methods. The memory requirement is the order of magnitude less than the recent Naïve Bayesian NN-based approaches. The proposed D-HKTree classification scheme is evaluated on several challenging benchmark databases and achieves the state-of-the-art accuracies, while with significantly lower computation cost and memory requirement.

Partial inversion of elliptic operator to speed up computation of likelihood in Bayesian inference

KAUST Repository

Litvinenko, Alexander

2017-08-09

In this paper, we speed up the solution of inverse problems in Bayesian settings. By computing the likelihood, the most expensive part of the Bayesian formula, one compares the available measurement data with the simulated data. To get simulated data, repeated solution of the forward problem is required. This could be a great challenge. Often, the available measurement is a functional $F(u)$ of the solution $u$ or a small part of $u$. Typical examples of $F(u)$ are the solution in a point, solution on a coarser grid, in a small subdomain, the mean value in a subdomain. It is a waste of computational resources to evaluate, first, the whole solution and then compute a part of it. In this work, we compute the functional $F(u)$ direct, without computing the full inverse operator and without computing the whole solution $u$. The main ingredients of the developed approach are the hierarchical domain decomposition technique, the finite element method and the Schur complements. To speed up computations and to reduce the storage cost, we approximate the forward operator and the Schur complement in the hierarchical matrix format. Applying the hierarchical matrix technique, we reduced the computing cost to $\\\\mathcal{O}(k^2n \\\\log^2 n)$, where $k\\\\ll n$ and $n$ is the number of degrees of freedom. Up to the $\\\\H$-matrix accuracy, the computation of the functional $F(u)$ is exact. To reduce the computational resources further, we can approximate $F(u)$ on, for instance, multiple coarse meshes. The offered method is well suited for solving multiscale problems. A disadvantage of this method is the assumption that one has to have access to the discretisation and to the procedure of assembling the Galerkin matrix.

Bayesian Mediation Analysis

OpenAIRE

Yuan, Ying; MacKinnon, David P.

2009-01-01

This article proposes Bayesian analysis of mediation effects. Compared to conventional frequentist mediation analysis, the Bayesian approach has several advantages. First, it allows researchers to incorporate prior information into the mediation analysis, thus potentially improving the efficiency of estimates. Second, under the Bayesian mediation analysis, inference is straightforward and exact, which makes it appealing for studies with small samples. Third, the Bayesian approach is conceptua...

Global trends and factors associated with the illegal killing of elephants: A hierarchical bayesian analysis of carcass encounter data.

Science.gov (United States)

Burn, Robert W; Underwood, Fiona M; Blanc, Julian

2011-01-01

Elephant poaching and the ivory trade remain high on the agenda at meetings of the Convention on International Trade in Endangered Species of Wild Fauna and Flora (CITES). Well-informed debates require robust estimates of trends, the spatial distribution of poaching, and drivers of poaching. We present an analysis of trends and drivers of an indicator of elephant poaching of all elephant species. The site-based monitoring system known as Monitoring the Illegal Killing of Elephants (MIKE), set up by the 10(th) Conference of the Parties of CITES in 1997, produces carcass encounter data reported mainly by anti-poaching patrols. Data analyzed were site by year totals of 6,337 carcasses from 66 sites in Africa and Asia from 2002-2009. Analysis of these observational data is a serious challenge to traditional statistical methods because of the opportunistic and non-random nature of patrols, and the heterogeneity across sites. Adopting a bayesian hierarchical modeling approach, we used the proportion of carcasses that were illegally killed (PIKE) as a poaching index, to estimate the trend and the effects of site- and country-level factors associated with poaching. Important drivers of illegal killing that emerged at country level were poor governance and low levels of human development, and at site level, forest cover and area of the site in regions where human population density is low. After a drop from 2002, PIKE remained fairly constant from 2003 until 2006, after which it increased until 2008. The results for 2009 indicate a decline. Sites with PIKE ranging from the lowest to the highest were identified. The results of the analysis provide a sound information base for scientific evidence-based decision making in the CITES process.

Global trends and factors associated with the illegal killing of elephants: A hierarchical bayesian analysis of carcass encounter data.

Directory of Open Access Journals (Sweden)

Robert W Burn

Full Text Available Elephant poaching and the ivory trade remain high on the agenda at meetings of the Convention on International Trade in Endangered Species of Wild Fauna and Flora (CITES. Well-informed debates require robust estimates of trends, the spatial distribution of poaching, and drivers of poaching. We present an analysis of trends and drivers of an indicator of elephant poaching of all elephant species. The site-based monitoring system known as Monitoring the Illegal Killing of Elephants (MIKE, set up by the 10(th Conference of the Parties of CITES in 1997, produces carcass encounter data reported mainly by anti-poaching patrols. Data analyzed were site by year totals of 6,337 carcasses from 66 sites in Africa and Asia from 2002-2009. Analysis of these observational data is a serious challenge to traditional statistical methods because of the opportunistic and non-random nature of patrols, and the heterogeneity across sites. Adopting a bayesian hierarchical modeling approach, we used the proportion of carcasses that were illegally killed (PIKE as a poaching index, to estimate the trend and the effects of site- and country-level factors associated with poaching. Important drivers of illegal killing that emerged at country level were poor governance and low levels of human development, and at site level, forest cover and area of the site in regions where human population density is low. After a drop from 2002, PIKE remained fairly constant from 2003 until 2006, after which it increased until 2008. The results for 2009 indicate a decline. Sites with PIKE ranging from the lowest to the highest were identified. The results of the analysis provide a sound information base for scientific evidence-based decision making in the CITES process.

Introduction to Bayesian statistics

CERN Document Server

Bolstad, William M

2017-01-01

There is a strong upsurge in the use of Bayesian methods in applied statistical analysis, yet most introductory statistics texts only present frequentist methods. Bayesian statistics has many important advantages that students should learn about if they are going into fields where statistics will be used. In this Third Edition, four newly-added chapters address topics that reflect the rapid advances in the field of Bayesian staistics. The author continues to provide a Bayesian treatment of introductory statistical topics, such as scientific data gathering, discrete random variables, robust Bayesian methods, and Bayesian approaches to inferenfe cfor discrete random variables, bionomial proprotion, Poisson, normal mean, and simple linear regression. In addition, newly-developing topics in the field are presented in four new chapters: Bayesian inference with unknown mean and variance; Bayesian inference for Multivariate Normal mean vector; Bayesian inference for Multiple Linear RegressionModel; and Computati...

High-speed hierarchical pipeline for radiological projection data acquisition

International Nuclear Information System (INIS)

Kang Kejun; Wang Jingjin; Xu Qichun; Gao Wenhuan; Fu Changqing

1993-01-01

Modern radiological imaging system needs fast data acquisition technology of high density projection acquiring. For this reason, a new type of pipeline, which has multi-stage and hierarchical structure, was developed. By this pipeline, the dead time of the data acquisition system was greatly reduced, and then the throughput of the whole system was increased

A BAYESIAN SPATIAL AND TEMPORAL MODELING APPROACH TO MAPPING GEOGRAPHIC VARIATION IN MORTALITY RATES FOR SUBNATIONAL AREAS WITH R-INLA.

Science.gov (United States)

Khana, Diba; Rossen, Lauren M; Hedegaard, Holly; Warner, Margaret

2018-01-01

Hierarchical Bayes models have been used in disease mapping to examine small scale geographic variation. State level geographic variation for less common causes of mortality outcomes have been reported however county level variation is rarely examined. Due to concerns about statistical reliability and confidentiality, county-level mortality rates based on fewer than 20 deaths are suppressed based on Division of Vital Statistics, National Center for Health Statistics (NCHS) statistical reliability criteria, precluding an examination of spatio-temporal variation in less common causes of mortality outcomes such as suicide rates (SRs) at the county level using direct estimates. Existing Bayesian spatio-temporal modeling strategies can be applied via Integrated Nested Laplace Approximation (INLA) in R to a large number of rare causes of mortality outcomes to enable examination of spatio-temporal variations on smaller geographic scales such as counties. This method allows examination of spatiotemporal variation across the entire U.S., even where the data are sparse. We used mortality data from 2005-2015 to explore spatiotemporal variation in SRs, as one particular application of the Bayesian spatio-temporal modeling strategy in R-INLA to predict year and county-specific SRs. Specifically, hierarchical Bayesian spatio-temporal models were implemented with spatially structured and unstructured random effects, correlated time effects, time varying confounders and space-time interaction terms in the software R-INLA, borrowing strength across both counties and years to produce smoothed county level SRs. Model-based estimates of SRs were mapped to explore geographic variation.

Reuse, Recycle, Reweigh: Combating Influenza through Efficient Sequential Bayesian Computation for Massive Data.

Science.gov (United States)

Tom, Jennifer A; Sinsheimer, Janet S; Suchard, Marc A

Massive datasets in the gigabyte and terabyte range combined with the availability of increasingly sophisticated statistical tools yield analyses at the boundary of what is computationally feasible. Compromising in the face of this computational burden by partitioning the dataset into more tractable sizes results in stratified analyses, removed from the context that justified the initial data collection. In a Bayesian framework, these stratified analyses generate intermediate realizations, often compared using point estimates that fail to account for the variability within and correlation between the distributions these realizations approximate. However, although the initial concession to stratify generally precludes the more sensible analysis using a single joint hierarchical model, we can circumvent this outcome and capitalize on the intermediate realizations by extending the dynamic iterative reweighting MCMC algorithm. In doing so, we reuse the available realizations by reweighting them with importance weights, recycling them into a now tractable joint hierarchical model. We apply this technique to intermediate realizations generated from stratified analyses of 687 influenza A genomes spanning 13 years allowing us to revisit hypotheses regarding the evolutionary history of influenza within a hierarchical statistical framework.

FuncPatch: a web server for the fast Bayesian inference of conserved functional patches in protein 3D structures.

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Huang, Yi-Fei; Golding, G Brian

2015-02-15

A number of statistical phylogenetic methods have been developed to infer conserved functional sites or regions in proteins. Many methods, e.g. Rate4Site, apply the standard phylogenetic models to infer site-specific substitution rates and totally ignore the spatial correlation of substitution rates in protein tertiary structures, which may reduce their power to identify conserved functional patches in protein tertiary structures when the sequences used in the analysis are highly similar. The 3D sliding window method has been proposed to infer conserved functional patches in protein tertiary structures, but the window size, which reflects the strength of the spatial correlation, must be predefined and is not inferred from data. We recently developed GP4Rate to solve these problems under the Bayesian framework. Unfortunately, GP4Rate is computationally slow. Here, we present an intuitive web server, FuncPatch, to perform a fast approximate Bayesian inference of conserved functional patches in protein tertiary structures. Both simulations and four case studies based on empirical data suggest that FuncPatch is a good approximation to GP4Rate. However, FuncPatch is orders of magnitudes faster than GP4Rate. In addition, simulations suggest that FuncPatch is potentially a useful tool complementary to Rate4Site, but the 3D sliding window method is less powerful than FuncPatch and Rate4Site. The functional patches predicted by FuncPatch in the four case studies are supported by experimental evidence, which corroborates the usefulness of FuncPatch. The software FuncPatch is freely available at the web site, http://info.mcmaster.ca/yifei/FuncPatch golding@mcmaster.ca Supplementary data are available at Bioinformatics online. © The Author 2014. Published by Oxford University Press. All rights reserved. For Permissions, please e-mail: journals.permissions@oup.com.

Hierarchical modelling of temperature and habitat size effects on population dynamics of North Atlantic cod

DEFF Research Database (Denmark)

Mantzouni, Irene; Sørensen, Helle; O'Hara, Robert B.

2010-01-01

and Beverton and Holt stock–recruitment (SR) models were extended by applying hierarchical methods, mixed-effects models, and Bayesian inference to incorporate the influence of these ecosystem factors on model parameters representing cod maximum reproductive rate and carrying capacity. We identified......Understanding how temperature affects cod (Gadus morhua) ecology is important for forecasting how populations will develop as climate changes in future. The effects of spawning-season temperature and habitat size on cod recruitment dynamics have been investigated across the North Atlantic. Ricker...

Online Dectection and Modeling of Safety Boundaries for Aerospace Application Using Bayesian Statistics

Science.gov (United States)

He, Yuning

2015-01-01

The behavior of complex aerospace systems is governed by numerous parameters. For safety analysis it is important to understand how the system behaves with respect to these parameter values. In particular, understanding the boundaries between safe and unsafe regions is of major importance. In this paper, we describe a hierarchical Bayesian statistical modeling approach for the online detection and characterization of such boundaries. Our method for classification with active learning uses a particle filter-based model and a boundary-aware metric for best performance. From a library of candidate shapes incorporated with domain expert knowledge, the location and parameters of the boundaries are estimated using advanced Bayesian modeling techniques. The results of our boundary analysis are then provided in a form understandable by the domain expert. We illustrate our approach using a simulation model of a NASA neuro-adaptive flight control system, as well as a system for the detection of separation violations in the terminal airspace.

Release the BEESTS: Bayesian Estimation of Ex-Gaussian STop-Signal Reaction Time Distributions

Directory of Open Access Journals (Sweden)

Dora eMatzke

2013-12-01

Full Text Available The stop-signal paradigm is frequently used to study response inhibition. Inthis paradigm, participants perform a two-choice response time task wherethe primary task is occasionally interrupted by a stop-signal that promptsparticipants to withhold their response. The primary goal is to estimatethe latency of the unobservable stop response (stop signal reaction timeor SSRT. Recently, Matzke, Dolan, Logan, Brown, and Wagenmakers (inpress have developed a Bayesian parametric approach that allows for theestimation of the entire distribution of SSRTs. The Bayesian parametricapproach assumes that SSRTs are ex-Gaussian distributed and uses Markovchain Monte Carlo sampling to estimate the parameters of the SSRT distri-bution. Here we present an efficient and user-friendly software implementa-tion of the Bayesian parametric approach —BEESTS— that can be appliedto individual as well as hierarchical stop-signal data. BEESTS comes withan easy-to-use graphical user interface and provides users with summarystatistics of the posterior distribution of the parameters as well various diag-nostic tools to assess the quality of the parameter estimates. The softwareis open source and runs on Windows and OS X operating systems. In sum,BEESTS allows experimental and clinical psychologists to estimate entiredistributions of SSRTs and hence facilitates the more rigorous analysis ofstop-signal data.

Support agnostic Bayesian matching pursuit for block sparse signals

KAUST Repository

Masood, Mudassir

2013-05-01

A fast matching pursuit method using a Bayesian approach is introduced for block-sparse signal recovery. This method performs Bayesian estimates of block-sparse signals even when the distribution of active blocks is non-Gaussian or unknown. It is agnostic to the distribution of active blocks in the signal and utilizes a priori statistics of additive noise and the sparsity rate of the signal, which are shown to be easily estimated from data and no user intervention is required. The method requires a priori knowledge of block partition and utilizes a greedy approach and order-recursive updates of its metrics to find the most dominant sparse supports to determine the approximate minimum mean square error (MMSE) estimate of the block-sparse signal. Simulation results demonstrate the power and robustness of our proposed estimator. © 2013 IEEE.

Statistical dynamics of ultradiffusion in hierarchical systems

International Nuclear Information System (INIS)

Gardner, S.

1987-01-01

In many types of disordered systems which exhibit frustration and competition, an ultrametric topology is found to exist in the space of allowable states. This ultrametric topology of states is associated with a hierarchical relaxation process called ultradiffusion. Ultradiffusion occurs in hierarchical non-linear (HNL) dynamical systems when constraints cause large scale, slow modes of motion to be subordinated to small scale, fast modes. Examples of ultradiffusion are found throughout condensed matter physics and critical phenomena (e.g. the states of spin glasses), in biophysics (e.g. the states of Hopfield networks) and in many other fields including layered computing based upon nonlinear dynamics. The statistical dynamics of ultradiffusion can be treated as a random walk on an ultrametric space. For reversible bifurcating ultrametric spaces the evolution equation governing the probability of a particle being found at site i at time t has a highly degenerate transition matrix. This transition matrix has a fractal geometry similar to the replica form proposed for spin glasses. The authors invert this fractal matrix using a recursive quad-tree (QT) method. Possible applications of hierarchical systems to communications and symbolic computing are discussed briefly

Looking for Sustainable Urban Mobility through Bayesian Networks

Directory of Open Access Journals (Sweden)

Giovanni Fusco

2004-11-01

Full Text Available There is no formalised theory of sustainable urban mobility systems. Observed patterns of urban mobility are often considered unsustainable. But we don’t know what a city with sustainable mobility should look like. It is nevertheless increasingly apparent that the urban mobility system plays an important role in the achievement of the city’s wider sustainability objectives.In this paper we explore the characteristics of sustainable urban mobility systems through the technique of Bayesian networks. At the frontier between multivariate statistics and artificial intelligence, Bayesian networks provide powerful models of causal knowledge in an uncertain context. Using data on urban structure, transportation offer, mobility demand, resource consumption and environmental externalities from seventy-five world cities, we developed a systemic model of the city-transportation-environment interaction in the form of a Bayesian network. The network could then be used to infer the features of the city with sustainable mobility.The Bayesian model indicates that the city with sustainable mobility is most probably a dense city with highly efficient transit and multimodal mobility. It produces high levels of accessibility without relying on a fast road network. The achievement of sustainability objectives for urban mobility is probably compatible with all socioeconomic contexts.By measuring the distance of world cities from the inferred sustainability profile, we finally derive a geography of sustainability for mobility systems. The cities closest to the sustainability profile are in Central Europe as well as in affluent countries of the Far East. Car-dependent American cities are the farthest from the desired sustainability profile.

Bayesian estimation of covariance matrices: Application to market risk management at EDF

International Nuclear Information System (INIS)

Jandrzejewski-Bouriga, M.

2012-01-01

In this thesis, we develop new methods of regularized covariance matrix estimation, under the Bayesian setting. The regularization methodology employed is first related to shrinkage. We investigate a new Bayesian modeling of covariance matrix, based on hierarchical inverse-Wishart distribution, and then derive different estimators under standard loss functions. Comparisons between shrunk and empirical estimators are performed in terms of frequentist performance under different losses. It allows us to highlight the critical importance of the definition of cost function and show the persistent effect of the shrinkage-type prior on inference. In a second time, we consider the problem of covariance matrix estimation in Gaussian graphical models. If the issue is well treated for the decomposable case, it is not the case if you also consider non-decomposable graphs. We then describe a Bayesian and operational methodology to carry out the estimation of covariance matrix of Gaussian graphical models, decomposable or not. This procedure is based on a new and objective method of graphical-model selection, combined with a constrained and regularized estimation of the covariance matrix of the model chosen. The procedures studied effectively manage missing data. These estimation techniques were applied to calculate the covariance matrices involved in the market risk management for portfolios of EDF (Electricity of France), in particular for problems of calculating Value-at-Risk or in Asset Liability Management. (author)

An analysis of the costs of treating schizophrenia in Spain: a hierarchical Bayesian approach.

Science.gov (United States)

Vázquez-Polo, Francisco-Jose; Negrín, Miguel; Cabasés, Juan M; Sánchez, Eduardo; Haro, Joseph M; Salvador-Carulla, Luis

2005-09-01

Health care decisions should incorporate cost of illness and treatment data, particularly for disorders such as schizophrenia with a high morbidity rate and a disproportionately low allocation of resources. Previous cost of illness analyses may have disregarded geographical aspects relevant for resource consumption and unit cost calculation. To compare the utilisation of resources and the care costs of schizophrenic patients in four mental-health districts in Spain (in Madrid, Catalonia, Navarra and Andalusia), and to analyse factors that determine the costs and the differences between areas. A treated prevalence bottom-up three year follow-up design was used for obtaining data concerning socio-demography, clinical evolution and the utilisation of services. 1997 reference prices were updated for years 1998-2000 in euros. We propose two different scenarios, varying in the prices applied. In the first (Scenario 0) the reference prices are those obtained for a single geographic area, and so the cost variations are only due to differences in the use of resources. In the second situation (Scenario 1), we analyse the variations in resource utilisation at different levels, using the prices applicable to each healthcare area. Bayesian hierarchical models are used to discuss the factors that determine such costs and the differences between geographic areas. In scenario 0, the estimated mean cost was 4918.948 euros for the first year. In scenario 1 the highest cost was in Gava (Catalonia) and the lowest in Loja (Andalusia). Mean costs were respectively 4547.24 and 2473.98 euros. With respect to the evolution of costs over time, we observed an increase during the second year and a reduction during the third year. Geographical differences appeared in follow-up costs. The variables related to lower treatment costs were: residence in the family household, higher patient age and being in work. On the contrary, the number of relapses is directly related to higher treatment costs

Fast Bayesian experimental design: Laplace-based importance sampling for the expected information gain

KAUST Repository

Beck, Joakim

2018-02-19

In calculating expected information gain in optimal Bayesian experimental design, the computation of the inner loop in the classical double-loop Monte Carlo requires a large number of samples and suffers from underflow if the number of samples is small. These drawbacks can be avoided by using an importance sampling approach. We present a computationally efficient method for optimal Bayesian experimental design that introduces importance sampling based on the Laplace method to the inner loop. We derive the optimal values for the method parameters in which the average computational cost is minimized for a specified error tolerance. We use three numerical examples to demonstrate the computational efficiency of our method compared with the classical double-loop Monte Carlo, and a single-loop Monte Carlo method that uses the Laplace approximation of the return value of the inner loop. The first demonstration example is a scalar problem that is linear in the uncertain parameter. The second example is a nonlinear scalar problem. The third example deals with the optimal sensor placement for an electrical impedance tomography experiment to recover the fiber orientation in laminate composites.

Fast Bayesian experimental design: Laplace-based importance sampling for the expected information gain

Science.gov (United States)

Beck, Joakim; Dia, Ben Mansour; Espath, Luis F. R.; Long, Quan; Tempone, Raúl

2018-06-01

In calculating expected information gain in optimal Bayesian experimental design, the computation of the inner loop in the classical double-loop Monte Carlo requires a large number of samples and suffers from underflow if the number of samples is small. These drawbacks can be avoided by using an importance sampling approach. We present a computationally efficient method for optimal Bayesian experimental design that introduces importance sampling based on the Laplace method to the inner loop. We derive the optimal values for the method parameters in which the average computational cost is minimized according to the desired error tolerance. We use three numerical examples to demonstrate the computational efficiency of our method compared with the classical double-loop Monte Carlo, and a more recent single-loop Monte Carlo method that uses the Laplace method as an approximation of the return value of the inner loop. The first example is a scalar problem that is linear in the uncertain parameter. The second example is a nonlinear scalar problem. The third example deals with the optimal sensor placement for an electrical impedance tomography experiment to recover the fiber orientation in laminate composites.

Bayesian biostatistics

CERN Document Server

Lesaffre, Emmanuel

2012-01-01

The growth of biostatistics has been phenomenal in recent years and has been marked by considerable technical innovation in both methodology and computational practicality. One area that has experienced significant growth is Bayesian methods. The growing use of Bayesian methodology has taken place partly due to an increasing number of practitioners valuing the Bayesian paradigm as matching that of scientific discovery. In addition, computational advances have allowed for more complex models to be fitted routinely to realistic data sets. Through examples, exercises and a combination of introd

Internal cycling, not external loading, decides the nutrient limitation in eutrophic lake: A dynamic model with temporal Bayesian hierarchical inference.

Science.gov (United States)

Wu, Zhen; Liu, Yong; Liang, Zhongyao; Wu, Sifeng; Guo, Huaicheng

2017-06-01

Lake eutrophication is associated with excessive anthropogenic nutrients (mainly nitrogen (N) and phosphorus (P)) and unobserved internal nutrient cycling. Despite the advances in understanding the role of external loadings, the contribution of internal nutrient cycling is still an open question. A dynamic mass-balance model was developed to simulate and measure the contributions of internal cycling and external loading. It was based on the temporal Bayesian Hierarchical Framework (BHM), where we explored the seasonal patterns in the dynamics of nutrient cycling processes and the limitation of N and P on phytoplankton growth in hyper-eutrophic Lake Dianchi, China. The dynamic patterns of the five state variables (Chla, TP, ammonia, nitrate and organic N) were simulated based on the model. Five parameters (algae growth rate, sediment exchange rate of N and P, nitrification rate and denitrification rate) were estimated based on BHM. The model provided a good fit to observations. Our model results highlighted the role of internal cycling of N and P in Lake Dianchi. The internal cycling processes contributed more than external loading to the N and P changes in the water column. Further insights into the nutrient limitation analysis indicated that the sediment exchange of P determined the P limitation. Allowing for the contribution of denitrification to N removal, N was the more limiting nutrient in most of the time, however, P was the more important nutrient for eutrophication management. For Lake Dianchi, it would not be possible to recover solely by reducing the external watershed nutrient load; the mechanisms of internal cycling should also be considered as an approach to inhibit the release of sediments and to enhance denitrification. Copyright © 2017 Elsevier Ltd. All rights reserved.

Bayesian data analysis for newcomers.

Science.gov (United States)

Kruschke, John K; Liddell, Torrin M

2018-02-01

This article explains the foundational concepts of Bayesian data analysis using virtually no mathematical notation. Bayesian ideas already match your intuitions from everyday reasoning and from traditional data analysis. Simple examples of Bayesian data analysis are presented that illustrate how the information delivered by a Bayesian analysis can be directly interpreted. Bayesian approaches to null-value assessment are discussed. The article clarifies misconceptions about Bayesian methods that newcomers might have acquired elsewhere. We discuss prior distributions and explain how they are not a liability but an important asset. We discuss the relation of Bayesian data analysis to Bayesian models of mind, and we briefly discuss what methodological problems Bayesian data analysis is not meant to solve. After you have read this article, you should have a clear sense of how Bayesian data analysis works and the sort of information it delivers, and why that information is so intuitive and useful for drawing conclusions from data.

How to practise Bayesian statistics outside the Bayesian church: What philosophy for Bayesian statistical modelling?

NARCIS (Netherlands)

Borsboom, D.; Haig, B.D.

2013-01-01

Unlike most other statistical frameworks, Bayesian statistical inference is wedded to a particular approach in the philosophy of science (see Howson & Urbach, 2006); this approach is called Bayesianism. Rather than being concerned with model fitting, this position in the philosophy of science

cudaBayesreg: Parallel Implementation of a Bayesian Multilevel Model for fMRI Data Analysis

Directory of Open Access Journals (Sweden)

Adelino R. Ferreira da Silva

2011-10-01

Full Text Available Graphic processing units (GPUs are rapidly gaining maturity as powerful general parallel computing devices. A key feature in the development of modern GPUs has been the advancement of the programming model and programming tools. Compute Unified Device Architecture (CUDA is a software platform for massively parallel high-performance computing on Nvidia many-core GPUs. In functional magnetic resonance imaging (fMRI, the volume of the data to be processed, and the type of statistical analysis to perform call for high-performance computing strategies. In this work, we present the main features of the R-CUDA package cudaBayesreg which implements in CUDA the core of a Bayesian multilevel model for the analysis of brain fMRI data. The statistical model implements a Gibbs sampler for multilevel/hierarchical linear models with a normal prior. The main contribution for the increased performance comes from the use of separate threads for fitting the linear regression model at each voxel in parallel. The R-CUDA implementation of the Bayesian model proposed here has been able to reduce significantly the run-time processing of Markov chain Monte Carlo (MCMC simulations used in Bayesian fMRI data analyses. Presently, cudaBayesreg is only configured for Linux systems with Nvidia CUDA support.

Bayesian Probability Theory

Science.gov (United States)

von der Linden, Wolfgang; Dose, Volker; von Toussaint, Udo

2014-06-01

Preface; Part I. Introduction: 1. The meaning of probability; 2. Basic definitions; 3. Bayesian inference; 4. Combinatrics; 5. Random walks; 6. Limit theorems; 7. Continuous distributions; 8. The central limit theorem; 9. Poisson processes and waiting times; Part II. Assigning Probabilities: 10. Transformation invariance; 11. Maximum entropy; 12. Qualified maximum entropy; 13. Global smoothness; Part III. Parameter Estimation: 14. Bayesian parameter estimation; 15. Frequentist parameter estimation; 16. The Cramer-Rao inequality; Part IV. Testing Hypotheses: 17. The Bayesian way; 18. The frequentist way; 19. Sampling distributions; 20. Bayesian vs frequentist hypothesis tests; Part V. Real World Applications: 21. Regression; 22. Inconsistent data; 23. Unrecognized signal contributions; 24. Change point problems; 25. Function estimation; 26. Integral equations; 27. Model selection; 28. Bayesian experimental design; Part VI. Probabilistic Numerical Techniques: 29. Numerical integration; 30. Monte Carlo methods; 31. Nested sampling; Appendixes; References; Index.

Robust Pseudo-Hierarchical Support Vector Clustering

DEFF Research Database (Denmark)

Hansen, Michael Sass; Sjöstrand, Karl; Olafsdóttir, Hildur

2007-01-01

Support vector clustering (SVC) has proven an efficient algorithm for clustering of noisy and high-dimensional data sets, with applications within many fields of research. An inherent problem, however, has been setting the parameters of the SVC algorithm. Using the recent emergence of a method...... for calculating the entire regularization path of the support vector domain description, we propose a fast method for robust pseudo-hierarchical support vector clustering (HSVC). The method is demonstrated to work well on generated data, as well as for detecting ischemic segments from multidimensional myocardial...

Variational Bayesian Learning for Wavelet Independent Component Analysis

Science.gov (United States)

Roussos, E.; Roberts, S.; Daubechies, I.

2005-11-01

In an exploratory approach to data analysis, it is often useful to consider the observations as generated from a set of latent generators or "sources" via a generally unknown mapping. For the noisy overcomplete case, where we have more sources than observations, the problem becomes extremely ill-posed. Solutions to such inverse problems can, in many cases, be achieved by incorporating prior knowledge about the problem, captured in the form of constraints. This setting is a natural candidate for the application of the Bayesian methodology, allowing us to incorporate "soft" constraints in a natural manner. The work described in this paper is mainly driven by problems in functional magnetic resonance imaging of the brain, for the neuro-scientific goal of extracting relevant "maps" from the data. This can be stated as a `blind' source separation problem. Recent experiments in the field of neuroscience show that these maps are sparse, in some appropriate sense. The separation problem can be solved by independent component analysis (ICA), viewed as a technique for seeking sparse components, assuming appropriate distributions for the sources. We derive a hybrid wavelet-ICA model, transforming the signals into a domain where the modeling assumption of sparsity of the coefficients with respect to a dictionary is natural. We follow a graphical modeling formalism, viewing ICA as a probabilistic generative model. We use hierarchical source and mixing models and apply Bayesian inference to the problem. This allows us to perform model selection in order to infer the complexity of the representation, as well as automatic denoising. Since exact inference and learning in such a model is intractable, we follow a variational Bayesian mean-field approach in the conjugate-exponential family of distributions, for efficient unsupervised learning in multi-dimensional settings. The performance of the proposed algorithm is demonstrated on some representative experiments.

Bayesian modeling of the mass and density of asteroids

Science.gov (United States)

Dotson, Jessie L.; Mathias, Donovan

2017-10-01

Mass and density are two of the fundamental properties of any object. In the case of near earth asteroids, knowledge about the mass of an asteroid is essential for estimating the risk due to (potential) impact and planning possible mitigation options. The density of an asteroid can illuminate the structure of the asteroid. A low density can be indicative of a rubble pile structure whereas a higher density can imply a monolith and/or higher metal content. The damage resulting from an impact of an asteroid with Earth depends on its interior structure in addition to its total mass, and as a result, density is a key parameter to understanding the risk of asteroid impact. Unfortunately, measuring the mass and density of asteroids is challenging and often results in measurements with large uncertainties. In the absence of mass / density measurements for a specific object, understanding the range and distribution of likely values can facilitate probabilistic assessments of structure and impact risk. Hierarchical Bayesian models have recently been developed to investigate the mass - radius relationship of exoplanets (Wolfgang, Rogers & Ford 2016) and to probabilistically forecast the mass of bodies large enough to establish hydrostatic equilibrium over a range of 9 orders of magnitude in mass (from planemos to main sequence stars; Chen & Kipping 2017). Here, we extend this approach to investigate the mass and densities of asteroids. Several candidate Bayesian models are presented, and their performance is assessed relative to a synthetic asteroid population. In addition, a preliminary Bayesian model for probablistically forecasting masses and densities of asteroids is presented. The forecasting model is conditioned on existing asteroid data and includes observational errors, hyper-parameter uncertainties and intrinsic scatter.

Hierarchical Bayesian modelling of gene expression time series across irregularly sampled replicates and clusters.

Science.gov (United States)

Hensman, James; Lawrence, Neil D; Rattray, Magnus

2013-08-20

Time course data from microarrays and high-throughput sequencing experiments require simple, computationally efficient and powerful statistical models to extract meaningful biological signal, and for tasks such as data fusion and clustering. Existing methodologies fail to capture either the temporal or replicated nature of the experiments, and often impose constraints on the data collection process, such as regularly spaced samples, or similar sampling schema across replications. We propose hierarchical Gaussian processes as a general model of gene expression time-series, with application to a variety of problems. In particular, we illustrate the method's capacity for missing data imputation, data fusion and clustering.The method can impute data which is missing both systematically and at random: in a hold-out test on real data, performance is significantly better than commonly used imputation methods. The method's ability to model inter- and intra-cluster variance leads to more biologically meaningful clusters. The approach removes the necessity for evenly spaced samples, an advantage illustrated on a developmental Drosophila dataset with irregular replications. The hierarchical Gaussian process model provides an excellent statistical basis for several gene-expression time-series tasks. It has only a few additional parameters over a regular GP, has negligible additional complexity, is easily implemented and can be integrated into several existing algorithms. Our experiments were implemented in python, and are available from the authors' website: http://staffwww.dcs.shef.ac.uk/people/J.Hensman/.

Theoretical evaluation of the detectability of random lesions in bayesian emission reconstruction

International Nuclear Information System (INIS)

Qi, Jinyi

2003-01-01

Detecting cancerous lesion is an important task in positron emission tomography (PET). Bayesian methods based on the maximum a posteriori principle (also called penalized maximum likelihood methods) have been developed to deal with the low signal to noise ratio in the emission data. Similar to the filter cut-off frequency in the filtered backprojection method, the prior parameters in Bayesian reconstruction control the resolution and noise trade-off and hence affect detectability of lesions in reconstructed images. Bayesian reconstructions are difficult to analyze because the resolution and noise properties are nonlinear and object-dependent. Most research has been based on Monte Carlo simulations, which are very time consuming. Building on the recent progress on the theoretical analysis of image properties of statistical reconstructions and the development of numerical observers, here we develop a theoretical approach for fast computation of lesion detectability in Bayesian reconstruction. The results can be used to choose the optimum hyperparameter for the maximum lesion detectability. New in this work is the use of theoretical expressions that explicitly model the statistical variation of the lesion and background without assuming that the object variation is (locally) stationary. The theoretical results are validated using Monte Carlo simulations. The comparisons show good agreement between the theoretical predications and the Monte Carlo results

Designing and testing inflationary models with Bayesian networks

Energy Technology Data Exchange (ETDEWEB)

Price, Layne C. [Carnegie Mellon Univ., Pittsburgh, PA (United States). Dept. of Physics; Auckland Univ. (New Zealand). Dept. of Physics; Peiris, Hiranya V. [Univ. College London (United Kingdom). Dept. of Physics and Astronomy; Frazer, Jonathan [DESY Hamburg (Germany). Theory Group; Univ. of the Basque Country, Bilbao (Spain). Dept. of Theoretical Physics; Basque Foundation for Science, Bilbao (Spain). IKERBASQUE; Easther, Richard [Auckland Univ. (New Zealand). Dept. of Physics

2015-11-15

Even simple inflationary scenarios have many free parameters. Beyond the variables appearing in the inflationary action, these include dynamical initial conditions, the number of fields, and couplings to other sectors. These quantities are often ignored but cosmological observables can depend on the unknown parameters. We use Bayesian networks to account for a large set of inflationary parameters, deriving generative models for the primordial spectra that are conditioned on a hierarchical set of prior probabilities describing the initial conditions, reheating physics, and other free parameters. We use N{sub f}-quadratic inflation as an illustrative example, finding that the number of e-folds N{sub *} between horizon exit for the pivot scale and the end of inflation is typically the most important parameter, even when the number of fields, their masses and initial conditions are unknown, along with possible conditional dependencies between these parameters.

Designing and testing inflationary models with Bayesian networks

Energy Technology Data Exchange (ETDEWEB)

Price, Layne C. [McWilliams Center for Cosmology, Department of Physics, Carnegie Mellon University, Pittsburgh, PA 15213 (United States); Peiris, Hiranya V. [Department of Physics and Astronomy, University College London, London WC1E 6BT (United Kingdom); Frazer, Jonathan [Deutsches Elektronen-Synchrotron DESY, Theory Group, 22603 Hamburg (Germany); Easther, Richard, E-mail: laynep@andrew.cmu.edu, E-mail: h.peiris@ucl.ac.uk, E-mail: jonathan.frazer@desy.de, E-mail: r.easther@auckland.ac.nz [Department of Physics, University of Auckland, Private Bag 92019, Auckland (New Zealand)

2016-02-01

Even simple inflationary scenarios have many free parameters. Beyond the variables appearing in the inflationary action, these include dynamical initial conditions, the number of fields, and couplings to other sectors. These quantities are often ignored but cosmological observables can depend on the unknown parameters. We use Bayesian networks to account for a large set of inflationary parameters, deriving generative models for the primordial spectra that are conditioned on a hierarchical set of prior probabilities describing the initial conditions, reheating physics, and other free parameters. We use N{sub f}-quadratic inflation as an illustrative example, finding that the number of e-folds N{sub *} between horizon exit for the pivot scale and the end of inflation is typically the most important parameter, even when the number of fields, their masses and initial conditions are unknown, along with possible conditional dependencies between these parameters.

Designing and testing inflationary models with Bayesian networks

International Nuclear Information System (INIS)

Price, Layne C.; Auckland Univ.; Peiris, Hiranya V.; Frazer, Jonathan; Univ. of the Basque Country, Bilbao; Basque Foundation for Science, Bilbao; Easther, Richard

2015-11-01

Even simple inflationary scenarios have many free parameters. Beyond the variables appearing in the inflationary action, these include dynamical initial conditions, the number of fields, and couplings to other sectors. These quantities are often ignored but cosmological observables can depend on the unknown parameters. We use Bayesian networks to account for a large set of inflationary parameters, deriving generative models for the primordial spectra that are conditioned on a hierarchical set of prior probabilities describing the initial conditions, reheating physics, and other free parameters. We use N f -quadratic inflation as an illustrative example, finding that the number of e-folds N * between horizon exit for the pivot scale and the end of inflation is typically the most important parameter, even when the number of fields, their masses and initial conditions are unknown, along with possible conditional dependencies between these parameters.

A Hierarchical Approach to Real-time Activity Recognition in Body Sensor Networks

DEFF Research Database (Denmark)

Wang, Liang; Gu, Tao; Tao, Xianping

2012-01-01

Real-time activity recognition in body sensor networks is an important and challenging task. In this paper, we propose a real-time, hierarchical model to recognize both simple gestures and complex activities using a wireless body sensor network. In this model, we rst use a fast and lightweight al...

Systemic antibiotics in the treatment of aggressive periodontitis. A systematic review and a Bayesian Network meta-analysis.

Science.gov (United States)

Rabelo, Cleverton Correa; Feres, Magda; Gonçalves, Cristiane; Figueiredo, Luciene C; Faveri, Marcelo; Tu, Yu-Kang; Chambrone, Leandro

2015-07-01

The aim of this study was to assess the effect of systemic antibiotic therapy on the treatment of aggressive periodontitis (AgP). This study was conducted and reported in accordance with the PRISMA statement. The MEDLINE, EMBASE and CENTRAL databases were searched up to June 2014 for randomized clinical trials comparing the treatment of subjects with AgP with either scaling and root planing (SRP) alone or associated with systemic antibiotics. Bayesian network meta-analysis was prepared using the Bayesian random-effects hierarchical models and the outcomes reported at 6-month post-treatment. Out of 350 papers identified, 14 studies were eligible. Greater gain in clinical attachment (CA) (mean difference [MD]: 1.08 mm; p benefits in CA gain and PD reduction when SRP was associated with systemic antibiotics. SRP plus systemic antibiotics led to an additional clinical effect compared with SRP alone in the treatment of AgP. Of the antibiotic protocols available for inclusion into the Bayesian network meta-analysis, Mtz and Mtz/Amx provided to the most beneficial outcomes. © 2015 John Wiley & Sons A/S. Published by John Wiley & Sons Ltd.

Bayesian benefits with JASP

NARCIS (Netherlands)

Marsman, M.; Wagenmakers, E.-J.

2017-01-01

We illustrate the Bayesian approach to data analysis using the newly developed statistical software program JASP. With JASP, researchers are able to take advantage of the benefits that the Bayesian framework has to offer in terms of parameter estimation and hypothesis testing. The Bayesian

Scalable Hierarchical Algorithms for stochastic PDEs and UQ

KAUST Repository

Litvinenko, Alexander

2015-01-07

H-matrices and Fast Multipole (FMM) are powerful methods to approximate linear operators coming from partial differential and integral equations as well as speed up computational cost from quadratic or cubic to log-linear (O(n log n)), where n number of degrees of freedom in the discretization. The storage is reduced to the log-linear as well. This hierarchical structure is a good starting point for parallel algorithms. Parallelization on shared and distributed memory systems was pioneered by Kriemann [1,2]. Since 2005, the area of parallel architectures and software is developing very fast. Progress in GPUs and Many-Core Systems (e.g. XeonPhi with 64 cores) motivated us to extend work started in [1,2,7,8].

A self-defining hierarchical data system

Science.gov (United States)

Bailey, J.

1992-01-01

The Self-Defining Data System (SDS) is a system which allows the creation of self-defining hierarchical data structures in a form which allows the data to be moved between different machine architectures. Because the structures are self-defining they can be used for communication between independent modules in a distributed system. Unlike disk-based hierarchical data systems such as Starlink's HDS, SDS works entirely in memory and is very fast. Data structures are created and manipulated as internal dynamic structures in memory managed by SDS itself. A structure may then be exported into a caller supplied memory buffer in a defined external format. This structure can be written as a file or sent as a message to another machine. It remains static in structure until it is reimported into SDS. SDS is written in portable C and has been run on a number of different machine architectures. Structures are portable between machines with SDS looking after conversion of byte order, floating point format, and alignment. A Fortran callable version is also available for some machines.

Segmental Bayesian estimation of gap-junctional and inhibitory conductance of inferior olive neurons from spike trains with complicated dynamics

Directory of Open Access Journals (Sweden)

Huu eHoang

2015-05-01

Full Text Available The inverse problem for estimating model parameters from brain spike data is an ill-posed problem because of a huge mismatch in the system complexity between the model and the brain as well as its non-stationary dynamics, and needs a stochastic approach that finds the most likely solution among many possible solutions. In the present study, we developed a segmental Bayesian method to estimate the two parameters of interest, the gap-junctional (gc and inhibitory conductance (gi from inferior olive spike data. Feature vectors were estimated for the spike data in a segment-wise fashion to compensate for the non-stationary firing dynamics. Hierarchical Bayesian estimation was conducted to estimate the gc and gi for every spike segment using a forward model constructed in the principal component analysis (PCA space of the feature vectors, and to merge the segmental estimates into single estimates for every neuron. The segmental Bayesian estimation gave smaller fitting errors than the conventional Bayesian inference, which finds the estimates once across the entire spike data, or the minimum error method, which directly finds the closest match in the PCA space. The segmental Bayesian inference has the potential to overcome the problem of non-stationary dynamics and resolve the ill-posedness of the inverse problem because of the mismatch between the model and the brain under the constraints based, and it is a useful tool to evaluate parameters of interest for neuroscience from experimental spike train data.

Social Influence on Information Technology Adoption and Sustained Use in Healthcare: A Hierarchical Bayesian Learning Method Analysis

Science.gov (United States)

Hao, Haijing

2013-01-01

Information technology adoption and diffusion is currently a significant challenge in the healthcare delivery setting. This thesis includes three papers that explore social influence on information technology adoption and sustained use in the healthcare delivery environment using conventional regression models and novel hierarchical Bayesian…

Facile synthesis of three dimensional hierarchical Co-Al layered double hydroxides on graphene as high-performance materials for supercapacitor electrode.

Science.gov (United States)

Hao, Jinhui; Yang, Wenshu; Zhang, Zhe; Lu, Baoping; Ke, Xi; Zhang, Bailin; Tang, Jilin

2014-07-15

A facile simple hydrothermal method combined with a post-solution reaction is developed to grow interconnected three dimensional (3D) hierarchical Co-Al layered double hydroxides (LDHs) on reduced graphene oxide (rGO). The obtained 3D hierarchical rGO-LDHs are characterized by field emission scanning electron microscopy, X-ray diffraction, and X-ray photo-electron spectroscopy. As LDHs nanosheets directly grow on the surface of rGO via chemical covalent bonding, the rGO could provide facile electron transport paths in the electrode for the fast Faradaic reaction. Moreover, benefiting from the rational 3D hierarchical structural, the rGO-LDHs demonstrate excellent electrochemical properties with a combination of high charge storage capacitance, fast rate capability and stable cycling performance. Remarkably, the 3D hierarchical rGO-LDHs exhibit specific capacitance values of 599 F g(-1) at a constant current density of 4 A g(-1). The rGO-LDHs also show high charge-discharge reversibility with an efficiency of 92.4% after 5000 cycles. Copyright © 2014 Elsevier Inc. All rights reserved.

Bayesian estimation and use of high-throughput remote sensing indices for quantitative genetic analyses of leaf growth.

Science.gov (United States)

Baker, Robert L; Leong, Wen Fung; An, Nan; Brock, Marcus T; Rubin, Matthew J; Welch, Stephen; Weinig, Cynthia

2018-02-01

importance for evolutionary biologists and plant breeders, hierarchical Bayesian models estimating FVT parameters improve heritabilities compared to frequentist approaches.

Bayesian optimization for materials science

CERN Document Server

Packwood, Daniel

2017-01-01

This book provides a short and concise introduction to Bayesian optimization specifically for experimental and computational materials scientists. After explaining the basic idea behind Bayesian optimization and some applications to materials science in Chapter 1, the mathematical theory of Bayesian optimization is outlined in Chapter 2. Finally, Chapter 3 discusses an application of Bayesian optimization to a complicated structure optimization problem in computational surface science. Bayesian optimization is a promising global optimization technique that originates in the field of machine learning and is starting to gain attention in materials science. For the purpose of materials design, Bayesian optimization can be used to predict new materials with novel properties without extensive screening of candidate materials. For the purpose of computational materials science, Bayesian optimization can be incorporated into first-principles calculations to perform efficient, global structure optimizations. While re...

Evaluation of spatio-temporal Bayesian models for the spread of infectious diseases in oil palm.

Science.gov (United States)

Denis, Marie; Cochard, Benoît; Syahputra, Indra; de Franqueville, Hubert; Tisné, Sébastien

2018-02-01

In the field of epidemiology, studies are often focused on mapping diseases in relation to time and space. Hierarchical modeling is a common flexible and effective tool for modeling problems related to disease spread. In the context of oil palm plantations infected by the fungal pathogen Ganoderma boninense, we propose and compare two spatio-temporal hierarchical Bayesian models addressing the lack of information on propagation modes and transmission vectors. We investigate two alternative process models to study the unobserved mechanism driving the infection process. The models help gain insight into the spatio-temporal dynamic of the infection by identifying a genetic component in the disease spread and by highlighting a spatial component acting at the end of the experiment. In this challenging context, we propose models that provide assumptions on the unobserved mechanism driving the infection process while making short-term predictions using ready-to-use software. Copyright © 2018 Elsevier Ltd. All rights reserved.

Prediction of community prevalence of human onchocerciasis in the Amazonian onchocerciasis focus: Bayesian approach.

Science.gov (United States)

Carabin, Hélène; Escalona, Marisela; Marshall, Clare; Vivas-Martínez, Sarai; Botto, Carlos; Joseph, Lawrence; Basáñez, María-Gloria

2003-01-01

To develop a Bayesian hierarchical model for human onchocerciasis with which to explore the factors that influence prevalence of microfilariae in the Amazonian focus of onchocerciasis and predict the probability of any community being at least mesoendemic (>20% prevalence of microfilariae), and thus in need of priority ivermectin treatment. Models were developed with data from 732 individuals aged > or =15 years who lived in 29 Yanomami communities along four rivers of the south Venezuelan Orinoco basin. The models' abilities to predict prevalences of microfilariae in communities were compared. The deviance information criterion, Bayesian P-values, and residual values were used to select the best model with an approximate cross-validation procedure. A three-level model that acknowledged clustering of infection within communities performed best, with host age and sex included at the individual level, a river-dependent altitude effect at the community level, and additional clustering of communities along rivers. This model correctly classified 25/29 (86%) villages with respect to their need for priority ivermectin treatment. Bayesian methods are a flexible and useful approach for public health research and control planning. Our model acknowledges the clustering of infection within communities, allows investigation of links between individual- or community-specific characteristics and infection, incorporates additional uncertainty due to missing covariate data, and informs policy decisions by predicting the probability that a new community is at least mesoendemic.

Understanding Computational Bayesian Statistics

CERN Document Server

Bolstad, William M

2011-01-01

A hands-on introduction to computational statistics from a Bayesian point of view Providing a solid grounding in statistics while uniquely covering the topics from a Bayesian perspective, Understanding Computational Bayesian Statistics successfully guides readers through this new, cutting-edge approach. With its hands-on treatment of the topic, the book shows how samples can be drawn from the posterior distribution when the formula giving its shape is all that is known, and how Bayesian inferences can be based on these samples from the posterior. These ideas are illustrated on common statistic

Bayesian statistics an introduction

CERN Document Server

Lee, Peter M

2012-01-01

Bayesian Statistics is the school of thought that combines prior beliefs with the likelihood of a hypothesis to arrive at posterior beliefs. The first edition of Peter Lee’s book appeared in 1989, but the subject has moved ever onwards, with increasing emphasis on Monte Carlo based techniques. This new fourth edition looks at recent techniques such as variational methods, Bayesian importance sampling, approximate Bayesian computation and Reversible Jump Markov Chain Monte Carlo (RJMCMC), providing a concise account of the way in which the Bayesian approach to statistics develops as wel

Spatio-temporal interpolation of precipitation during monsoon periods in Pakistan

Science.gov (United States)

Hussain, Ijaz; Spöck, Gunter; Pilz, Jürgen; Yu, Hwa-Lung

2010-08-01

Spatio-temporal estimation of precipitation over a region is essential to the modeling of hydrologic processes for water resources management. The changes of magnitude and space-time heterogeneity of rainfall observations make space-time estimation of precipitation a challenging task. In this paper we propose a Box-Cox transformed hierarchical Bayesian multivariate spatio-temporal interpolation method for the skewed response variable. The proposed method is applied to estimate space-time monthly precipitation in the monsoon periods during 1974-2000, and 27-year monthly average precipitation data are obtained from 51 stations in Pakistan. The results of transformed hierarchical Bayesian multivariate spatio-temporal interpolation are compared to those of non-transformed hierarchical Bayesian interpolation by using cross-validation. The software developed by [11] is used for Bayesian non-stationary multivariate space-time interpolation. It is observed that the transformed hierarchical Bayesian method provides more accuracy than the non-transformed hierarchical Bayesian method.

Bayesian networks with examples in R

CERN Document Server

Scutari, Marco

2014-01-01

Introduction. The Discrete Case: Multinomial Bayesian Networks. The Continuous Case: Gaussian Bayesian Networks. More Complex Cases. Theory and Algorithms for Bayesian Networks. Real-World Applications of Bayesian Networks. Appendices. Bibliography.

A Bayesian nonparametric approach to reconstruction and prediction of random dynamical systems

Science.gov (United States)

Merkatas, Christos; Kaloudis, Konstantinos; Hatjispyros, Spyridon J.

2017-06-01

We propose a Bayesian nonparametric mixture model for the reconstruction and prediction from observed time series data, of discretized stochastic dynamical systems, based on Markov Chain Monte Carlo methods. Our results can be used by researchers in physical modeling interested in a fast and accurate estimation of low dimensional stochastic models when the size of the observed time series is small and the noise process (perhaps) is non-Gaussian. The inference procedure is demonstrated specifically in the case of polynomial maps of an arbitrary degree and when a Geometric Stick Breaking mixture process prior over the space of densities, is applied to the additive errors. Our method is parsimonious compared to Bayesian nonparametric techniques based on Dirichlet process mixtures, flexible and general. Simulations based on synthetic time series are presented.

A Bayesian nonparametric approach to reconstruction and prediction of random dynamical systems.

Science.gov (United States)

Merkatas, Christos; Kaloudis, Konstantinos; Hatjispyros, Spyridon J

2017-06-01

We propose a Bayesian nonparametric mixture model for the reconstruction and prediction from observed time series data, of discretized stochastic dynamical systems, based on Markov Chain Monte Carlo methods. Our results can be used by researchers in physical modeling interested in a fast and accurate estimation of low dimensional stochastic models when the size of the observed time series is small and the noise process (perhaps) is non-Gaussian. The inference procedure is demonstrated specifically in the case of polynomial maps of an arbitrary degree and when a Geometric Stick Breaking mixture process prior over the space of densities, is applied to the additive errors. Our method is parsimonious compared to Bayesian nonparametric techniques based on Dirichlet process mixtures, flexible and general. Simulations based on synthetic time series are presented.

Prior processes and their applications nonparametric Bayesian estimation

CERN Document Server

Phadia, Eswar G

2016-01-01

This book presents a systematic and comprehensive treatment of various prior processes that have been developed over the past four decades for dealing with Bayesian approach to solving selected nonparametric inference problems. This revised edition has been substantially expanded to reflect the current interest in this area. After an overview of different prior processes, it examines the now pre-eminent Dirichlet process and its variants including hierarchical processes, then addresses new processes such as dependent Dirichlet, local Dirichlet, time-varying and spatial processes, all of which exploit the countable mixture representation of the Dirichlet process. It subsequently discusses various neutral to right type processes, including gamma and extended gamma, beta and beta-Stacy processes, and then describes the Chinese Restaurant, Indian Buffet and infinite gamma-Poisson processes, which prove to be very useful in areas such as machine learning, information retrieval and featural modeling. Tailfree and P...

Tractography segmentation using a hierarchical Dirichlet processes mixture model.

Science.gov (United States)

Wang, Xiaogang; Grimson, W Eric L; Westin, Carl-Fredrik

2011-01-01

In this paper, we propose a new nonparametric Bayesian framework to cluster white matter fiber tracts into bundles using a hierarchical Dirichlet processes mixture (HDPM) model. The number of clusters is automatically learned driven by data with a Dirichlet process (DP) prior instead of being manually specified. After the models of bundles have been learned from training data without supervision, they can be used as priors to cluster/classify fibers of new subjects for comparison across subjects. When clustering fibers of new subjects, new clusters can be created for structures not observed in the training data. Our approach does not require computing pairwise distances between fibers and can cluster a huge set of fibers across multiple subjects. We present results on several data sets, the largest of which has more than 120,000 fibers. Copyright © 2010 Elsevier Inc. All rights reserved.

CTAB-Assisted Hydrothermal Synthesis of WO3 Hierarchical Porous Structures and Investigation of Their Sensing Properties

Directory of Open Access Journals (Sweden)

Dan Meng

2015-01-01

Full Text Available WO3 hierarchical porous structures were successfully synthesized via cetyltrimethylammonium bromide- (CTAB- assisted hydrothermal method. The structure and morphology were investigated using scanning electron microscope, X-ray diffractometer, transmission electron microscopy, X-ray photoelectron spectra, Brunauer-Emmett-Teller nitrogen adsorption-desorption, and thermogravimetry and differential thermal analysis. The result demonstrated that WO3 hierarchical porous structures with an orthorhombic structure were constructed by a number of nanoparticles about 50–100 nm in diameters. The H2 gas sensing measurements showed that well-defined WO3 hierarchical porous structures with a large specific surface area exhibited the higher sensitivity compared with products without CTAB at all operating temperatures. Moreover, the reversible and fast response to H2 gas and good selectivity were obtained. The results indicated that the WO3 hierarchical porous structures are promising materials for gas sensors.

Hierarchical model-based predictive control of a power plant portfolio

DEFF Research Database (Denmark)

Edlund, Kristian; Bendtsen, Jan Dimon; Jørgensen, John Bagterp

2011-01-01

One of the main difficulties in large-scale implementation of renewable energy in existing power systems is that the production from renewable sources is difficult to predict and control. For this reason, fast and efficient control of controllable power producing units – so-called “portfolio...... design for power system portfolio control, which aims specifically at meeting these demands.The design involves a two-layer hierarchical structure with clearly defined interfaces that facilitate an object-oriented implementation approach. The same hierarchical structure is reflected in the underlying...... optimisation problem, which is solved using Dantzig–Wolfe decomposition. This decomposition yields improved computational efficiency and better scalability compared to centralised methods.The proposed control scheme is compared to an existing, state-of-the-art portfolio control system (operated by DONG Energy...

Mechanochemistry-assisted synthesis of hierarchical porous carbons applied as supercapacitors

Science.gov (United States)

Leistenschneider, Desirée; Jäckel, Nicolas; Hippauf, Felix; Presser, Volker

2017-01-01

A solvent-free synthesis of hierarchical porous carbons is conducted by a facile and fast mechanochemical reaction in a ball mill. By means of a mechanochemical ball-milling approach, we obtained titanium(IV) citrate-based polymers, which have been processed via high temperature chlorine treatment to hierarchical porous carbons with a high specific surface area of up to 1814 m2 g−1 and well-defined pore structures. The carbons are applied as electrode materials in electric double-layer capacitors showing high specific capacitances with 98 F g−1 in organic and 138 F g−1 in an ionic liquid electrolyte as well as good rate capabilities, maintaining 87% of the initial capacitance with 1 M TEA-BF4 in acetonitrile (ACN) and 81% at 10 A g−1 in EMIM-BF4. PMID:28781699

Design of a fast runback feature for PRISM control

International Nuclear Information System (INIS)

Wagner, W.K.; Rhow, S.K.; Daniel, W.R.; Dayal, Y.; Gaubatz, D.C.

1988-01-01

The nine power reactor inherently safe modules (PRISM) are controlled and their operation coordinated by a hierarchical, distributed, digital plant control system (PCS). This paper describes the fast runback features of the PCS. Fast runback consists of PCS directed reactor module shutdown with accompanying reductions of coolant flows. Analyses have shown that the PCS fast runback adequately terminates duty cycle events initiated in the balance of plant and the steam generating system, results in lower thermal shock to the reactor than scram, and reduces the number of scrams by approximately a factor of five

Scalable Hierarchical Algorithms for stochastic PDEs and Uncertainty Quantification

KAUST Repository

Litvinenko, Alexander

2015-01-05

H-matrices and Fast Multipole (FMM) are powerful methods to approximate linear operators coming from partial differential and integral equations as well as speed up computational cost from quadratic or cubic to log-linear (O(n log n)), where n number of degrees of freedom in the discretization. The storage is reduced to the log-linear as well. This hierarchical structure is a good starting point for parallel algorithms. Parallelization on shared and distributed memory systems was pioneered by R. Kriemann, 2005. Since 2005, the area of parallel architectures and software is developing very fast. Progress in GPUs and Many-Core Systems (e.g. XeonPhi with 64 cores) motivated us to extend work started in [1,2,7,8].

Hierarchical ordering with partial pairwise hierarchical relationships on the macaque brain data sets.

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Woosang Lim

Full Text Available Hierarchical organizations of information processing in the brain networks have been known to exist and widely studied. To find proper hierarchical structures in the macaque brain, the traditional methods need the entire pairwise hierarchical relationships between cortical areas. In this paper, we present a new method that discovers hierarchical structures of macaque brain networks by using partial information of pairwise hierarchical relationships. Our method uses a graph-based manifold learning to exploit inherent relationship, and computes pseudo distances of hierarchical levels for every pair of cortical areas. Then, we compute hierarchy levels of all cortical areas by minimizing the sum of squared hierarchical distance errors with the hierarchical information of few cortical areas. We evaluate our method on the macaque brain data sets whose true hierarchical levels are known as the FV91 model. The experimental results show that hierarchy levels computed by our method are similar to the FV91 model, and its errors are much smaller than the errors of hierarchical clustering approaches.

Hierarchical modeling of active materials

International Nuclear Information System (INIS)

Taya, Minoru

2003-01-01

Intelligent (or smart) materials are increasingly becoming key materials for use in actuators and sensors. If an intelligent material is used as a sensor, it can be embedded in a variety of structure functioning as a health monitoring system to make their life longer with high reliability. If an intelligent material is used as an active material in an actuator, it plays a key role of making dynamic movement of the actuator under a set of stimuli. This talk intends to cover two different active materials in actuators, (1) piezoelectric laminate with FGM microstructure, (2) ferromagnetic shape memory alloy (FSMA). The advantage of using the FGM piezo laminate is to enhance its fatigue life while maintaining large bending displacement, while that of use in FSMA is its fast actuation while providing a large force and stroke capability. Use of hierarchical modeling of the above active materials is a key design step in optimizing its microstructure for enhancement of their performance. I will discuss briefly hierarchical modeling of the above two active materials. For FGM piezo laminate, we will use both micromechanical model and laminate theory, while for FSMA, the modeling interfacing nano-structure, microstructure and macro-behavior is discussed. (author)

Bayesian Mediation Analysis

Science.gov (United States)

Yuan, Ying; MacKinnon, David P.

2009-01-01

In this article, we propose Bayesian analysis of mediation effects. Compared with conventional frequentist mediation analysis, the Bayesian approach has several advantages. First, it allows researchers to incorporate prior information into the mediation analysis, thus potentially improving the efficiency of estimates. Second, under the Bayesian…

Evaluating impacts using a BACI design, ratios, and a Bayesian approach with a focus on restoration.

Science.gov (United States)

Conner, Mary M; Saunders, W Carl; Bouwes, Nicolaas; Jordan, Chris

2015-10-01

Before-after-control-impact (BACI) designs are an effective method to evaluate natural and human-induced perturbations on ecological variables when treatment sites cannot be randomly chosen. While effect sizes of interest can be tested with frequentist methods, using Bayesian Markov chain Monte Carlo (MCMC) sampling methods, probabilities of effect sizes, such as a ≥20 % increase in density after restoration, can be directly estimated. Although BACI and Bayesian methods are used widely for assessing natural and human-induced impacts for field experiments, the application of hierarchal Bayesian modeling with MCMC sampling to BACI designs is less common. Here, we combine these approaches and extend the typical presentation of results with an easy to interpret ratio, which provides an answer to the main study question-"How much impact did a management action or natural perturbation have?" As an example of this approach, we evaluate the impact of a restoration project, which implemented beaver dam analogs, on survival and density of juvenile steelhead. Results indicated the probabilities of a ≥30 % increase were high for survival and density after the dams were installed, 0.88 and 0.99, respectively, while probabilities for a higher increase of ≥50 % were variable, 0.17 and 0.82, respectively. This approach demonstrates a useful extension of Bayesian methods that can easily be generalized to other study designs from simple (e.g., single factor ANOVA, paired t test) to more complicated block designs (e.g., crossover, split-plot). This approach is valuable for estimating the probabilities of restoration impacts or other management actions.

Upper-Lower Bounds Candidate Sets Searching Algorithm for Bayesian Network Structure Learning

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Guangyi Liu

2014-01-01

Full Text Available Bayesian network is an important theoretical model in artificial intelligence field and also a powerful tool for processing uncertainty issues. Considering the slow convergence speed of current Bayesian network structure learning algorithms, a fast hybrid learning method is proposed in this paper. We start with further analysis of information provided by low-order conditional independence testing, and then two methods are given for constructing graph model of network, which is theoretically proved to be upper and lower bounds of the structure space of target network, so that candidate sets are given as a result; after that a search and scoring algorithm is operated based on the candidate sets to find the final structure of the network. Simulation results show that the algorithm proposed in this paper is more efficient than similar algorithms with the same learning precision.

Bayesian CP Factorization of Incomplete Tensors with Automatic Rank Determination.

Science.gov (United States)

Zhao, Qibin; Zhang, Liqing; Cichocki, Andrzej

2015-09-01

CANDECOMP/PARAFAC (CP) tensor factorization of incomplete data is a powerful technique for tensor completion through explicitly capturing the multilinear latent factors. The existing CP algorithms require the tensor rank to be manually specified, however, the determination of tensor rank remains a challenging problem especially for CP rank . In addition, existing approaches do not take into account uncertainty information of latent factors, as well as missing entries. To address these issues, we formulate CP factorization using a hierarchical probabilistic model and employ a fully Bayesian treatment by incorporating a sparsity-inducing prior over multiple latent factors and the appropriate hyperpriors over all hyperparameters, resulting in automatic rank determination. To learn the model, we develop an efficient deterministic Bayesian inference algorithm, which scales linearly with data size. Our method is characterized as a tuning parameter-free approach, which can effectively infer underlying multilinear factors with a low-rank constraint, while also providing predictive distributions over missing entries. Extensive simulations on synthetic data illustrate the intrinsic capability of our method to recover the ground-truth of CP rank and prevent the overfitting problem, even when a large amount of entries are missing. Moreover, the results from real-world applications, including image inpainting and facial image synthesis, demonstrate that our method outperforms state-of-the-art approaches for both tensor factorization and tensor completion in terms of predictive performance.

Molecular simulation of adsorption and transport in hierarchical porous materials.

Science.gov (United States)

Coasne, Benoit; Galarneau, Anne; Gerardin, Corine; Fajula, François; Villemot, François

2013-06-25

Adsorption and transport in hierarchical porous solids with micro- (~1 nm) and mesoporosities (>2 nm) are investigated by molecular simulation. Two models of hierarchical solids are considered: microporous materials in which mesopores are carved out (model A) and mesoporous materials in which microporous nanoparticles are inserted (model B). Adsorption isotherms for model A can be described as a linear combination of the adsorption isotherms for pure mesoporous and microporous solids. In contrast, adsorption in model B departs from adsorption in pure microporous and mesoporous solids; the inserted microporous particles act as defects, which help nucleate the liquid phase within the mesopore and shift capillary condensation toward lower pressures. As far as transport under a pressure gradient is concerned, the flux in hierarchical materials consisting of microporous solids in which mesopores are carved out obeys the Navier-Stokes equation so that Darcy's law is verified within the mesopore. Moreover, the flow in such materials is larger than in a single mesopore, due to the transfer between micropores and mesopores. This nonzero velocity at the mesopore surface implies that transport in such hierarchical materials involves slippage at the mesopore surface, although the adsorbate has a strong affinity for the surface. In contrast to model A, flux in model B is smaller than in a single mesopore, as the nanoparticles act as constrictions that hinder transport. By a subtle effect arising from fast transport in the mesopores, the presence of mesopores increases the number of molecules in the microporosity in hierarchical materials and, hence, decreases the flow in the micropores (due to mass conservation). As a result, we do not observe faster diffusion in the micropores of hierarchical materials upon flow but slower diffusion, which increases the contact time between the adsorbate and the surface of the microporosity.

Application of an efficient Bayesian discretization method to biomedical data

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Gopalakrishnan Vanathi

2011-07-01

Full Text Available Abstract Background Several data mining methods require data that are discrete, and other methods often perform better with discrete data. We introduce an efficient Bayesian discretization (EBD method for optimal discretization of variables that runs efficiently on high-dimensional biomedical datasets. The EBD method consists of two components, namely, a Bayesian score to evaluate discretizations and a dynamic programming search procedure to efficiently search the space of possible discretizations. We compared the performance of EBD to Fayyad and Irani's (FI discretization method, which is commonly used for discretization. Results On 24 biomedical datasets obtained from high-throughput transcriptomic and proteomic studies, the classification performances of the C4.5 classifier and the naïve Bayes classifier were statistically significantly better when the predictor variables were discretized using EBD over FI. EBD was statistically significantly more stable to the variability of the datasets than FI. However, EBD was less robust, though not statistically significantly so, than FI and produced slightly more complex discretizations than FI. Conclusions On a range of biomedical datasets, a Bayesian discretization method (EBD yielded better classification performance and stability but was less robust than the widely used FI discretization method. The EBD discretization method is easy to implement, permits the incorporation of prior knowledge and belief, and is sufficiently fast for application to high-dimensional data.

Intensity-based hierarchical clustering in CT-scans: application to interactive segmentation in cardiology

Science.gov (United States)

Hadida, Jonathan; Desrosiers, Christian; Duong, Luc

2011-03-01

The segmentation of anatomical structures in Computed Tomography Angiography (CTA) is a pre-operative task useful in image guided surgery. Even though very robust and precise methods have been developed to help achieving a reliable segmentation (level sets, active contours, etc), it remains very time consuming both in terms of manual interactions and in terms of computation time. The goal of this study is to present a fast method to find coarse anatomical structures in CTA with few parameters, based on hierarchical clustering. The algorithm is organized as follows: first, a fast non-parametric histogram clustering method is proposed to compute a piecewise constant mask. A second step then indexes all the space-connected regions in the piecewise constant mask. Finally, a hierarchical clustering is achieved to build a graph representing the connections between the various regions in the piecewise constant mask. This step builds up a structural knowledge about the image. Several interactive features for segmentation are presented, for instance association or disassociation of anatomical structures. A comparison with the Mean-Shift algorithm is presented.

High-performance supercapacitors based on hierarchically porous graphite particles

Energy Technology Data Exchange (ETDEWEB)

Chen, Zheng; Wen, Jing; Yan, Chunzhu; Rice, Lynn; Sohn, Hiesang; Lu, Yunfeng [Department of Chemical and Biomolecular Engineering, University of California, Los Angeles, CA 90095 (United States); Shen, Meiqing [School of Chemical Engineering and Technology, Tianjin University, Tianjin, 300072 (China); Cai, Mei [General Motor R and D Center, Warren, MI 48090 (United States); Dunn, Bruce [Department of Materials Science and Engineering, University of California, Los Angeles, CA 90095 (United States)

2011-07-15

Hierarchically porous graphite particles are synthesized using a continuous, scalable aerosol approach. The unique porous graphite architecture provides the particles with high surface area, fast ion transportation, and good electronic conductivity, which endows the resulting supercapacitors with high energy and power densities. This work provides a new material platform for high-performance supercapacitors with high packing density, and is adaptable to battery electrodes, fuel-cell catalyst supports, and other applications. (Copyright copyright 2011 WILEY-VCH Verlag GmbH and Co. KGaA, Weinheim)

Bayesian Inference on Gravitational Waves

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Asad Ali

2015-12-01

Full Text Available The Bayesian approach is increasingly becoming popular among the astrophysics data analysis communities. However, the Pakistan statistics communities are unaware of this fertile interaction between the two disciplines. Bayesian methods have been in use to address astronomical problems since the very birth of the Bayes probability in eighteenth century. Today the Bayesian methods for the detection and parameter estimation of gravitational waves have solid theoretical grounds with a strong promise for the realistic applications. This article aims to introduce the Pakistan statistics communities to the applications of Bayesian Monte Carlo methods in the analysis of gravitational wave data with an  overview of the Bayesian signal detection and estimation methods and demonstration by a couple of simplified examples.

Optimization of Bayesian Emission tomographic reconstruction for region of interest quantitation

International Nuclear Information System (INIS)

Qi, Jinyi

2003-01-01

Region of interest (ROI) quantitation is an important task in emission tomography (e.g., positron emission tomography and single photon emission computed tomography). It is essential for exploring clinical factors such as tumor activity, growth rate, and the efficacy of therapeutic interventions. Bayesian methods based on the maximum a posteriori principle (or called penalized maximum likelihood methods) have been developed for emission image reconstructions to deal with the low signal to noise ratio of the emission data. Similar to the filter cut-off frequency in the filtered backprojection method, the smoothing parameter of the image prior in Bayesian reconstruction controls the resolution and noise trade-off and hence affects ROI quantitation. In this paper we present an approach for choosing the optimum smoothing parameter in Bayesian reconstruction for ROI quantitation. Bayesian reconstructions are difficult to analyze because the resolution and noise properties are nonlinear and object-dependent. Building on the recent progress on deriving the approximate expressions for the local impulse response function and the covariance matrix, we derived simplied theoretical expressions for the bias, the variance, and the ensemble mean squared error (EMSE) of the ROI quantitation. One problem in evaluating ROI quantitation is that the truth is often required for calculating the bias. This is overcome by using ensemble distribution of the activity inside the ROI and computing the average EMSE. The resulting expressions allow fast evaluation of the image quality for different smoothing parameters. The optimum smoothing parameter of the image prior can then be selected to minimize the EMSE

Bayesian hierarchical modelling of continuous non-negative longitudinal data with a spike at zero: An application to a study of birds visiting gardens in winter.

Science.gov (United States)

Swallow, Ben; Buckland, Stephen T; King, Ruth; Toms, Mike P

2016-03-01

The development of methods for dealing with continuous data with a spike at zero has lagged behind those for overdispersed or zero-inflated count data. We consider longitudinal ecological data corresponding to an annual average of 26 weekly maximum counts of birds, and are hence effectively continuous, bounded below by zero but also with a discrete mass at zero. We develop a Bayesian hierarchical Tweedie regression model that can directly accommodate the excess number of zeros common to this type of data, whilst accounting for both spatial and temporal correlation. Implementation of the model is conducted in a Markov chain Monte Carlo (MCMC) framework, using reversible jump MCMC to explore uncertainty across both parameter and model spaces. This regression modelling framework is very flexible and removes the need to make strong assumptions about mean-variance relationships a priori. It can also directly account for the spike at zero, whilst being easily applicable to other types of data and other model formulations. Whilst a correlative study such as this cannot prove causation, our results suggest that an increase in an avian predator may have led to an overall decrease in the number of one of its prey species visiting garden feeding stations in the United Kingdom. This may reflect a change in behaviour of house sparrows to avoid feeding stations frequented by sparrowhawks, or a reduction in house sparrow population size as a result of sparrowhawk increase. © 2015 The Author. Biometrical Journal published by WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim.

Bayesian Reliability Analysis of Non-Stationarity in Multi-agent Systems

Directory of Open Access Journals (Sweden)

TONT Gabriela

2013-05-01

Full Text Available The Bayesian methods provide information about the meaningful parameters in a statistical analysis obtained by combining the prior and sampling distributions to form the posterior distribution of theparameters. The desired inferences are obtained from this joint posterior. An estimation strategy for hierarchical models, where the resulting joint distribution of the associated model parameters cannotbe evaluated analytically, is to use sampling algorithms, known as Markov Chain Monte Carlo (MCMC methods, from which approximate solutions can be obtained. Both serial and parallel configurations of subcomponents are permitted. The capability of time-dependent method to describe a multi-state system is based on a case study, assessingthe operatial situation of studied system. The rationality and validity of the presented model are demonstrated via a case of study. The effect of randomness of the structural parameters is alsoexamined.

Bayesian models and meta analysis for multiple tissue gene expression data following corticosteroid administration

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Kelemen Arpad

2008-08-01

Full Text Available Abstract Background This paper addresses key biological problems and statistical issues in the analysis of large gene expression data sets that describe systemic temporal response cascades to therapeutic doses in multiple tissues such as liver, skeletal muscle, and kidney from the same animals. Affymetrix time course gene expression data U34A are obtained from three different tissues including kidney, liver and muscle. Our goal is not only to find the concordance of gene in different tissues, identify the common differentially expressed genes over time and also examine the reproducibility of the findings by integrating the results through meta analysis from multiple tissues in order to gain a significant increase in the power of detecting differentially expressed genes over time and to find the differential differences of three tissues responding to the drug. Results and conclusion Bayesian categorical model for estimating the proportion of the 'call' are used for pre-screening genes. Hierarchical Bayesian Mixture Model is further developed for the identifications of differentially expressed genes across time and dynamic clusters. Deviance information criterion is applied to determine the number of components for model comparisons and selections. Bayesian mixture model produces the gene-specific posterior probability of differential/non-differential expression and the 95% credible interval, which is the basis for our further Bayesian meta-inference. Meta-analysis is performed in order to identify commonly expressed genes from multiple tissues that may serve as ideal targets for novel treatment strategies and to integrate the results across separate studies. We have found the common expressed genes in the three tissues. However, the up/down/no regulations of these common genes are different at different time points. Moreover, the most differentially expressed genes were found in the liver, then in kidney, and then in muscle.

Mechanochemistry-assisted synthesis of hierarchical porous carbons applied as supercapacitors

Directory of Open Access Journals (Sweden)

Desirée Leistenschneider

2017-07-01

Full Text Available A solvent-free synthesis of hierarchical porous carbons is conducted by a facile and fast mechanochemical reaction in a ball mill. By means of a mechanochemical ball-milling approach, we obtained titanium(IV citrate-based polymers, which have been processed via high temperature chlorine treatment to hierarchical porous carbons with a high specific surface area of up to 1814 m2 g−1 and well-defined pore structures. The carbons are applied as electrode materials in electric double-layer capacitors showing high specific capacitances with 98 F g−1 in organic and 138 F g−1 in an ionic liquid electrolyte as well as good rate capabilities, maintaining 87% of the initial capacitance with 1 M TEA-BF4 in acetonitrile (ACN and 81% at 10 A g−1 in EMIM-BF4.

Bayesian analysis in plant pathology.

Science.gov (United States)

Mila, A L; Carriquiry, A L

2004-09-01

ABSTRACT Bayesian methods are currently much discussed and applied in several disciplines from molecular biology to engineering. Bayesian inference is the process of fitting a probability model to a set of data and summarizing the results via probability distributions on the parameters of the model and unobserved quantities such as predictions for new observations. In this paper, after a short introduction of Bayesian inference, we present the basic features of Bayesian methodology using examples from sequencing genomic fragments and analyzing microarray gene-expressing levels, reconstructing disease maps, and designing experiments.

Diagnostics for generalized linear hierarchical models in network meta-analysis.

Science.gov (United States)

Zhao, Hong; Hodges, James S; Carlin, Bradley P

2017-09-01

Network meta-analysis (NMA) combines direct and indirect evidence comparing more than 2 treatments. Inconsistency arises when these 2 information sources differ. Previous work focuses on inconsistency detection, but little has been done on how to proceed after identifying inconsistency. The key issue is whether inconsistency changes an NMA's substantive conclusions. In this paper, we examine such discrepancies from a diagnostic point of view. Our methods seek to detect influential and outlying observations in NMA at a trial-by-arm level. These observations may have a large effect on the parameter estimates in NMA, or they may deviate markedly from other observations. We develop formal diagnostics for a Bayesian hierarchical model to check the effect of deleting any observation. Diagnostics are specified for generalized linear hierarchical NMA models and investigated for both published and simulated datasets. Results from our example dataset using either contrast- or arm-based models and from the simulated datasets indicate that the sources of inconsistency in NMA tend not to be influential, though results from the example dataset suggest that they are likely to be outliers. This mimics a familiar result from linear model theory, in which outliers with low leverage are not influential. Future extensions include incorporating baseline covariates and individual-level patient data. Copyright © 2017 John Wiley & Sons, Ltd.

Parallel iterative solvers and preconditioners using approximate hierarchical methods

Energy Technology Data Exchange (ETDEWEB)

Grama, A.; Kumar, V.; Sameh, A. [Univ. of Minnesota, Minneapolis, MN (United States)

1996-12-31

In this paper, we report results of the performance, convergence, and accuracy of a parallel GMRES solver for Boundary Element Methods. The solver uses a hierarchical approximate matrix-vector product based on a hybrid Barnes-Hut / Fast Multipole Method. We study the impact of various accuracy parameters on the convergence and show that with minimal loss in accuracy, our solver yields significant speedups. We demonstrate the excellent parallel efficiency and scalability of our solver. The combined speedups from approximation and parallelism represent an improvement of several orders in solution time. We also develop fast and paralellizable preconditioners for this problem. We report on the performance of an inner-outer scheme and a preconditioner based on truncated Green`s function. Experimental results on a 256 processor Cray T3D are presented.

Metastable states in the hierarchical Dyson model drive parallel processing in the hierarchical Hopfield network

International Nuclear Information System (INIS)

Agliari, Elena; Barra, Adriano; Guerra, Francesco; Galluzzi, Andrea; Tantari, Daniele; Tavani, Flavia

2015-01-01

In this paper, we introduce and investigate the statistical mechanics of hierarchical neural networks. First, we approach these systems à la Mattis, by thinking of the Dyson model as a single-pattern hierarchical neural network. We also discuss the stability of different retrievable states as predicted by the related self-consistencies obtained both from a mean-field bound and from a bound that bypasses the mean-field limitation. The latter is worked out by properly reabsorbing the magnetization fluctuations related to higher levels of the hierarchy into effective fields for the lower levels. Remarkably, mixing Amit's ansatz technique for selecting candidate-retrievable states with the interpolation procedure for solving for the free energy of these states, we prove that, due to gauge symmetry, the Dyson model accomplishes both serial and parallel processing. We extend this scenario to multiple stored patterns by implementing the Hebb prescription for learning within the couplings. This results in Hopfield-like networks constrained on a hierarchical topology, for which, by restricting to the low-storage regime where the number of patterns grows at its most logarithmical with the amount of neurons, we prove the existence of the thermodynamic limit for the free energy, and we give an explicit expression of its mean-field bound and of its related improved bound. We studied the resulting self-consistencies for the Mattis magnetizations, which act as order parameters, are studied and the stability of solutions is analyzed to get a picture of the overall retrieval capabilities of the system according to both mean-field and non-mean-field scenarios. Our main finding is that embedding the Hebbian rule on a hierarchical topology allows the network to accomplish both serial and parallel processing. By tuning the level of fast noise affecting it or triggering the decay of the interactions with the distance among neurons, the system may switch from sequential retrieval to

A surrogate-based sensitivity quantification and Bayesian inversion of a regional groundwater flow model

Science.gov (United States)

Chen, Mingjie; Izady, Azizallah; Abdalla, Osman A.; Amerjeed, Mansoor

2018-02-01

Bayesian inference using Markov Chain Monte Carlo (MCMC) provides an explicit framework for stochastic calibration of hydrogeologic models accounting for uncertainties; however, the MCMC sampling entails a large number of model calls, and could easily become computationally unwieldy if the high-fidelity hydrogeologic model simulation is time consuming. This study proposes a surrogate-based Bayesian framework to address this notorious issue, and illustrates the methodology by inverse modeling a regional MODFLOW model. The high-fidelity groundwater model is approximated by a fast statistical model using Bagging Multivariate Adaptive Regression Spline (BMARS) algorithm, and hence the MCMC sampling can be efficiently performed. In this study, the MODFLOW model is developed to simulate the groundwater flow in an arid region of Oman consisting of mountain-coast aquifers, and used to run representative simulations to generate training dataset for BMARS model construction. A BMARS-based Sobol' method is also employed to efficiently calculate input parameter sensitivities, which are used to evaluate and rank their importance for the groundwater flow model system. According to sensitivity analysis, insensitive parameters are screened out of Bayesian inversion of the MODFLOW model, further saving computing efforts. The posterior probability distribution of input parameters is efficiently inferred from the prescribed prior distribution using observed head data, demonstrating that the presented BMARS-based Bayesian framework is an efficient tool to reduce parameter uncertainties of a groundwater system.

Hierarchical Load Tracking Control of a Grid-connected Solid Oxide Fuel Cell for Maximum Electrical Efficiency Operation

DEFF Research Database (Denmark)

Li, Yonghui; Wu, Qiuwei; Zhu, Haiyu

2015-01-01

efficiency operation obtained at different active power output levels, a hierarchical load tracking control scheme for the grid-connected SOFC was proposed to realize the maximum electrical efficiency operation with the stack temperature bounded. The hierarchical control scheme consists of a fast active...... power control and a slower stack temperature control. The active power control was developed by using a decentralized control method. The efficiency of the proposed hierarchical control scheme was demonstrated by case studies using the benchmark SOFC dynamic model......Based on the benchmark solid oxide fuel cell (SOFC) dynamic model for power system studies and the analysis of the SOFC operating conditions, the nonlinear programming (NLP) optimization method was used to determine the maximum electrical efficiency of the grid-connected SOFC subject...

Estimation of breeding values for mean and dispersion, their variance and correlation using double hierarchical generalized linear models.

Science.gov (United States)

Felleki, M; Lee, D; Lee, Y; Gilmour, A R; Rönnegård, L

2012-12-01

The possibility of breeding for uniform individuals by selecting animals expressing a small response to environment has been studied extensively in animal breeding. Bayesian methods for fitting models with genetic components in the residual variance have been developed for this purpose, but have limitations due to the computational demands. We use the hierarchical (h)-likelihood from the theory of double hierarchical generalized linear models (DHGLM) to derive an estimation algorithm that is computationally feasible for large datasets. Random effects for both the mean and residual variance parts of the model are estimated together with their variance/covariance components. An important feature of the algorithm is that it can fit a correlation between the random effects for mean and variance. An h-likelihood estimator is implemented in the R software and an iterative reweighted least square (IRWLS) approximation of the h-likelihood is implemented using ASReml. The difference in variance component estimates between the two implementations is investigated, as well as the potential bias of the methods, using simulations. IRWLS gives the same results as h-likelihood in simple cases with no severe indication of bias. For more complex cases, only IRWLS could be used, and bias did appear. The IRWLS is applied on the pig litter size data previously analysed by Sorensen & Waagepetersen (2003) using Bayesian methodology. The estimates we obtained by using IRWLS are similar to theirs, with the estimated correlation between the random genetic effects being -0·52 for IRWLS and -0·62 in Sorensen & Waagepetersen (2003).

Bayesian model calibration of computational models in velocimetry diagnosed dynamic compression experiments.

Energy Technology Data Exchange (ETDEWEB)

Brown, Justin [Sandia National Lab. (SNL-NM), Albuquerque, NM (United States); Hund, Lauren [Sandia National Lab. (SNL-NM), Albuquerque, NM (United States)

2017-02-01

Dynamic compression experiments are being performed on complicated materials using increasingly complex drivers. The data produced in these experiments are beginning to reach a regime where traditional analysis techniques break down; requiring the solution of an inverse problem. A common measurement in dynamic experiments is an interface velocity as a function of time, and often this functional output can be simulated using a hydrodynamics code. Bayesian model calibration is a statistical framework to estimate inputs into a computational model in the presence of multiple uncertainties, making it well suited to measurements of this type. In this article, we apply Bayesian model calibration to high pressure (250 GPa) ramp compression measurements in tantalum. We address several issues speci c to this calibration including the functional nature of the output as well as parameter and model discrepancy identi ability. Speci cally, we propose scaling the likelihood function by an e ective sample size rather than modeling the autocorrelation function to accommodate the functional output and propose sensitivity analyses using the notion of `modularization' to assess the impact of experiment-speci c nuisance input parameters on estimates of material properties. We conclude that the proposed Bayesian model calibration procedure results in simple, fast, and valid inferences on the equation of state parameters for tantalum.

Bayesian computation with R

CERN Document Server

Albert, Jim

2009-01-01

There has been a dramatic growth in the development and application of Bayesian inferential methods. Some of this growth is due to the availability of powerful simulation-based algorithms to summarize posterior distributions. There has been also a growing interest in the use of the system R for statistical analyses. R's open source nature, free availability, and large number of contributor packages have made R the software of choice for many statisticians in education and industry. Bayesian Computation with R introduces Bayesian modeling by the use of computation using the R language. The earl

The Bayesian Score Statistic

NARCIS (Netherlands)

Kleibergen, F.R.; Kleijn, R.; Paap, R.

2000-01-01

We propose a novel Bayesian test under a (noninformative) Jeffreys'priorspecification. We check whether the fixed scalar value of the so-calledBayesian Score Statistic (BSS) under the null hypothesis is aplausiblerealization from its known and standardized distribution under thealternative. Unlike

Bayesian methods for proteomic biomarker development

Directory of Open Access Journals (Sweden)

Belinda Hernández

2015-12-01

In this review we provide an introduction to Bayesian inference and demonstrate some of the advantages of using a Bayesian framework. We summarize how Bayesian methods have been used previously in proteomics and other areas of bioinformatics. Finally, we describe some popular and emerging Bayesian models from the statistical literature and provide a worked tutorial including code snippets to show how these methods may be applied for the evaluation of proteomic biomarkers.

Current trends in Bayesian methodology with applications

CERN Document Server

Upadhyay, Satyanshu K; Dey, Dipak K; Loganathan, Appaia

2015-01-01

Collecting Bayesian material scattered throughout the literature, Current Trends in Bayesian Methodology with Applications examines the latest methodological and applied aspects of Bayesian statistics. The book covers biostatistics, econometrics, reliability and risk analysis, spatial statistics, image analysis, shape analysis, Bayesian computation, clustering, uncertainty assessment, high-energy astrophysics, neural networking, fuzzy information, objective Bayesian methodologies, empirical Bayes methods, small area estimation, and many more topics.Each chapter is self-contained and focuses on

Bayesian spatio-temporal discard model in a demersal trawl fishery

Science.gov (United States)

Grazia Pennino, M.; Muñoz, Facundo; Conesa, David; López-Quílez, Antonio; Bellido, José M.

2014-07-01

Spatial management of discards has recently been proposed as a useful tool for the protection of juveniles, by reducing discard rates and can be used as a buffer against management errors and recruitment failure. In this study Bayesian hierarchical spatial models have been used to analyze about 440 trawl fishing operations of two different metiers, sampled between 2009 and 2012, in order to improve our understanding of factors that influence the quantity of discards and to identify their spatio-temporal distribution in the study area. Our analysis showed that the relative importance of each variable was different for each metier, with a few similarities. In particular, the random vessel effect and seasonal variability were identified as main driving variables for both metiers. Predictive maps of the abundance of discards and maps of the posterior mean of the spatial component show several hot spots with high discard concentration for each metier. We argue how the seasonal/spatial effects, and the knowledge about the factors influential to discarding, could potentially be exploited as potential mitigation measures for future fisheries management strategies. However, misidentification of hotspots and uncertain predictions can culminate in inappropriate mitigation practices which can sometimes be irreversible. The proposed Bayesian spatial method overcomes these issues, since it offers a unified approach which allows the incorporation of spatial random-effect terms, spatial correlation of the variables and the uncertainty of the parameters in the modeling process, resulting in a better quantification of the uncertainty and accurate predictions.

A Bayesian framework for risk perception

NARCIS (Netherlands)

van Erp, H.R.N.

2017-01-01

We present here a Bayesian framework of risk perception. This framework encompasses plausibility judgments, decision making, and question asking. Plausibility judgments are modeled by way of Bayesian probability theory, decision making is modeled by way of a Bayesian decision theory, and relevancy

Bayesian flood forecasting methods: A review

Science.gov (United States)

Han, Shasha; Coulibaly, Paulin

2017-08-01

Over the past few decades, floods have been seen as one of the most common and largely distributed natural disasters in the world. If floods could be accurately forecasted in advance, then their negative impacts could be greatly minimized. It is widely recognized that quantification and reduction of uncertainty associated with the hydrologic forecast is of great importance for flood estimation and rational decision making. Bayesian forecasting system (BFS) offers an ideal theoretic framework for uncertainty quantification that can be developed for probabilistic flood forecasting via any deterministic hydrologic model. It provides suitable theoretical structure, empirically validated models and reasonable analytic-numerical computation method, and can be developed into various Bayesian forecasting approaches. This paper presents a comprehensive review on Bayesian forecasting approaches applied in flood forecasting from 1999 till now. The review starts with an overview of fundamentals of BFS and recent advances in BFS, followed with BFS application in river stage forecasting and real-time flood forecasting, then move to a critical analysis by evaluating advantages and limitations of Bayesian forecasting methods and other predictive uncertainty assessment approaches in flood forecasting, and finally discusses the future research direction in Bayesian flood forecasting. Results show that the Bayesian flood forecasting approach is an effective and advanced way for flood estimation, it considers all sources of uncertainties and produces a predictive distribution of the river stage, river discharge or runoff, thus gives more accurate and reliable flood forecasts. Some emerging Bayesian forecasting methods (e.g. ensemble Bayesian forecasting system, Bayesian multi-model combination) were shown to overcome limitations of single model or fixed model weight and effectively reduce predictive uncertainty. In recent years, various Bayesian flood forecasting approaches have been

Hierarchical cluster analysis of progression patterns in open-angle glaucoma patients with medical treatment.

Science.gov (United States)

Bae, Hyoung Won; Rho, Seungsoo; Lee, Hye Sun; Lee, Naeun; Hong, Samin; Seong, Gong Je; Sung, Kyung Rim; Kim, Chan Yun

2014-04-29

To classify medically treated open-angle glaucoma (OAG) by the pattern of progression using hierarchical cluster analysis, and to determine OAG progression characteristics by comparing clusters. Ninety-five eyes of 95 OAG patients who received medical treatment, and who had undergone visual field (VF) testing at least once per year for 5 or more years. OAG was classified into subgroups using hierarchical cluster analysis based on the following five variables: baseline mean deviation (MD), baseline visual field index (VFI), MD slope, VFI slope, and Glaucoma Progression Analysis (GPA) printout. After that, other parameters were compared between clusters. Two clusters were made after a hierarchical cluster analysis. Cluster 1 showed -4.06 ± 2.43 dB baseline MD, 92.58% ± 6.27% baseline VFI, -0.28 ± 0.38 dB per year MD slope, -0.52% ± 0.81% per year VFI slope, and all "no progression" cases in GPA printout, whereas cluster 2 showed -8.68 ± 3.81 baseline MD, 77.54 ± 12.98 baseline VFI, -0.72 ± 0.55 MD slope, -2.22 ± 1.89 VFI slope, and seven "possible" and four "likely" progression cases in GPA printout. There were no significant differences in age, sex, mean IOP, central corneal thickness, and axial length between clusters. However, cluster 2 included more high-tension glaucoma patients and used a greater number of antiglaucoma eye drops significantly compared with cluster 1. Hierarchical cluster analysis of progression patterns divided OAG into slow and fast progression groups, evidenced by assessing the parameters of glaucomatous progression in VF testing. In the fast progression group, the prevalence of high-tension glaucoma was greater and the number of antiglaucoma medications administered was increased versus the slow progression group. Copyright 2014 The Association for Research in Vision and Ophthalmology, Inc.

Micronutrients in HIV: a Bayesian meta-analysis.

Directory of Open Access Journals (Sweden)

George M Carter

Full Text Available Approximately 28.5 million people living with HIV are eligible for treatment (CD4<500, but currently have no access to antiretroviral therapy. Reduced serum level of micronutrients is common in HIV disease. Micronutrient supplementation (MNS may mitigate disease progression and mortality.We synthesized evidence on the effect of micronutrient supplementation on mortality and rate of disease progression in HIV disease.We searched MEDLINE, EMBASE, the Cochrane Central, AMED and CINAHL databases through December 2014, without language restriction, for studies of greater than 3 micronutrients versus any or no comparator. We built a hierarchical Bayesian random effects model to synthesize results. Inferences are based on the posterior distribution of the population effects; posterior distributions were approximated by Markov chain Monte Carlo in OpenBugs.From 2166 initial references, we selected 49 studies for full review and identified eight reporting on disease progression and/or mortality. Bayesian synthesis of data from 2,249 adults in three studies estimated the relative risk of disease progression in subjects on MNS vs. control as 0.62 (95% credible interval, 0.37, 0.96. Median number needed to treat is 8.4 (4.8, 29.9 and the Bayes Factor 53.4. Based on data reporting on 4,095 adults reporting mortality in 7 randomized controlled studies, the RR was 0.84 (0.38, 1.85, NNT is 25 (4.3, ∞.MNS significantly and substantially slows disease progression in HIV+ adults not on ARV, and possibly reduces mortality. Micronutrient supplements are effective in reducing progression with a posterior probability of 97.9%. Considering MNS low cost and lack of adverse effects, MNS should be standard of care for HIV+ adults not yet on ARV.

A Hierarchical and Distributed Approach for Mapping Large Applications to Heterogeneous Grids using Genetic Algorithms

Science.gov (United States)

Sanyal, Soumya; Jain, Amit; Das, Sajal K.; Biswas, Rupak

2003-01-01

In this paper, we propose a distributed approach for mapping a single large application to a heterogeneous grid environment. To minimize the execution time of the parallel application, we distribute the mapping overhead to the available nodes of the grid. This approach not only provides a fast mapping of tasks to resources but is also scalable. We adopt a hierarchical grid model and accomplish the job of mapping tasks to this topology using a scheduler tree. Results show that our three-phase algorithm provides high quality mappings, and is fast and scalable.

Two-Level Micro-to-Nanoscale Hierarchical TiO2 Nanolayers on Titanium Surface

Directory of Open Access Journals (Sweden)

Elena G. Zemtsova

2016-12-01

Full Text Available Joint replacement is being actively developed within modern orthopedics. One novel material providing fast implantation is bioactive coatings. The synthesis of targeted nanocoatings on metallic nanotitanium surface is reported in this paper. TiO2-based micro- and nanocoatings were produced by sol-gel synthesis using dip-coating technology with subsequent fast (shock drying in hot plate mode at 400 °C. As a result of shock drying, the two-level hierarchical TiO2 nanolayer on the nanotitanium was obtained. This two-level hierarchy includes nanorelief of porous xerogel and microrelief of the micron-sized “defect” network (a crack network. The thickness of TiO2 nanolayers was controlled by repeating dip-coating process the necessary number of times after the first layer deposition. The state of the MS3T3-E1 osteoblast cell line (young cells that form bone tissue on the two-level hierarchical surface has been studied. Particularly, adhesion character, adhesion time and morphology have been studied. The reported results may serve the starting point for the development of novel bioactive coatings for bone and teeth implants.

Fast Multipole Method as a Matrix-Free Hierarchical Low-Rank Approximation

KAUST Repository

Yokota, Rio; Ibeid, Huda; Keyes, David E.

2018-01-01

There has been a large increase in the amount of work on hierarchical low-rank approximation methods, where the interest is shared by multiple communities that previously did not intersect. This objective of this article is two-fold; to provide a thorough review of the recent advancements in this field from both analytical and algebraic perspectives, and to present a comparative benchmark of two highly optimized implementations of contrasting methods for some simple yet representative test cases. The first half of this paper has the form of a survey paper, to achieve the former objective. We categorize the recent advances in this field from the perspective of compute-memory tradeoff, which has not been considered in much detail in this area. Benchmark tests reveal that there is a large difference in the memory consumption and performance between the different methods.

Fast Multipole Method as a Matrix-Free Hierarchical Low-Rank Approximation

KAUST Repository

Yokota, Rio

2018-01-03

There has been a large increase in the amount of work on hierarchical low-rank approximation methods, where the interest is shared by multiple communities that previously did not intersect. This objective of this article is two-fold; to provide a thorough review of the recent advancements in this field from both analytical and algebraic perspectives, and to present a comparative benchmark of two highly optimized implementations of contrasting methods for some simple yet representative test cases. The first half of this paper has the form of a survey paper, to achieve the former objective. We categorize the recent advances in this field from the perspective of compute-memory tradeoff, which has not been considered in much detail in this area. Benchmark tests reveal that there is a large difference in the memory consumption and performance between the different methods.

Bayesian analysis of non-linear differential equation models with application to a gut microbial ecosystem.

Science.gov (United States)

Lawson, Daniel J; Holtrop, Grietje; Flint, Harry

2011-07-01

Process models specified by non-linear dynamic differential equations contain many parameters, which often must be inferred from a limited amount of data. We discuss a hierarchical Bayesian approach combining data from multiple related experiments in a meaningful way, which permits more powerful inference than treating each experiment as independent. The approach is illustrated with a simulation study and example data from experiments replicating the aspects of the human gut microbial ecosystem. A predictive model is obtained that contains prediction uncertainty caused by uncertainty in the parameters, and we extend the model to capture situations of interest that cannot easily be studied experimentally. Copyright © 2011 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim.

Topics in Bayesian statistics and maximum entropy

International Nuclear Information System (INIS)

Mutihac, R.; Cicuttin, A.; Cerdeira, A.; Stanciulescu, C.

1998-12-01

Notions of Bayesian decision theory and maximum entropy methods are reviewed with particular emphasis on probabilistic inference and Bayesian modeling. The axiomatic approach is considered as the best justification of Bayesian analysis and maximum entropy principle applied in natural sciences. Particular emphasis is put on solving the inverse problem in digital image restoration and Bayesian modeling of neural networks. Further topics addressed briefly include language modeling, neutron scattering, multiuser detection and channel equalization in digital communications, genetic information, and Bayesian court decision-making. (author)

Book review: Bayesian analysis for population ecology

Science.gov (United States)

Link, William A.

2011-01-01

Brian Dennis described the field of ecology as “fertile, uncolonized ground for Bayesian ideas.” He continued: “The Bayesian propagule has arrived at the shore. Ecologists need to think long and hard about the consequences of a Bayesian ecology. The Bayesian outlook is a successful competitor, but is it a weed? I think so.” (Dennis 2004)

Advance Liquid Metal Reactor Discrete Dynamic Event Tree/Bayesian Network Analysis and Incident Management Guidelines (Risk Management for Sodium Fast Reactors)

Energy Technology Data Exchange (ETDEWEB)

Denman, Matthew R. [Sandia National Lab. (SNL-NM), Albuquerque, NM (United States); Groth, Katrina M. [Sandia National Lab. (SNL-NM), Albuquerque, NM (United States); Cardoni, Jeffrey N. [Sandia National Lab. (SNL-NM), Albuquerque, NM (United States); Wheeler, Timothy A. [Sandia National Lab. (SNL-NM), Albuquerque, NM (United States)

2015-04-01

Accident management is an important component to maintaining risk at acceptable levels for all complex systems, such as nuclear power plants. With the introduction of self-correcting, or inherently safe, reactor designs the focus has shifted from management by operators to allowing the system's design to manage the accident. Inherently and passively safe designs are laudable, but nonetheless extreme boundary conditions can interfere with the design attributes which facilitate inherent safety, thus resulting in unanticipated and undesirable end states. This report examines an inherently safe and small sodium fast reactor experiencing a beyond design basis seismic event with the intend of exploring two issues : (1) can human intervention either improve or worsen the potential end states and (2) can a Bayesian Network be constructed to infer the state of the reactor to inform (1). ACKNOWLEDGEMENTS The authors would like to acknowledge the U.S. Department of Energy's Office of Nuclear Energy for funding this research through Work Package SR-14SN100303 under the Advanced Reactor Concepts program. The authors also acknowledge the PRA teams at Argonne National Laboratory, Oak Ridge National Laboratory, and Idaho National Laboratory for their continue d contributions to the advanced reactor PRA mission area.

A hierarchical community occurrence model for North Carolina stream fish

Science.gov (United States)

Midway, S.R.; Wagner, Tyler; Tracy, B.H.

2016-01-01

The southeastern USA is home to one of the richest—and most imperiled and threatened—freshwater fish assemblages in North America. For many of these rare and threatened species, conservation efforts are often limited by a lack of data. Drawing on a unique and extensive data set spanning over 20 years, we modeled occurrence probabilities of 126 stream fish species sampled throughout North Carolina, many of which occur more broadly in the southeastern USA. Specifically, we developed species-specific occurrence probabilities from hierarchical Bayesian multispecies models that were based on common land use and land cover covariates. We also used index of biotic integrity tolerance classifications as a second level in the model hierarchy; we identify this level as informative for our work, but it is flexible for future model applications. Based on the partial-pooling property of the models, we were able to generate occurrence probabilities for many imperiled and data-poor species in addition to highlighting a considerable amount of occurrence heterogeneity that supports species-specific investigations whenever possible. Our results provide critical species-level information on many threatened and imperiled species as well as information that may assist with re-evaluation of existing management strategies, such as the use of surrogate species. Finally, we highlight the use of a relatively simple hierarchical model that can easily be generalized for similar situations in which conventional models fail to provide reliable estimates for data-poor groups.

Bayesian data analysis of severe fatal accident risk in the oil chain.

Science.gov (United States)

Eckle, Petrissa; Burgherr, Peter

2013-01-01

We analyze the risk of severe fatal accidents causing five or more fatalities and for nine different activities covering the entire oil chain. Included are exploration and extraction, transport by different modes, refining and final end use in power plants, heating or gas stations. The risks are quantified separately for OECD and non-OECD countries and trends are calculated. Risk is analyzed by employing a Bayesian hierarchical model yielding analytical functions for both frequency (Poisson) and severity distributions (Generalized Pareto) as well as frequency trends. This approach addresses a key problem in risk estimation-namely the scarcity of data resulting in high uncertainties in particular for the risk of extreme events, where the risk is extrapolated beyond the historically most severe accidents. Bayesian data analysis allows the pooling of information from different data sets covering, for example, the different stages of the energy chains or different modes of transportation. In addition, it also inherently delivers a measure of uncertainty. This approach provides a framework, which comprehensively covers risk throughout the oil chain, allowing the allocation of risk in sustainability assessments. It also permits the progressive addition of new data to refine the risk estimates. Frequency, severity, and trends show substantial differences between the activities, emphasizing the need for detailed risk analysis. © 2012 Paul Scherrer Institut.

Applied Bayesian hierarchical methods

National Research Council Canada - National Science Library

Congdon, P

2010-01-01

... . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.2 Posterior Inference from Bayes Formula . . . . . . . . . . . . 1.3 Markov Chain Monte Carlo Sampling in Relation to Monte Carlo Methods: Obtaining Posterior...

Applied Bayesian hierarchical methods

National Research Council Canada - National Science Library

Congdon, P

2010-01-01

.... It also incorporates BayesX code, which is particularly useful in nonlinear regression. To demonstrate MCMC sampling from first principles, the author includes worked examples using the R package...

Bayesian Fundamentalism or Enlightenment? On the explanatory status and theoretical contributions of Bayesian models of cognition.

Science.gov (United States)

Jones, Matt; Love, Bradley C

2011-08-01

The prominence of Bayesian modeling of cognition has increased recently largely because of mathematical advances in specifying and deriving predictions from complex probabilistic models. Much of this research aims to demonstrate that cognitive behavior can be explained from rational principles alone, without recourse to psychological or neurological processes and representations. We note commonalities between this rational approach and other movements in psychology - namely, Behaviorism and evolutionary psychology - that set aside mechanistic explanations or make use of optimality assumptions. Through these comparisons, we identify a number of challenges that limit the rational program's potential contribution to psychological theory. Specifically, rational Bayesian models are significantly unconstrained, both because they are uninformed by a wide range of process-level data and because their assumptions about the environment are generally not grounded in empirical measurement. The psychological implications of most Bayesian models are also unclear. Bayesian inference itself is conceptually trivial, but strong assumptions are often embedded in the hypothesis sets and the approximation algorithms used to derive model predictions, without a clear delineation between psychological commitments and implementational details. Comparing multiple Bayesian models of the same task is rare, as is the realization that many Bayesian models recapitulate existing (mechanistic level) theories. Despite the expressive power of current Bayesian models, we argue they must be developed in conjunction with mechanistic considerations to offer substantive explanations of cognition. We lay out several means for such an integration, which take into account the representations on which Bayesian inference operates, as well as the algorithms and heuristics that carry it out. We argue this unification will better facilitate lasting contributions to psychological theory, avoiding the pitfalls

Coulomb blockade in hierarchical quantum Hall droplets

International Nuclear Information System (INIS)

Cappelli, Andrea; Georgiev, Lachezar S; Zemba, Guillermo R

2009-01-01

The degeneracy of energy levels in a quantum dot of Hall fluid, leading to conductance peaks, can be readily derived from the partition functions of conformal field theory. Their complete expressions can be found for Hall states with both Abelian and non-Abelian statistics, upon adapting known results for the annulus geometry. We analyze the Abelian states with hierarchical filling fractions, ν = m/(mp ± 1), and find a non-trivial pattern of conductance peaks. In particular, each one of them occurs with a characteristic multiplicity, which is due to the extended symmetry of the m-folded edge. Experimental tests of the multiplicity can shed more light on the dynamics of this composite edge. (fast track communication)

Uncertainty in perception and the Hierarchical Gaussian Filter

Directory of Open Access Journals (Sweden)

Christoph Daniel Mathys

2014-11-01

Full Text Available In its full sense, perception rests on an agent’s model of how its sensory input comes about and the inferences it draws based on this model. These inferences are necessarily uncertain. Here, we illustrate how the hierarchical Gaussian filter (HGF offers a principled and generic way to deal with the several forms that uncertainty in perception takes. The HGF is a recent derivation of one-step update equations from Bayesian principles that rests on a hierarchical generative model of the environment and its (instability. It is computationally highly efficient, allows for online estimates of hidden states, and has found numerous applications to experimental data from human subjects. In this paper, we generalize previous descriptions of the HGF and its account of perceptual uncertainty. First, we explicitly formulate the extension of the HGF’s hierarchy to any number of levels; second, we discuss how various forms of uncertainty are accommodated by the minimization of variational free energy as encoded in the update equations; third, we combine the HGF with decision models and demonstrate the inversion of this combination; finally, we report a simulation study that compared four optimization methods for inverting the HGF/decision model combination at different noise levels. These four methods (Nelder-Mead simplex algorithm, Gaussian process-based global optimization, variational Bayes and Markov chain Monte Carlo sampling all performed well even under considerable noise, with variational Bayes offering the best combination of efficiency and informativeness of inference. Our results demonstrate that the HGF provides a principled, flexible, and efficient - but at the same time intuitive - framework for the resolution of perceptual uncertainty in behaving agents.

Hierarchical Network Design

DEFF Research Database (Denmark)

Thomadsen, Tommy

2005-01-01

Communication networks are immensely important today, since both companies and individuals use numerous services that rely on them. This thesis considers the design of hierarchical (communication) networks. Hierarchical networks consist of layers of networks and are well-suited for coping...... with changing and increasing demands. Two-layer networks consist of one backbone network, which interconnects cluster networks. The clusters consist of nodes and links, which connect the nodes. One node in each cluster is a hub node, and the backbone interconnects the hub nodes of each cluster and thus...... the clusters. The design of hierarchical networks involves clustering of nodes, hub selection, and network design, i.e. selection of links and routing of ows. Hierarchical networks have been in use for decades, but integrated design of these networks has only been considered for very special types of networks...

3rd Bayesian Young Statisticians Meeting

CERN Document Server

Lanzarone, Ettore; Villalobos, Isadora; Mattei, Alessandra

2017-01-01

This book is a selection of peer-reviewed contributions presented at the third Bayesian Young Statisticians Meeting, BAYSM 2016, Florence, Italy, June 19-21. The meeting provided a unique opportunity for young researchers, M.S. students, Ph.D. students, and postdocs dealing with Bayesian statistics to connect with the Bayesian community at large, to exchange ideas, and to network with others working in the same field. The contributions develop and apply Bayesian methods in a variety of fields, ranging from the traditional (e.g., biostatistics and reliability) to the most innovative ones (e.g., big data and networks).

Hierarchical polypyrrole based composites for high performance asymmetric supercapacitors

Science.gov (United States)

Chen, Gao-Feng; Liu, Zhao-Qing; Lin, Jia-Ming; Li, Nan; Su, Yu-Zhi

2015-06-01

An advanced asymmetric supercapacitor with high energy density, exploiting hierarchical polypyrrole (PPy) based composites as both the anode [three dimensional (3D) chuzzle-like Ni@PPy@MnO2] and (3D cochleate-like Ni@MnO2@PPy) cathode, has been developed. The ultrathin PPy and flower-like MnO2 orderly coating on the high-conductivity 3D-Ni enhance charge storage while the unique 3D chuzzle-like and 3D cochleate-like structures provide storage chambers and fast ion transport pathways for benefiting the transport of electrolyte ions. The 3D cochleate-like Ni@MnO2@PPy possesses excellent pseudocapacitance with a relatively negative voltage window while preserved EDLC and free transmission channels conducive to hold the high power, providing an ideal cathode for the asymmetric supercapacitor. It is the first report of assembling hierarchical PPy based composites as both the anode and cathode for asymmetric supercapacitor, which exhibits wide operation voltage of 1.3-1.5 V with maximum energy and power densities of 59.8 Wh kg-1 and 7500 W kg-1.

Calibrating the sqHIMMELI v1.0 wetland methane emission model with hierarchical modeling and adaptive MCMC

Science.gov (United States)

Susiluoto, Jouni; Raivonen, Maarit; Backman, Leif; Laine, Marko; Makela, Jarmo; Peltola, Olli; Vesala, Timo; Aalto, Tuula

2018-03-01

Estimating methane (CH4) emissions from natural wetlands is complex, and the estimates contain large uncertainties. The models used for the task are typically heavily parameterized and the parameter values are not well known. In this study, we perform a Bayesian model calibration for a new wetland CH4 emission model to improve the quality of the predictions and to understand the limitations of such models.The detailed process model that we analyze contains descriptions for CH4 production from anaerobic respiration, CH4 oxidation, and gas transportation by diffusion, ebullition, and the aerenchyma cells of vascular plants. The processes are controlled by several tunable parameters. We use a hierarchical statistical model to describe the parameters and obtain the posterior distributions of the parameters and uncertainties in the processes with adaptive Markov chain Monte Carlo (MCMC), importance resampling, and time series analysis techniques. For the estimation, the analysis utilizes measurement data from the Siikaneva flux measurement site in southern Finland. The uncertainties related to the parameters and the modeled processes are described quantitatively. At the process level, the flux measurement data are able to constrain the CH4 production processes, methane oxidation, and the different gas transport processes. The posterior covariance structures explain how the parameters and the processes are related. Additionally, the flux and flux component uncertainties are analyzed both at the annual and daily levels. The parameter posterior densities obtained provide information regarding importance of the different processes, which is also useful for development of wetland methane emission models other than the square root HelsinkI Model of MEthane buiLd-up and emIssion for peatlands (sqHIMMELI). The hierarchical modeling allows us to assess the effects of some of the parameters on an annual basis. The results of the calibration and the cross validation suggest that

Bayesian Inference for Linear Parabolic PDEs with Noisy Boundary Conditions

KAUST Repository

Ruggeri, Fabrizio; Sawlan, Zaid A; Scavino, Marco; Tempone, Raul

2016-01-01

In this work we develop a hierarchical Bayesian setting to infer unknown parameters in initial-boundary value problems (IBVPs) for one-dimensional linear parabolic partial differential equations. Noisy boundary data and known initial condition are assumed. We derive the likelihood function associated with the forward problem, given some measurements of the solution field subject to Gaussian noise. Such function is then analytically marginalized using the linearity of the equation. Gaussian priors have been assumed for the time-dependent Dirichlet boundary values. Our approach is applied to synthetic data for the one-dimensional heat equation model, where the thermal diffusivity is the unknown parameter. We show how to infer the thermal diffusivity parameter when its prior distribution is lognormal or modeled by means of a space-dependent stationary lognormal random field. We use the Laplace method to provide approximated Gaussian posterior distributions for the thermal diffusivity. Expected information gains and predictive posterior densities for observable quantities are numerically estimated for different experimental setups.

Bayesian Inference for Linear Parabolic PDEs with Noisy Boundary Conditions

KAUST Repository

Ruggeri, Fabrizio

2015-01-07

In this work we develop a hierarchical Bayesian setting to infer unknown parameters in initial-boundary value problems (IBVPs) for one-dimensional linear parabolic partial differential equations. Noisy boundary data and known initial condition are assumed. We derive the likelihood function associated with the forward problem, given some measurements of the solution field subject to Gaussian noise. Such function is then analytically marginalized using the linearity of the equation. Gaussian priors have been assumed for the time-dependent Dirichlet boundary values. Our approach is applied to synthetic data for the one-dimensional heat equation model, where the thermal diffusivity is the unknown parameter. We show how to infer the thermal diffusivity parameter when its prior distribution is lognormal or modeled by means of a space-dependent stationary lognormal random field. We use the Laplace method to provide approximated Gaussian posterior distributions for the thermal diffusivity. Expected information gains and predictive posterior densities for observable quantities are numerically estimated for different experimental setups.

Bayesian Inference for Linear Parabolic PDEs with Noisy Boundary Conditions

KAUST Repository

Ruggeri, Fabrizio

2016-01-06

In this work we develop a hierarchical Bayesian setting to infer unknown parameters in initial-boundary value problems (IBVPs) for one-dimensional linear parabolic partial differential equations. Noisy boundary data and known initial condition are assumed. We derive the likelihood function associated with the forward problem, given some measurements of the solution field subject to Gaussian noise. Such function is then analytically marginalized using the linearity of the equation. Gaussian priors have been assumed for the time-dependent Dirichlet boundary values. Our approach is applied to synthetic data for the one-dimensional heat equation model, where the thermal diffusivity is the unknown parameter. We show how to infer the thermal diffusivity parameter when its prior distribution is lognormal or modeled by means of a space-dependent stationary lognormal random field. We use the Laplace method to provide approximated Gaussian posterior distributions for the thermal diffusivity. Expected information gains and predictive posterior densities for observable quantities are numerically estimated for different experimental setups.

Global, regional, and subregional trends in unintended pregnancy and its outcomes from 1990 to 2014: estimates from a Bayesian hierarchical model

Directory of Open Access Journals (Sweden)

Jonathan Bearak, PhD

2018-04-01

Full Text Available Summary: Background: Estimates of pregnancy incidence by intention status and outcome indicate how effectively women and couples are able to fulfil their childbearing aspirations, and can be used to monitor the impact of family-planning programmes. We estimate global, regional, and subregional pregnancy rates by intention status and outcome for 1990–2014. Methods: We developed a Bayesian hierarchical time series model whereby the unintended pregnancy rate is a function of the distribution of women across subgroups defined by marital status and contraceptive need and use, and of the risk of unintended pregnancy in each subgroup. Data included numbers of births and of women estimated by the UN Population Division, recently published abortion incidence estimates, and findings from surveys of women on the percentage of births or pregnancies that were unintended. Some 298 datapoints on the intention status of births or pregnancies were obtained for 105 countries. Findings: Worldwide, an estimated 44% (90% uncertainty interval [UI] 42–48 of pregnancies were unintended in 2010–14. The unintended pregnancy rate declined by 30% (90% UI 21–39 in developed regions, from 64 (59–81 per 1000 women aged 15–44 years in 1990–94 to 45 (42–56 in 2010–14. In developing regions, the unintended pregnancy rate fell 16% (90% UI 5–24, from 77 (74–88 per 1000 women aged 15–44 years to 65 (62–76. Whereas the decline in the unintended pregnancy rate in developed regions coincided with a declining abortion rate, the decline in developing regions coincided with a declining unintended birth rate. In 2010–14, 59% (90% UI 54–65 of unintended pregnancies ended in abortion in developed regions, as did 55% (52–60 of unintended pregnancies in developing regions. Interpretation: The unintended pregnancy rate remains substantially higher in developing regions than in developed regions. Sexual and reproductive health services are needed to help women

Robust bayesian analysis of an autoregressive model with ...

African Journals Online (AJOL)

In this work, robust Bayesian analysis of the Bayesian estimation of an autoregressive model with exponential innovations is performed. Using a Bayesian robustness methodology, we show that, using a suitable generalized quadratic loss, we obtain optimal Bayesian estimators of the parameters corresponding to the ...

Plug & Play object oriented Bayesian networks

DEFF Research Database (Denmark)

Bangsø, Olav; Flores, J.; Jensen, Finn Verner

2003-01-01

been shown to be quite suitable for dynamic domains as well. However, processing object oriented Bayesian networks in practice does not take advantage of their modular structure. Normally the object oriented Bayesian network is transformed into a Bayesian network and, inference is performed...... dynamic domains. The communication needed between instances is achieved by means of a fill-in propagation scheme....

The Bayesian New Statistics: Hypothesis testing, estimation, meta-analysis, and power analysis from a Bayesian perspective.

Science.gov (United States)

Kruschke, John K; Liddell, Torrin M

2018-02-01

In the practice of data analysis, there is a conceptual distinction between hypothesis testing, on the one hand, and estimation with quantified uncertainty on the other. Among frequentists in psychology, a shift of emphasis from hypothesis testing to estimation has been dubbed "the New Statistics" (Cumming 2014). A second conceptual distinction is between frequentist methods and Bayesian methods. Our main goal in this article is to explain how Bayesian methods achieve the goals of the New Statistics better than frequentist methods. The article reviews frequentist and Bayesian approaches to hypothesis testing and to estimation with confidence or credible intervals. The article also describes Bayesian approaches to meta-analysis, randomized controlled trials, and power analysis.

A hierarchical scheme for geodesic anatomical labeling of airway trees

DEFF Research Database (Denmark)

Feragen, Aasa; Petersen, Jens; Owen, Megan

2012-01-01

We present a fast and robust supervised algorithm for label- ing anatomical airway trees, based on geodesic distances in a geometric tree-space. Possible branch label configurations for a given unlabeled air- way tree are evaluated based on the distances to a training set of labeled airway trees....... In tree-space, the airway tree topology and geometry change continuously, giving a natural way to automatically handle anatomical differences and noise. The algorithm is made efficient using a hierarchical approach, in which labels are assigned from the top down. We only use features of the airway...

2nd Bayesian Young Statisticians Meeting

CERN Document Server

Bitto, Angela; Kastner, Gregor; Posekany, Alexandra

2015-01-01

The Second Bayesian Young Statisticians Meeting (BAYSM 2014) and the research presented here facilitate connections among researchers using Bayesian Statistics by providing a forum for the development and exchange of ideas. WU Vienna University of Business and Economics hosted BAYSM 2014 from September 18th to 19th. The guidance of renowned plenary lecturers and senior discussants is a critical part of the meeting and this volume, which follows publication of contributions from BAYSM 2013. The meeting's scientific program reflected the variety of fields in which Bayesian methods are currently employed or could be introduced in the future. Three brilliant keynote lectures by Chris Holmes (University of Oxford), Christian Robert (Université Paris-Dauphine), and Mike West (Duke University), were complemented by 24 plenary talks covering the major topics Dynamic Models, Applications, Bayesian Nonparametrics, Biostatistics, Bayesian Methods in Economics, and Models and Methods, as well as a lively poster session ...

Bayesian natural language semantics and pragmatics

CERN Document Server

Zeevat, Henk

2015-01-01

The contributions in this volume focus on the Bayesian interpretation of natural languages, which is widely used in areas of artificial intelligence, cognitive science, and computational linguistics. This is the first volume to take up topics in Bayesian Natural Language Interpretation and make proposals based on information theory, probability theory, and related fields. The methodologies offered here extend to the target semantic and pragmatic analyses of computational natural language interpretation. Bayesian approaches to natural language semantics and pragmatics are based on methods from signal processing and the causal Bayesian models pioneered by especially Pearl. In signal processing, the Bayesian method finds the most probable interpretation by finding the one that maximizes the product of the prior probability and the likelihood of the interpretation. It thus stresses the importance of a production model for interpretation as in Grice's contributions to pragmatics or in interpretation by abduction.

Bayesian inference for hybrid discrete-continuous stochastic kinetic models

International Nuclear Information System (INIS)

Sherlock, Chris; Golightly, Andrew; Gillespie, Colin S

2014-01-01

We consider the problem of efficiently performing simulation and inference for stochastic kinetic models. Whilst it is possible to work directly with the resulting Markov jump process (MJP), computational cost can be prohibitive for networks of realistic size and complexity. In this paper, we consider an inference scheme based on a novel hybrid simulator that classifies reactions as either ‘fast’ or ‘slow’ with fast reactions evolving as a continuous Markov process whilst the remaining slow reaction occurrences are modelled through a MJP with time-dependent hazards. A linear noise approximation (LNA) of fast reaction dynamics is employed and slow reaction events are captured by exploiting the ability to solve the stochastic differential equation driving the LNA. This simulation procedure is used as a proposal mechanism inside a particle MCMC scheme, thus allowing Bayesian inference for the model parameters. We apply the scheme to a simple application and compare the output with an existing hybrid approach and also a scheme for performing inference for the underlying discrete stochastic model. (paper)

Hierarchical modeling of bycatch rates of sea turtles in the western North Atlantic

Science.gov (United States)

Gardner, B.; Sullivan, P.J.; Epperly, S.; Morreale, S.J.

2008-01-01

Previous studies indicate that the locations of the endangered loggerhead Caretta caretta and critically endangered leatherback Dermochelys coriacea sea turtles are influenced by water temperatures, and that incidental catch rates in the pelagic longline fishery vary by region. We present a Bayesian hierarchical model to examine the effects of environmental variables, including water temperature, on the number of sea turtles captured in the US pelagic longline fishery in the western North Atlantic. The modeling structure is highly flexible, utilizes a Bayesian model selection technique, and is fully implemented in the software program WinBUGS. The number of sea turtles captured is modeled as a zero-inflated Poisson distribution and the model incorporates fixed effects to examine region-specific differences in the parameter estimates. Results indicate that water temperature, region, bottom depth, and target species are all significant predictors of the number of loggerhead sea turtles captured. For leatherback sea turtles, the model with only target species had the most posterior model weight, though a re-parameterization of the model indicates that temperature influences the zero-inflation parameter. The relationship between the number of sea turtles captured and the variables of interest all varied by region. This suggests that management decisions aimed at reducing sea turtle bycatch may be more effective if they are spatially explicit. ?? Inter-Research 2008.

Design of hierarchical CuS/graphene architectures with enhanced lithium storage capability

Energy Technology Data Exchange (ETDEWEB)

Ding, Caihua; Su, Dezhi [Beijing Key Laboratory of Construction Tailorable Advanced Functional Materials and Green Applications, School of Materials Science & Engineering, Beijing Institute of Technology, Beijing, 100081 (China); Ma, Wenxian [State Key Laboratory for Advanced Metals and Materials, University of Science and Technology Beijing, Beijing, 100083 (China); Zhao, Yongjie, E-mail: zhaoyjpeace@gmail.com [Beijing Key Laboratory of Construction Tailorable Advanced Functional Materials and Green Applications, School of Materials Science & Engineering, Beijing Institute of Technology, Beijing, 100081 (China); Yan, Dong [Department of Mechanical Engineering, Tsinghua University, Beijing, 100084 (China); State Key Laboratory of Tribology, Tsinghua University, Beijing, 100084 (China); Li, Jingbo; Jin, Haibo [Beijing Key Laboratory of Construction Tailorable Advanced Functional Materials and Green Applications, School of Materials Science & Engineering, Beijing Institute of Technology, Beijing, 100081 (China)

2017-05-01

Highlights: • A delicate route was proposed for rational design of CuS/graphene composite. • Hierarchical CuS was composed of large amounts of well-arranged nanosheets. • The rationally designed structure of composite offered stable-hosts for Li{sup +} insertion. • The graphene constructed conductive paths and a network for fast transport of Li{sup +}. • The presence of the graphene in the composite reduced the dissolution of polysulfides. - Abstract: Metal-sulfides electrode materials usually suffer from poor cyclability and low rate capability in rechargeable batteries as a result of the pulverization of active materials and the loss of sulfur material induced by polysulfide dissolution. Herein, we reported a delicate and scalable route for rational design of CuS/graphene composites. Hierarchical CuS microparticles comprising of large amounts of self-assembled and well-arranged nanosheets uniformly mixed with flexible graphene layers. The obtained CuS/graphene electrodes exhibited high specific capacities, excellent cycling stability and desirable rate capability when being evaluated as anode materials for lithium-ion batteries. The high specific capacities of 568 mA h g{sup −1} after 100 cycles at 50 mA g{sup −1} and 143 mA h g{sup −1} at 1000 mA g{sup −1} (in rate testing) were achieved, suggesting a very promising candidate for high-performance lithium-ion batteries. The rationally designed structures of the CuS/graphene composites offered stable-hosts for Li{sup +} insertion and alleviated the volume changes upon cycling. The presence of the graphene in composite not only constructed conductive paths and a network for fast transport of Li{sup +}, but also effectively reduced the dissolution of polysulfides into electrolyte. This graphene-based composite with hierarchical structure could be used as a safe, low-cost, and versatile material for extensively potential applications.

Design of hierarchical CuS/graphene architectures with enhanced lithium storage capability

International Nuclear Information System (INIS)

Ding, Caihua; Su, Dezhi; Ma, Wenxian; Zhao, Yongjie; Yan, Dong; Li, Jingbo; Jin, Haibo

2017-01-01

Highlights: • A delicate route was proposed for rational design of CuS/graphene composite. • Hierarchical CuS was composed of large amounts of well-arranged nanosheets. • The rationally designed structure of composite offered stable-hosts for Li + insertion. • The graphene constructed conductive paths and a network for fast transport of Li + . • The presence of the graphene in the composite reduced the dissolution of polysulfides. - Abstract: Metal-sulfides electrode materials usually suffer from poor cyclability and low rate capability in rechargeable batteries as a result of the pulverization of active materials and the loss of sulfur material induced by polysulfide dissolution. Herein, we reported a delicate and scalable route for rational design of CuS/graphene composites. Hierarchical CuS microparticles comprising of large amounts of self-assembled and well-arranged nanosheets uniformly mixed with flexible graphene layers. The obtained CuS/graphene electrodes exhibited high specific capacities, excellent cycling stability and desirable rate capability when being evaluated as anode materials for lithium-ion batteries. The high specific capacities of 568 mA h g −1 after 100 cycles at 50 mA g −1 and 143 mA h g −1 at 1000 mA g −1 (in rate testing) were achieved, suggesting a very promising candidate for high-performance lithium-ion batteries. The rationally designed structures of the CuS/graphene composites offered stable-hosts for Li + insertion and alleviated the volume changes upon cycling. The presence of the graphene in composite not only constructed conductive paths and a network for fast transport of Li + , but also effectively reduced the dissolution of polysulfides into electrolyte. This graphene-based composite with hierarchical structure could be used as a safe, low-cost, and versatile material for extensively potential applications.

Robust and scalable hierarchical matrix-based fast direct solver and preconditioner for the numerical solution of elliptic partial differential equations

KAUST Repository

Chavez Chavez, Gustavo Ivan

2017-01-01

Numerical experiments corroborate the robustness, accuracy, and complexity claims and provide a baseline of the performance and memory footprint by comparisons with competing approaches such as the multigrid solver hypre, and the STRUMPACK implementation of the multifrontal factorization with hierarchically semi-separable matrices. The companion implementation can utilize many thousands of cores of Shaheen, KAUST's Haswell-based Cray XC-40 supercomputer, and compares favorably with other implementations of hierarchical solvers in terms of time-to-solution and memory consumption.

Bayesian methods in reliability

Science.gov (United States)

Sander, P.; Badoux, R.

1991-11-01

The present proceedings from a course on Bayesian methods in reliability encompasses Bayesian statistical methods and their computational implementation, models for analyzing censored data from nonrepairable systems, the traits of repairable systems and growth models, the use of expert judgment, and a review of the problem of forecasting software reliability. Specific issues addressed include the use of Bayesian methods to estimate the leak rate of a gas pipeline, approximate analyses under great prior uncertainty, reliability estimation techniques, and a nonhomogeneous Poisson process. Also addressed are the calibration sets and seed variables of expert judgment systems for risk assessment, experimental illustrations of the use of expert judgment for reliability testing, and analyses of the predictive quality of software-reliability growth models such as the Weibull order statistics.

Bayesian analysis of genetic association across tree-structured routine healthcare data in the UK Biobank

DEFF Research Database (Denmark)

Cortes, Adrian; Dendrou, Calliope A; Motyer, Allan

2017-01-01

Genetic discovery from the multitude of phenotypes extractable from routine healthcare data can transform understanding of the human phenome and accelerate progress toward precision medicine. However, a critical question when analyzing high-dimensional and heterogeneous data is how best...... to interrogate increasingly specific subphenotypes while retaining statistical power to detect genetic associations. Here we develop and employ a new Bayesian analysis framework that exploits the hierarchical structure of diagnosis classifications to analyze genetic variants against UK Biobank disease phenotypes...... derived from self-reporting and hospital episode statistics. Our method displays a more than 20% increase in power to detect genetic effects over other approaches and identifies new associations between classical human leukocyte antigen (HLA) alleles and common immune-mediated diseases (IMDs). By applying...

Bayesian networks and food security - An introduction

NARCIS (Netherlands)

Stein, A.

2004-01-01

This paper gives an introduction to Bayesian networks. Networks are defined and put into a Bayesian context. Directed acyclical graphs play a crucial role here. Two simple examples from food security are addressed. Possible uses of Bayesian networks for implementation and further use in decision

Assessing global vegetation activity using spatio-temporal Bayesian modelling

Science.gov (United States)

Mulder, Vera L.; van Eck, Christel M.; Friedlingstein, Pierre; Regnier, Pierre A. G.

2016-04-01

This work demonstrates the potential of modelling vegetation activity using a hierarchical Bayesian spatio-temporal model. This approach allows modelling changes in vegetation and climate simultaneous in space and time. Changes of vegetation activity such as phenology are modelled as a dynamic process depending on climate variability in both space and time. Additionally, differences in observed vegetation status can be contributed to other abiotic ecosystem properties, e.g. soil and terrain properties. Although these properties do not change in time, they do change in space and may provide valuable information in addition to the climate dynamics. The spatio-temporal Bayesian models were calibrated at a regional scale because the local trends in space and time can be better captured by the model. The regional subsets were defined according to the SREX segmentation, as defined by the IPCC. Each region is considered being relatively homogeneous in terms of large-scale climate and biomes, still capturing small-scale (grid-cell level) variability. Modelling within these regions is hence expected to be less uncertain due to the absence of these large-scale patterns, compared to a global approach. This overall modelling approach allows the comparison of model behavior for the different regions and may provide insights on the main dynamic processes driving the interaction between vegetation and climate within different regions. The data employed in this study encompasses the global datasets for soil properties (SoilGrids), terrain properties (Global Relief Model based on SRTM DEM and ETOPO), monthly time series of satellite-derived vegetation indices (GIMMS NDVI3g) and climate variables (Princeton Meteorological Forcing Dataset). The findings proved the potential of a spatio-temporal Bayesian modelling approach for assessing vegetation dynamics, at a regional scale. The observed interrelationships of the employed data and the different spatial and temporal trends support

Dual Sticky Hierarchical Dirichlet Process Hidden Markov Model and Its Application to Natural Language Description of Motions.

Science.gov (United States)

Hu, Weiming; Tian, Guodong; Kang, Yongxin; Yuan, Chunfeng; Maybank, Stephen

2017-09-25

In this paper, a new nonparametric Bayesian model called the dual sticky hierarchical Dirichlet process hidden Markov model (HDP-HMM) is proposed for mining activities from a collection of time series data such as trajectories. All the time series data are clustered. Each cluster of time series data, corresponding to a motion pattern, is modeled by an HMM. Our model postulates a set of HMMs that share a common set of states (topics in an analogy with topic models for document processing), but have unique transition distributions. For the application to motion trajectory modeling, topics correspond to motion activities. The learnt topics are clustered into atomic activities which are assigned predicates. We propose a Bayesian inference method to decompose a given trajectory into a sequence of atomic activities. On combining the learnt sources and sinks, semantic motion regions, and the learnt sequence of atomic activities, the action represented by the trajectory can be described in natural language in as automatic a way as possible. The effectiveness of our dual sticky HDP-HMM is validated on several trajectory datasets. The effectiveness of the natural language descriptions for motions is demonstrated on the vehicle trajectories extracted from a traffic scene.

Embedding nano-Li{sub 4}Ti{sub 5}O{sub 12} in hierarchical porous carbon matrixes derived from water soluble polymers for ultra-fast lithium ion batteries anodic materials

Energy Technology Data Exchange (ETDEWEB)

Lan, Chun-Kai; Bao, Qi; Huang, Yao-Hui; Duh, Jenq-Gong, E-mail: jgd@mx.nthu.edu.tw

2016-07-15

Li{sub 4}Ti{sub 5}O{sub 12}/hierarchical porous carbon matrixes composites are successfully prepared by a facile and fast polymers assisted sol–gel method, aiming to promote both electronic and ionic conductivity. As indicated by Fourier transform infrared spectroscopy and X-ray photoelectron spectroscopy analysis, three less expensive cost and available water soluble polymers (e.g. PAA, CMC, and SA) can homogeneously react with Li–Ti–O precursor to incorporate into interior of nano-scale lithium titanate and provide a continues conductive network after pyrolysis. In addition, the results of scanning electron microscopy and transmission electron microscopy also prove that the Li{sub 4}Ti{sub 5}O{sub 12} nanoparticles are firmly embedded in porous carbon matrix with no obvious agglomeration. EIS measurement and cyclic voltammetry further reveal that the facilitated electrode kinetics and better ionic transport of Li{sub 4}Ti{sub 5}O{sub 12}/hierarchical porous carbon matrixes composites than that of Li{sub 4}Ti{sub 5}O{sub 12}. The c-CMC-LTO exhibits a superior capacity of 92 mAh g{sup −1} and retains its initial value with no obviously capacity decay over 200 cycles under an ultra-high C rate (50 C). - Graphical abstract: Schematic illustrations of the formation process of embedding LTO into Carbon matrixes derived from water soluable polymers (upper) and the electrochemical reaction paths in LTO/Carbon composites during charging/discharging processes (lower). - Highlights: • Hierarchical porous carbon matrixes were used to improve the Li{sub 4}Ti{sub 5}O{sub 12} anodes. • Carbon matrixes could suppress the agglomeration of Li{sub 4}Ti{sub 5}O{sub 12} nanoparticles. • meso-nanoporous carbon structure was beneficial for filtration of electrolyte. • The c-CMC-LTO exhibited superior high rate capability and cycling durability.

12th Brazilian Meeting on Bayesian Statistics

CERN Document Server

Louzada, Francisco; Rifo, Laura; Stern, Julio; Lauretto, Marcelo

2015-01-01

Through refereed papers, this volume focuses on the foundations of the Bayesian paradigm; their comparison to objectivistic or frequentist Statistics counterparts; and the appropriate application of Bayesian foundations. This research in Bayesian Statistics is applicable to data analysis in biostatistics, clinical trials, law, engineering, and the social sciences. EBEB, the Brazilian Meeting on Bayesian Statistics, is held every two years by the ISBrA, the International Society for Bayesian Analysis, one of the most active chapters of the ISBA. The 12th meeting took place March 10-14, 2014 in Atibaia. Interest in foundations of inductive Statistics has grown recently in accordance with the increasing availability of Bayesian methodological alternatives. Scientists need to deal with the ever more difficult choice of the optimal method to apply to their problem. This volume shows how Bayes can be the answer. The examination and discussion on the foundations work towards the goal of proper application of Bayesia...

Functional annotation of hierarchical modularity.

Directory of Open Access Journals (Sweden)

Kanchana Padmanabhan

Full Text Available In biological networks of molecular interactions in a cell, network motifs that are biologically relevant are also functionally coherent, or form functional modules. These functionally coherent modules combine in a hierarchical manner into larger, less cohesive subsystems, thus revealing one of the essential design principles of system-level cellular organization and function-hierarchical modularity. Arguably, hierarchical modularity has not been explicitly taken into consideration by most, if not all, functional annotation systems. As a result, the existing methods would often fail to assign a statistically significant functional coherence score to biologically relevant molecular machines. We developed a methodology for hierarchical functional annotation. Given the hierarchical taxonomy of functional concepts (e.g., Gene Ontology and the association of individual genes or proteins with these concepts (e.g., GO terms, our method will assign a Hierarchical Modularity Score (HMS to each node in the hierarchy of functional modules; the HMS score and its p-value measure functional coherence of each module in the hierarchy. While existing methods annotate each module with a set of "enriched" functional terms in a bag of genes, our complementary method provides the hierarchical functional annotation of the modules and their hierarchically organized components. A hierarchical organization of functional modules often comes as a bi-product of cluster analysis of gene expression data or protein interaction data. Otherwise, our method will automatically build such a hierarchy by directly incorporating the functional taxonomy information into the hierarchy search process and by allowing multi-functional genes to be part of more than one component in the hierarchy. In addition, its underlying HMS scoring metric ensures that functional specificity of the terms across different levels of the hierarchical taxonomy is properly treated. We have evaluated our

Kernel Bayesian ART and ARTMAP.

Science.gov (United States)

Masuyama, Naoki; Loo, Chu Kiong; Dawood, Farhan

2018-02-01

Adaptive Resonance Theory (ART) is one of the successful approaches to resolving "the plasticity-stability dilemma" in neural networks, and its supervised learning model called ARTMAP is a powerful tool for classification. Among several improvements, such as Fuzzy or Gaussian based models, the state of art model is Bayesian based one, while solving the drawbacks of others. However, it is known that the Bayesian approach for the high dimensional and a large number of data requires high computational cost, and the covariance matrix in likelihood becomes unstable. This paper introduces Kernel Bayesian ART (KBA) and ARTMAP (KBAM) by integrating Kernel Bayes' Rule (KBR) and Correntropy Induced Metric (CIM) to Bayesian ART (BA) and ARTMAP (BAM), respectively, while maintaining the properties of BA and BAM. The kernel frameworks in KBA and KBAM are able to avoid the curse of dimensionality. In addition, the covariance-free Bayesian computation by KBR provides the efficient and stable computational capability to KBA and KBAM. Furthermore, Correntropy-based similarity measurement allows improving the noise reduction ability even in the high dimensional space. The simulation experiments show that KBA performs an outstanding self-organizing capability than BA, and KBAM provides the superior classification ability than BAM, respectively. Copyright © 2017 Elsevier Ltd. All rights reserved.

Bayesian networks improve causal environmental ...

Science.gov (United States)

Rule-based weight of evidence approaches to ecological risk assessment may not account for uncertainties and generally lack probabilistic integration of lines of evidence. Bayesian networks allow causal inferences to be made from evidence by including causal knowledge about the problem, using this knowledge with probabilistic calculus to combine multiple lines of evidence, and minimizing biases in predicting or diagnosing causal relationships. Too often, sources of uncertainty in conventional weight of evidence approaches are ignored that can be accounted for with Bayesian networks. Specifying and propagating uncertainties improve the ability of models to incorporate strength of the evidence in the risk management phase of an assessment. Probabilistic inference from a Bayesian network allows evaluation of changes in uncertainty for variables from the evidence. The network structure and probabilistic framework of a Bayesian approach provide advantages over qualitative approaches in weight of evidence for capturing the impacts of multiple sources of quantifiable uncertainty on predictions of ecological risk. Bayesian networks can facilitate the development of evidence-based policy under conditions of uncertainty by incorporating analytical inaccuracies or the implications of imperfect information, structuring and communicating causal issues through qualitative directed graph formulations, and quantitatively comparing the causal power of multiple stressors on value

Bayesian Latent Class Analysis Tutorial.

Science.gov (United States)

Li, Yuelin; Lord-Bessen, Jennifer; Shiyko, Mariya; Loeb, Rebecca

2018-01-01

This article is a how-to guide on Bayesian computation using Gibbs sampling, demonstrated in the context of Latent Class Analysis (LCA). It is written for students in quantitative psychology or related fields who have a working knowledge of Bayes Theorem and conditional probability and have experience in writing computer programs in the statistical language R . The overall goals are to provide an accessible and self-contained tutorial, along with a practical computation tool. We begin with how Bayesian computation is typically described in academic articles. Technical difficulties are addressed by a hypothetical, worked-out example. We show how Bayesian computation can be broken down into a series of simpler calculations, which can then be assembled together to complete a computationally more complex model. The details are described much more explicitly than what is typically available in elementary introductions to Bayesian modeling so that readers are not overwhelmed by the mathematics. Moreover, the provided computer program shows how Bayesian LCA can be implemented with relative ease. The computer program is then applied in a large, real-world data set and explained line-by-line. We outline the general steps in how to extend these considerations to other methodological applications. We conclude with suggestions for further readings.

Bayesian policy reuse

CSIR Research Space (South Africa)

Rosman, Benjamin

2016-02-01

Full Text Available Keywords Policy Reuse · Reinforcement Learning · Online Learning · Online Bandits · Transfer Learning · Bayesian Optimisation · Bayesian Decision Theory. 1 Introduction As robots and software agents are becoming more ubiquitous in many applications.... The agent has access to a library of policies (pi1, pi2 and pi3), and has previously experienced a set of task instances (τ1, τ2, τ3, τ4), as well as samples of the utilities of the library policies on these instances (the black dots indicate the means...

Assembly of CdS Quantum Dots onto Hierarchical TiO2 Structure for Quantum Dots Sensitized Solar Cell Applications

Directory of Open Access Journals (Sweden)

Syed Mansoor Ali

2015-05-01

Full Text Available Quantum dot (QD sensitized solar cells based on Hierarchical TiO2 structure (HTS consisting of spherical nano-urchins on transparent conductive fluorine doped tin oxide glass substrate is fabricated. The hierarchical TiO2 structure consisting of spherical nano-urchins on transparent conductive fluorine doped tin oxide glass substrate synthesized by hydrothermal route. The CdS quantum dots were grown by the successive ionic layer adsorption and reaction deposition method. The quantum dot sensitized solar cell based on the hierarchical TiO2 structure shows a current density JSC = 1.44 mA, VOC = 0.46 V, FF = 0.42 and η = 0.27%. The QD provide a high surface area and nano-urchins offer a highway for fast charge collection and multiple scattering centers within the photoelectrode.

Inverse problems in the Bayesian framework

International Nuclear Information System (INIS)

Calvetti, Daniela; Somersalo, Erkki; Kaipio, Jari P

2014-01-01

The history of Bayesian methods dates back to the original works of Reverend Thomas Bayes and Pierre-Simon Laplace: the former laid down some of the basic principles on inverse probability in his classic article ‘An essay towards solving a problem in the doctrine of chances’ that was read posthumously in the Royal Society in 1763. Laplace, on the other hand, in his ‘Memoirs on inverse probability’ of 1774 developed the idea of updating beliefs and wrote down the celebrated Bayes’ formula in the form we know today. Although not identified yet as a framework for investigating inverse problems, Laplace used the formalism very much in the spirit it is used today in the context of inverse problems, e.g., in his study of the distribution of comets. With the evolution of computational tools, Bayesian methods have become increasingly popular in all fields of human knowledge in which conclusions need to be drawn based on incomplete and noisy data. Needless to say, inverse problems, almost by definition, fall into this category. Systematic work for developing a Bayesian inverse problem framework can arguably be traced back to the 1980s, (the original first edition being published by Elsevier in 1987), although articles on Bayesian methodology applied to inverse problems, in particular in geophysics, had appeared much earlier. Today, as testified by the articles in this special issue, the Bayesian methodology as a framework for considering inverse problems has gained a lot of popularity, and it has integrated very successfully with many traditional inverse problems ideas and techniques, providing novel ways to interpret and implement traditional procedures in numerical analysis, computational statistics, signal analysis and data assimilation. The range of applications where the Bayesian framework has been fundamental goes from geophysics, engineering and imaging to astronomy, life sciences and economy, and continues to grow. There is no question that Bayesian

Effect of hierarchical meso–macroporous alumina-supported copper catalyst for methanol synthesis from CO2 hydrogenation

International Nuclear Information System (INIS)

Witoon, Thongthai; Bumrungsalee, Sittisut; Chareonpanich, Metta; Limtrakul, Jumras

2015-01-01

Highlights: • CO 2 hydrogenation over Cu-loaded unimodal and hierarchical alumina catalysts. • Cu-loaded hierarchical catalyst exhibited higher methanol selectivity and stability. • The presence of macropores reduced the probability of side reaction. - Abstract: Effects of pore structures of alumina on the catalytic performance of copper catalysts for CO 2 hydrogenation were investigated. Copper-loaded hierarchical meso–macroporous alumina (Cu/HAl) catalyst exhibited no significant difference in terms of CO 2 conversion with copper-loaded unimodal mesoporous alumina (Cu/UAl) catalyst. However, the selectivity to methanol and dimethyl ether of the Cu/HAl catalyst was much higher than that of the Cu/UAl catalyst. This was attributed to the presence of macropores which diminished the occurrence of side reaction by the shortening the mesopores diffusion path length. The Cu/HAl catalyst also exhibited much higher stability than the Cu/UAl catalyst due to the fast diffusion of water out from the catalyst pellets, alleviating the oxidation of metallic copper to CuO

The current state of Bayesian methods in medical product development: survey results and recommendations from the DIA Bayesian Scientific Working Group.

Science.gov (United States)

Natanegara, Fanni; Neuenschwander, Beat; Seaman, John W; Kinnersley, Nelson; Heilmann, Cory R; Ohlssen, David; Rochester, George

2014-01-01

Bayesian applications in medical product development have recently gained popularity. Despite many advances in Bayesian methodology and computations, increase in application across the various areas of medical product development has been modest. The DIA Bayesian Scientific Working Group (BSWG), which includes representatives from industry, regulatory agencies, and academia, has adopted the vision to ensure Bayesian methods are well understood, accepted more broadly, and appropriately utilized to improve decision making and enhance patient outcomes. As Bayesian applications in medical product development are wide ranging, several sub-teams were formed to focus on various topics such as patient safety, non-inferiority, prior specification, comparative effectiveness, joint modeling, program-wide decision making, analytical tools, and education. The focus of this paper is on the recent effort of the BSWG Education sub-team to administer a Bayesian survey to statisticians across 17 organizations involved in medical product development. We summarize results of this survey, from which we provide recommendations on how to accelerate progress in Bayesian applications throughout medical product development. The survey results support findings from the literature and provide additional insight on regulatory acceptance of Bayesian methods and information on the need for a Bayesian infrastructure within an organization. The survey findings support the claim that only modest progress in areas of education and implementation has been made recently, despite substantial progress in Bayesian statistical research and software availability. Copyright © 2013 John Wiley & Sons, Ltd.

BayesTwin: An R Package for Bayesian Inference of Item-Level Twin Data

Directory of Open Access Journals (Sweden)

Inga Schwabe

2017-11-01

Full Text Available BayesTwin is an open-source R package that serves as a pipeline to the MCMC program JAGS to perform Bayesian inference on genetically-informative hierarchical twin data. Simultaneously to the biometric model, an item response theory (IRT measurement model is estimated, allowing analysis of the raw phenotypic (item-level data. The integration of such a measurement model is important since earlier research has shown that an analysis based on an aggregated measure (e.g., a sum-score based analysis can lead to an underestimation of heritability and the spurious finding of genotype-environment interactions. The package includes all common biometric and IRT models as well as functions that help plot relevant information or determine whether the analysis was performed well. Funding statement: Partly funded by the PROO grant 411-12-623 from the Netherlands Organisation for Scientific Research (NWO.

None of the above: A Bayesian account of the detection of novel categories.

Science.gov (United States)

Navarro, Daniel J; Kemp, Charles

2017-10-01

Every time we encounter a new object, action, or event, there is some chance that we will need to assign it to a novel category. We describe and evaluate a class of probabilistic models that detect when an object belongs to a category that has not previously been encountered. The models incorporate a prior distribution that is influenced by the distribution of previous objects among categories, and we present 2 experiments that demonstrate that people are also sensitive to this distributional information. Two additional experiments confirm that distributional information is combined with similarity when both sources of information are available. We compare our approach to previous models of unsupervised categorization and to several heuristic-based models, and find that a hierarchical Bayesian approach provides the best account of our data. (PsycINFO Database Record (c) 2017 APA, all rights reserved).

Bayesian Alternation During Tactile Augmentation

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Caspar Mathias Goeke

2016-10-01

Full Text Available A large number of studies suggest that the integration of multisensory signals by humans is well described by Bayesian principles. However, there are very few reports about cue combination between a native and an augmented sense. In particular, we asked the question whether adult participants are able to integrate an augmented sensory cue with existing native sensory information. Hence for the purpose of this study we build a tactile augmentation device. Consequently, we compared different hypotheses of how untrained adult participants combine information from a native and an augmented sense. In a two-interval forced choice (2 IFC task, while subjects were blindfolded and seated on a rotating platform, our sensory augmentation device translated information on whole body yaw rotation to tactile stimulation. Three conditions were realized: tactile stimulation only (augmented condition, rotation only (native condition, and both augmented and native information (bimodal condition. Participants had to choose one out of two consecutive rotations with higher angular rotation. For the analysis, we fitted the participants’ responses with a probit model and calculated the just notable difference (JND. Then we compared several models for predicting bimodal from unimodal responses. An objective Bayesian alternation model yielded a better prediction (χred2 = 1.67 than the Bayesian integration model (χred2= 4.34. Slightly higher accuracy showed a non-Bayesian winner takes all model (χred2= 1.64, which either used only native or only augmented values per subject for prediction. However the performance of the Bayesian alternation model could be substantially improved (χred2= 1.09 utilizing subjective weights obtained by a questionnaire. As a result, the subjective Bayesian alternation model predicted bimodal performance most accurately among all tested models. These results suggest that information from augmented and existing sensory modalities in

In situ fast pyrolysis of biomass with zeolite catalysts for bioaromatics/gasoline production: A review

International Nuclear Information System (INIS)

Galadima, Ahmad; Muraza, Oki

2015-01-01

Highlights: • Biomass upgrading by fast pyrolysis is an attractive bioaromatics production. • Zeolite catalysts are key important systems considered for the process. • Catalytic activity depend on zeolite structure, acidity and textural features. • Recent literature on the role of the zeolite catalysts critically tailored. • Hierarchical zeolites are prospective catalysts for industrial applications. - Abstract: The fast pyrolysis of biomass-based feedstocks is currently gaining considerable attention as an industrial and sustainable option for the production of gasoline-range bioaromatics. The complex composition of biomass molecules and a series of reactions involved during the upgrading process require the incorporation of sufficiently acidic and topological catalysts. This paper carefully documents and analyzes recent publications that have investigated the properties of zeolites to enhance the yield of bioaromatics during in situ fast pyrolysis. Issues related to the effects of zeolite’s textural, topological and acidic properties are critically examined. Factors responsible for catalyst deactivation and the mechanistic roles of the catalysts used are discussed. This paper also explores the prospects of hierarchical zeolites and municipal solid waste (MSW) as catalysts and feedstocks for the fast pyrolysis process.

Bayesian Network Induction via Local Neighborhoods

National Research Council Canada - National Science Library

Margaritis, Dimitris

1999-01-01

.... We present an efficient algorithm for learning Bayesian networks from data. Our approach constructs Bayesian networks by first identifying each node's Markov blankets, then connecting nodes in a consistent way...

Hierarchical hollow spheres of Fe2O3 @polyaniline for lithium ion battery anodes.

Science.gov (United States)

Jeong, Jae-Min; Choi, Bong Gill; Lee, Soon Chang; Lee, Kyoung G; Chang, Sung-Jin; Han, Young-Kyu; Lee, Young Boo; Lee, Hyun Uk; Kwon, Soonjo; Lee, Gaehang; Lee, Chang-Soo; Huh, Yun Suk

2013-11-20

Hierarchical hollow spheres of Fe2 O3 @polyaniline are fabricated by template-free synthesis of iron oxides followed by a post in- and exterior construction. A combination of large surface area with porous structure, fast ion/electron transport, and mechanical integrity renders this material attractive as a lithium-ion anode, showing superior rate capability and cycling performance. © 2013 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim.

Catalysis with hierarchical zeolites

DEFF Research Database (Denmark)

Holm, Martin Spangsberg; Taarning, Esben; Egeblad, Kresten

2011-01-01

Hierarchical (or mesoporous) zeolites have attracted significant attention during the first decade of the 21st century, and so far this interest continues to increase. There have already been several reviews giving detailed accounts of the developments emphasizing different aspects of this research...... topic. Until now, the main reason for developing hierarchical zeolites has been to achieve heterogeneous catalysts with improved performance but this particular facet has not yet been reviewed in detail. Thus, the present paper summaries and categorizes the catalytic studies utilizing hierarchical...... zeolites that have been reported hitherto. Prototypical examples from some of the different categories of catalytic reactions that have been studied using hierarchical zeolite catalysts are highlighted. This clearly illustrates the different ways that improved performance can be achieved with this family...

A Bayesian encourages dropout

OpenAIRE

Maeda, Shin-ichi

2014-01-01

Dropout is one of the key techniques to prevent the learning from overfitting. It is explained that dropout works as a kind of modified L2 regularization. Here, we shed light on the dropout from Bayesian standpoint. Bayesian interpretation enables us to optimize the dropout rate, which is beneficial for learning of weight parameters and prediction after learning. The experiment result also encourages the optimization of the dropout.

Bayesian Data Analysis (lecture 2)

CERN Multimedia

CERN. Geneva

2018-01-01

framework but we will also go into more detail and discuss for example the role of the prior. The second part of the lecture will cover further examples and applications that heavily rely on the bayesian approach, as well as some computational tools needed to perform a bayesian analysis.

Bayesian Data Analysis (lecture 1)

CERN Multimedia

CERN. Geneva

2018-01-01

framework but we will also go into more detail and discuss for example the role of the prior. The second part of the lecture will cover further examples and applications that heavily rely on the bayesian approach, as well as some computational tools needed to perform a bayesian analysis.

Probabilistic modeling of bifurcations in single-cell gene expression data using a Bayesian mixture of factor analyzers [version 1; referees: 2 approved

Directory of Open Access Journals (Sweden)

Kieran R Campbell

2017-03-01

Full Text Available Modeling bifurcations in single-cell transcriptomics data has become an increasingly popular field of research. Several methods have been proposed to infer bifurcation structure from such data, but all rely on heuristic non-probabilistic inference. Here we propose the first generative, fully probabilistic model for such inference based on a Bayesian hierarchical mixture of factor analyzers. Our model exhibits competitive performance on large datasets despite implementing full Markov-Chain Monte Carlo sampling, and its unique hierarchical prior structure enables automatic determination of genes driving the bifurcation process. We additionally propose an Empirical-Bayes like extension that deals with the high levels of zero-inflation in single-cell RNA-seq data and quantify when such models are useful. We apply or model to both real and simulated single-cell gene expression data and compare the results to existing pseudotime methods. Finally, we discuss both the merits and weaknesses of such a unified, probabilistic approach in the context practical bioinformatics analyses.

Parallel hierarchical radiosity rendering

Energy Technology Data Exchange (ETDEWEB)

Carter, Michael [Iowa State Univ., Ames, IA (United States)

1993-07-01

In this dissertation, the step-by-step development of a scalable parallel hierarchical radiosity renderer is documented. First, a new look is taken at the traditional radiosity equation, and a new form is presented in which the matrix of linear system coefficients is transformed into a symmetric matrix, thereby simplifying the problem and enabling a new solution technique to be applied. Next, the state-of-the-art hierarchical radiosity methods are examined for their suitability to parallel implementation, and scalability. Significant enhancements are also discovered which both improve their theoretical foundations and improve the images they generate. The resultant hierarchical radiosity algorithm is then examined for sources of parallelism, and for an architectural mapping. Several architectural mappings are discussed. A few key algorithmic changes are suggested during the process of making the algorithm parallel. Next, the performance, efficiency, and scalability of the algorithm are analyzed. The dissertation closes with a discussion of several ideas which have the potential to further enhance the hierarchical radiosity method, or provide an entirely new forum for the application of hierarchical methods.

Hierarchical prisoner’s dilemma in hierarchical game for resource competition

Science.gov (United States)

Fujimoto, Yuma; Sagawa, Takahiro; Kaneko, Kunihiko

2017-07-01

Dilemmas in cooperation are one of the major concerns in game theory. In a public goods game, each individual cooperates by paying a cost or defecting without paying it, and receives a reward from the group out of the collected cost. Thus, defecting is beneficial for each individual, while cooperation is beneficial for the group. Now, groups (say, countries) consisting of individuals also play games. To study such a multi-level game, we introduce a hierarchical game in which multiple groups compete for limited resources by utilizing the collected cost in each group, where the power to appropriate resources increases with the population of the group. Analyzing this hierarchical game, we found a hierarchical prisoner’s dilemma, in which groups choose the defecting policy (say, armament) as a Nash strategy to optimize each group’s benefit, while cooperation optimizes the total benefit. On the other hand, for each individual, refusing to pay the cost (say, tax) is a Nash strategy, which turns out to be a cooperation policy for the group, thus leading to a hierarchical dilemma. Here the group reward increases with the group size. However, we find that there exists an optimal group size that maximizes the individual payoff. Furthermore, when the population asymmetry between two groups is large, the smaller group will choose a cooperation policy (say, disarmament) to avoid excessive response from the larger group, and the prisoner’s dilemma between the groups is resolved. Accordingly, the relevance of this hierarchical game on policy selection in society and the optimal size of human or animal groups are discussed.

Learning Local Components to Understand Large Bayesian Networks

DEFF Research Database (Denmark)

Zeng, Yifeng; Xiang, Yanping; Cordero, Jorge

2009-01-01

(domain experts) to extract accurate information from a large Bayesian network due to dimensional difficulty. We define a formulation of local components and propose a clustering algorithm to learn such local components given complete data. The algorithm groups together most inter-relevant attributes......Bayesian networks are known for providing an intuitive and compact representation of probabilistic information and allowing the creation of models over a large and complex domain. Bayesian learning and reasoning are nontrivial for a large Bayesian network. In parallel, it is a tough job for users...... in a domain. We evaluate its performance on three benchmark Bayesian networks and provide results in support. We further show that the learned components may represent local knowledge more precisely in comparison to the full Bayesian networks when working with a small amount of data....

Philosophy and the practice of Bayesian statistics.

Science.gov (United States)

Gelman, Andrew; Shalizi, Cosma Rohilla

2013-02-01

A substantial school in the philosophy of science identifies Bayesian inference with inductive inference and even rationality as such, and seems to be strengthened by the rise and practical success of Bayesian statistics. We argue that the most successful forms of Bayesian statistics do not actually support that particular philosophy but rather accord much better with sophisticated forms of hypothetico-deductivism. We examine the actual role played by prior distributions in Bayesian models, and the crucial aspects of model checking and model revision, which fall outside the scope of Bayesian confirmation theory. We draw on the literature on the consistency of Bayesian updating and also on our experience of applied work in social science. Clarity about these matters should benefit not just philosophy of science, but also statistical practice. At best, the inductivist view has encouraged researchers to fit and compare models without checking them; at worst, theorists have actively discouraged practitioners from performing model checking because it does not fit into their framework. © 2012 The British Psychological Society.

Time-reversal and Bayesian inversion

Science.gov (United States)

Debski, Wojciech

2017-04-01

Probabilistic inversion technique is superior to the classical optimization-based approach in all but one aspects. It requires quite exhaustive computations which prohibit its use in huge size inverse problems like global seismic tomography or waveform inversion to name a few. The advantages of the approach are, however, so appealing that there is an ongoing continuous afford to make the large inverse task as mentioned above manageable with the probabilistic inverse approach. One of the perspective possibility to achieve this goal relays on exploring the internal symmetry of the seismological modeling problems in hand - a time reversal and reciprocity invariance. This two basic properties of the elastic wave equation when incorporating into the probabilistic inversion schemata open a new horizons for Bayesian inversion. In this presentation we discuss the time reversal symmetry property, its mathematical aspects and propose how to combine it with the probabilistic inverse theory into a compact, fast inversion algorithm. We illustrate the proposed idea with the newly developed location algorithm TRMLOC and discuss its efficiency when applied to mining induced seismic data.

A hierarchical bayesian analysis of parasite prevalence and sociocultural outcomes: The role of structural racism and sanitation infrastructure.

Science.gov (United States)

Ross, Cody T; Winterhalder, Bruce

2016-01-01

We conduct a revaluation of the Thornhill and Fincher research project on parasites using finely-resolved geographic data on parasite prevalence, individual-level sociocultural data, and multilevel Bayesian modeling. In contrast to the evolutionary psychological mechanisms linking parasites to human behavior and cultural characteristics proposed by Thornhill and Fincher, we offer an alternative hypothesis that structural racism and differential access to sanitation systems drive both variation in parasite prevalence and differential behaviors and cultural characteristics. We adopt a Bayesian framework to estimate parasite prevalence rates in 51 districts in eight Latin American countries using the disease status of 170,220 individuals tested for infection with the intestinal roundworm Ascaris lumbricoides (Hürlimann et al., []: PLoS Negl Trop Dis 5:e1404). We then use district-level estimates of parasite prevalence and individual-level social data from 5,558 individuals in the same 51 districts (Latinobarómetro, 2008) to assess claims of causal associations between parasite prevalence and sociocultural characteristics. We find, contrary to Thornhill and Fincher, that parasite prevalence is positively associated with preferences for democracy, negatively associated with preferences for collectivism, and not associated with violent crime rates or gender inequality. A positive association between parasite prevalence and religiosity, as in Fincher and Thornhill (: Behav Brain Sci 35:61-79), and a negative association between parasite prevalence and achieved education, as predicted by Eppig et al. (: Proc R S B: Biol Sci 277:3801-3808), become negative and unreliable when reasonable controls are included in the model. We find support for all predictions derived from our hypothesis linking structural racism to both parasite prevalence and cultural outcomes. We conclude that best practices in biocultural modeling require examining more than one hypothesis, retaining

Enhanced supercapacitor performance using hierarchical TiO2 nanorod/Co(OH)2 nanowall array electrodes

International Nuclear Information System (INIS)

Ramadoss, Ananthakumar; Kim, Sang Jae

2014-01-01

Graphical abstract: - Highlights: • TiO 2 /Co(OH) 2 hierarchical nanostructure was prepared by a combination of hydrothermal and cathodic electrodeposition method. • Hierarchical nanostructure electrode exhibited a maximum capacitance of 274.3 mF cm −2 at a scan rate of 5 mV s −1 . • Combination of Co(OH) 2 nanowall with TiO 2 NR into a single system enhanced the electrochemical behavior of supercapacitor electrode. - Abstract: We report novel hierarchical TiO 2 nanorod (NR)/porous Co(OH) 2 nanowall array electrodes for high-performance supercapacitors fabricated using a two-step process that involves hydrothermal and electrodeposition techniques. Field-emission scanning electron microscope images reveal a bilayer structure consisting of TiO 2 NR arrays with porous Co(OH) 2 nanowalls. Compared with the bare TiO 2 NRs, the hierarchical TiO 2 NRs/Co(OH) 2 electrodes showed improved pseudocapacitive performance in a 2-M KOH electrolyte solution, exhibiting an areal specific capacitance of 274.3 mF cm −2 at a scan rate of 5 mV s −1 . The electrodes exhibited good stability, retaining 82.5% of the initial capacitance after 4000 cycles. The good pseudocapacitive performance of the hierarchical nanostructures is mainly due to the porous structure, which provides fast ion and electron transfer, a large surface area, short ion diffusion paths, and a favourable volume change during the cycling process

Validation of Bayesian analysis of compartmental kinetic models in medical imaging.

Science.gov (United States)

Sitek, Arkadiusz; Li, Quanzheng; El Fakhri, Georges; Alpert, Nathaniel M

2016-10-01

Kinetic compartmental analysis is frequently used to compute physiologically relevant quantitative values from time series of images. In this paper, a new approach based on Bayesian analysis to obtain information about these parameters is presented and validated. The closed-form of the posterior distribution of kinetic parameters is derived with a hierarchical prior to model the standard deviation of normally distributed noise. Markov chain Monte Carlo methods are used for numerical estimation of the posterior distribution. Computer simulations of the kinetics of F18-fluorodeoxyglucose (FDG) are used to demonstrate drawing statistical inferences about kinetic parameters and to validate the theory and implementation. Additionally, point estimates of kinetic parameters and covariance of those estimates are determined using the classical non-linear least squares approach. Posteriors obtained using methods proposed in this work are accurate as no significant deviation from the expected shape of the posterior was found (one-sided P>0.08). It is demonstrated that the results obtained by the standard non-linear least-square methods fail to provide accurate estimation of uncertainty for the same data set (P<0.0001). The results of this work validate new methods for a computer simulations of FDG kinetics. Results show that in situations where the classical approach fails in accurate estimation of uncertainty, Bayesian estimation provides an accurate information about the uncertainties in the parameters. Although a particular example of FDG kinetics was used in the paper, the methods can be extended for different pharmaceuticals and imaging modalities. Copyright © 2016 Associazione Italiana di Fisica Medica. Published by Elsevier Ltd. All rights reserved.

Bayesian projection of life expectancy accounting for the HIV/AIDS epidemic

Directory of Open Access Journals (Sweden)

Jessica Godwin

2017-11-01

Full Text Available Background: While probabilistic projection methods for projecting life expectancy exist, few account for covariates related to life expectancy. Generalized HIV/AIDS epidemics have a large, immediate negative impact on the life expectancy in a country, but this impact can be mitigated by widespread use of antiretroviral therapy (ART. Thus, projection methods for countries with generalized HIV/AIDS epidemics could be improved by accounting for HIV prevalence, the future course of the epidemic, and ART coverage. Methods: We extend the current Bayesian probabilistic life expectancy projection methods of Raftery et al. (2013 to account for HIV prevalence and adult ART coverage in countries with generalized HIV/AIDS epidemics. Results: We evaluate our method using out-of-sample validation. We find that the proposed method performs better than the method that does not account for HIV prevalence or ART coverage for projections of life expectancy in countries with a generalized epidemic, while projections for countries without an epidemic remain essentially unchanged. Conclusions: In general, our projections show rapid recovery to pre-epidemic life expectancy levels in the presence of widespread ART coverage. After the initial life expectancy recovery, we project a steady rise in life expectancy until the end of the century. Contribution: We develop a simple Bayesian hierarchical model for long-term projections of life expectancy while accounting for HIV/AIDS prevalence and coverage of ART. The method produces well-calibrated projections for countries with generalized HIV/AIDS epidemics up to 2100 while having limited data demands.

Micromechanics of hierarchical materials

DEFF Research Database (Denmark)

Mishnaevsky, Leon, Jr.

2012-01-01

A short overview of micromechanical models of hierarchical materials (hybrid composites, biomaterials, fractal materials, etc.) is given. Several examples of the modeling of strength and damage in hierarchical materials are summarized, among them, 3D FE model of hybrid composites...... with nanoengineered matrix, fiber bundle model of UD composites with hierarchically clustered fibers and 3D multilevel model of wood considered as a gradient, cellular material with layered composite cell walls. The main areas of research in micromechanics of hierarchical materials are identified, among them......, the investigations of the effects of load redistribution between reinforcing elements at different scale levels, of the possibilities to control different material properties and to ensure synergy of strengthening effects at different scale levels and using the nanoreinforcement effects. The main future directions...

Bayesian Utilitarianism

OpenAIRE

ZHOU, Lin

1996-01-01

In this paper I consider social choices under uncertainty. I prove that any social choice rule that satisfies independence of irrelevant alternatives, translation invariance, and weak anonymity is consistent with ex post Bayesian utilitarianism

Bayesian tomographic reconstruction of microsystems

International Nuclear Information System (INIS)

Salem, Sofia Fekih; Vabre, Alexandre; Mohammad-Djafari, Ali

2007-01-01

The microtomography by X ray transmission plays an increasingly dominating role in the study and the understanding of microsystems. Within this framework, an experimental setup of high resolution X ray microtomography was developed at CEA-List to quantify the physical parameters related to the fluids flow in microsystems. Several difficulties rise from the nature of experimental data collected on this setup: enhanced error measurements due to various physical phenomena occurring during the image formation (diffusion, beam hardening), and specificities of the setup (limited angle, partial view of the object, weak contrast).To reconstruct the object we must solve an inverse problem. This inverse problem is known to be ill-posed. It therefore needs to be regularized by introducing prior information. The main prior information we account for is that the object is composed of a finite known number of different materials distributed in compact regions. This a priori information is introduced via a Gauss-Markov field for the contrast distributions with a hidden Potts-Markov field for the class materials in the Bayesian estimation framework. The computations are done by using an appropriate Markov Chain Monte Carlo (MCMC) technique.In this paper, we present first the basic steps of the proposed algorithms. Then we focus on one of the main steps in any iterative reconstruction method which is the computation of forward and adjoint operators (projection and backprojection). A fast implementation of these two operators is crucial for the real application of the method. We give some details on the fast computation of these steps and show some preliminary results of simulations

Learning Bayesian networks for discrete data

KAUST Repository

Liang, Faming; Zhang, Jian

2009-01-01

Bayesian networks have received much attention in the recent literature. In this article, we propose an approach to learn Bayesian networks using the stochastic approximation Monte Carlo (SAMC) algorithm. Our approach has two nice features. Firstly

Searching Algorithm Using Bayesian Updates

Science.gov (United States)

Caudle, Kyle

2010-01-01

In late October 1967, the USS Scorpion was lost at sea, somewhere between the Azores and Norfolk Virginia. Dr. Craven of the U.S. Navy's Special Projects Division is credited with using Bayesian Search Theory to locate the submarine. Bayesian Search Theory is a straightforward and interesting application of Bayes' theorem which involves searching…

Bayesian estimates of linkage disequilibrium

Directory of Open Access Journals (Sweden)

Abad-Grau María M

2007-06-01

Full Text Available Abstract Background The maximum likelihood estimator of D' – a standard measure of linkage disequilibrium – is biased toward disequilibrium, and the bias is particularly evident in small samples and rare haplotypes. Results This paper proposes a Bayesian estimation of D' to address this problem. The reduction of the bias is achieved by using a prior distribution on the pair-wise associations between single nucleotide polymorphisms (SNPs that increases the likelihood of equilibrium with increasing physical distances between pairs of SNPs. We show how to compute the Bayesian estimate using a stochastic estimation based on MCMC methods, and also propose a numerical approximation to the Bayesian estimates that can be used to estimate patterns of LD in large datasets of SNPs. Conclusion Our Bayesian estimator of D' corrects the bias toward disequilibrium that affects the maximum likelihood estimator. A consequence of this feature is a more objective view about the extent of linkage disequilibrium in the human genome, and a more realistic number of tagging SNPs to fully exploit the power of genome wide association studies.

A method for calculating Bayesian uncertainties on internal doses resulting from complex occupational exposures

International Nuclear Information System (INIS)

Puncher, M.; Birchall, A.; Bull, R. K.

2012-01-01

Estimating uncertainties on doses from bioassay data is of interest in epidemiology studies that estimate cancer risk from occupational exposures to radionuclides. Bayesian methods provide a logical framework to calculate these uncertainties. However, occupational exposures often consist of many intakes, and this can make the Bayesian calculation computationally intractable. This paper describes a novel strategy for increasing the computational speed of the calculation by simplifying the intake pattern to a single composite intake, termed as complex intake regime (CIR). In order to assess whether this approximation is accurate and fast enough for practical purposes, the method is implemented by the Weighted Likelihood Monte Carlo Sampling (WeLMoS) method and evaluated by comparing its performance with a Markov Chain Monte Carlo (MCMC) method. The MCMC method gives the full solution (all intakes are independent), but is very computationally intensive to apply routinely. Posterior distributions of model parameter values, intakes and doses are calculated for a representative sample of plutonium workers from the United Kingdom Atomic Energy cohort using the WeLMoS method with the CIR and the MCMC method. The distributions are in good agreement: posterior means and Q 0.025 and Q 0.975 quantiles are typically within 20 %. Furthermore, the WeLMoS method using the CIR converges quickly: a typical case history takes around 10-20 min on a fast workstation, whereas the MCMC method took around 12-hr. The advantages and disadvantages of the method are discussed. (authors)

Communication Reducing Algorithms for Distributed Hierarchical N-Body Problems with Boundary Distributions

KAUST Repository

AbdulJabbar, Mustafa Abdulmajeed

2017-05-11

Reduction of communication and efficient partitioning are key issues for achieving scalability in hierarchical N-Body algorithms like Fast Multipole Method (FMM). In the present work, we propose three independent strategies to improve partitioning and reduce communication. First, we show that the conventional wisdom of using space-filling curve partitioning may not work well for boundary integral problems, which constitute a significant portion of FMM’s application user base. We propose an alternative method that modifies orthogonal recursive bisection to relieve the cell-partition misalignment that has kept it from scaling previously. Secondly, we optimize the granularity of communication to find the optimal balance between a bulk-synchronous collective communication of the local essential tree and an RDMA per task per cell. Finally, we take the dynamic sparse data exchange proposed by Hoefler et al. [1] and extend it to a hierarchical sparse data exchange, which is demonstrated at scale to be faster than the MPI library’s MPI_Alltoallv that is commonly used.

Artificial muscle-like function from hierarchical supramolecular assembly of photoresponsive molecular motors.

Science.gov (United States)

Chen, Jiawen; Leung, Franco King-Chi; Stuart, Marc C A; Kajitani, Takashi; Fukushima, Takanori; van der Giessen, Erik; Feringa, Ben L

2018-02-01

A striking feature of living systems is their ability to produce motility by amplification of collective molecular motion from the nanoscale up to macroscopic dimensions. Some of nature's protein motors, such as myosin in muscle tissue, consist of a hierarchical supramolecular assembly of very large proteins, in which mechanical stress induces a coordinated movement. However, artificial molecular muscles have often relied on covalent polymer-based actuators. Here, we describe the macroscopic contractile muscle-like motion of a supramolecular system (comprising 95% water) formed by the hierarchical self-assembly of a photoresponsive amphiphilic molecular motor. The molecular motor first assembles into nanofibres, which further assemble into aligned bundles that make up centimetre-long strings. Irradiation induces rotary motion of the molecular motors, and propagation and accumulation of this motion lead to contraction of the fibres towards the light source. This system supports large-amplitude motion, fast response, precise control over shape, as well as weight-lifting experiments in water and air.

Artificial muscle-like function from hierarchical supramolecular assembly of photoresponsive molecular motors

Science.gov (United States)

Chen, Jiawen; Leung, Franco King-Chi; Stuart, Marc C. A.; Kajitani, Takashi; Fukushima, Takanori; van der Giessen, Erik; Feringa, Ben L.

2018-02-01

A striking feature of living systems is their ability to produce motility by amplification of collective molecular motion from the nanoscale up to macroscopic dimensions. Some of nature's protein motors, such as myosin in muscle tissue, consist of a hierarchical supramolecular assembly of very large proteins, in which mechanical stress induces a coordinated movement. However, artificial molecular muscles have often relied on covalent polymer-based actuators. Here, we describe the macroscopic contractile muscle-like motion of a supramolecular system (comprising 95% water) formed by the hierarchical self-assembly of a photoresponsive amphiphilic molecular motor. The molecular motor first assembles into nanofibres, which further assemble into aligned bundles that make up centimetre-long strings. Irradiation induces rotary motion of the molecular motors, and propagation and accumulation of this motion lead to contraction of the fibres towards the light source. This system supports large-amplitude motion, fast response, precise control over shape, as well as weight-lifting experiments in water and air.

How hierarchical is language use?

Science.gov (United States)

Frank, Stefan L.; Bod, Rens; Christiansen, Morten H.

2012-01-01

It is generally assumed that hierarchical phrase structure plays a central role in human language. However, considerations of simplicity and evolutionary continuity suggest that hierarchical structure should not be invoked too hastily. Indeed, recent neurophysiological, behavioural and computational studies show that sequential sentence structure has considerable explanatory power and that hierarchical processing is often not involved. In this paper, we review evidence from the recent literature supporting the hypothesis that sequential structure may be fundamental to the comprehension, production and acquisition of human language. Moreover, we provide a preliminary sketch outlining a non-hierarchical model of language use and discuss its implications and testable predictions. If linguistic phenomena can be explained by sequential rather than hierarchical structure, this will have considerable impact in a wide range of fields, such as linguistics, ethology, cognitive neuroscience, psychology and computer science. PMID:22977157

Learning Bayesian networks for discrete data

KAUST Repository

Liang, Faming

2009-02-01

Bayesian networks have received much attention in the recent literature. In this article, we propose an approach to learn Bayesian networks using the stochastic approximation Monte Carlo (SAMC) algorithm. Our approach has two nice features. Firstly, it possesses the self-adjusting mechanism and thus avoids essentially the local-trap problem suffered by conventional MCMC simulation-based approaches in learning Bayesian networks. Secondly, it falls into the class of dynamic importance sampling algorithms; the network features can be inferred by dynamically weighted averaging the samples generated in the learning process, and the resulting estimates can have much lower variation than the single model-based estimates. The numerical results indicate that our approach can mix much faster over the space of Bayesian networks than the conventional MCMC simulation-based approaches. © 2008 Elsevier B.V. All rights reserved.

Random resampling masks: a non-Bayesian one-shot strategy for noise reduction in digital holography.

Science.gov (United States)

Bianco, V; Paturzo, M; Memmolo, P; Finizio, A; Ferraro, P; Javidi, B

2013-03-01

Holographic imaging may become severely degraded by a mixture of speckle and incoherent additive noise. Bayesian approaches reduce the incoherent noise, but prior information is needed on the noise statistics. With no prior knowledge, one-shot reduction of noise is a highly desirable goal, as the recording process is simplified and made faster. Indeed, neither multiple acquisitions nor a complex setup are needed. So far, this result has been achieved at the cost of a deterministic resolution loss. Here we propose a fast non-Bayesian denoising method that avoids this trade-off by means of a numerical synthesis of a moving diffuser. In this way, only one single hologram is required as multiple uncorrelated reconstructions are provided by random complementary resampling masks. Experiments show a significant incoherent noise reduction, close to the theoretical improvement bound, resulting in image-contrast improvement. At the same time, we preserve the resolution of the unprocessed image.

On hierarchical models for visual recognition and learning of objects, scenes, and activities

CERN Document Server

Spehr, Jens

2015-01-01

In many computer vision applications, objects have to be learned and recognized in images or image sequences. This book presents new probabilistic hierarchical models that allow an efficient representation of multiple objects of different categories, scales, rotations, and views. The idea is to exploit similarities between objects and object parts in order to share calculations and avoid redundant information. Furthermore inference approaches for fast and robust detection are presented. These new approaches combine the idea of compositional and similarity hierarchies and overcome limitations of previous methods. Besides classical object recognition the book shows the use for detection of human poses in a project for gait analysis. The use of activity detection is presented for the design of environments for ageing, to identify activities and behavior patterns in smart homes. In a presented project for parking spot detection using an intelligent vehicle, the proposed approaches are used to hierarchically model...

Dynamic classification of fetal heart rates by hierarchical Dirichlet process mixture models.

Directory of Open Access Journals (Sweden)

Kezi Yu

Full Text Available In this paper, we propose an application of non-parametric Bayesian (NPB models for classification of fetal heart rate (FHR recordings. More specifically, we propose models that are used to differentiate between FHR recordings that are from fetuses with or without adverse outcomes. In our work, we rely on models based on hierarchical Dirichlet processes (HDP and the Chinese restaurant process with finite capacity (CRFC. Two mixture models were inferred from real recordings, one that represents healthy and another, non-healthy fetuses. The models were then used to classify new recordings and provide the probability of the fetus being healthy. First, we compared the classification performance of the HDP models with that of support vector machines on real data and concluded that the HDP models achieved better performance. Then we demonstrated the use of mixture models based on CRFC for dynamic classification of the performance of (FHR recordings in a real-time setting.

A default Bayesian hypothesis test for ANOVA designs

NARCIS (Netherlands)

Wetzels, R.; Grasman, R.P.P.P.; Wagenmakers, E.J.

2012-01-01

This article presents a Bayesian hypothesis test for analysis of variance (ANOVA) designs. The test is an application of standard Bayesian methods for variable selection in regression models. We illustrate the effect of various g-priors on the ANOVA hypothesis test. The Bayesian test for ANOVA

Hierarchical architecture of active knits

International Nuclear Information System (INIS)

Abel, Julianna; Luntz, Jonathan; Brei, Diann

2013-01-01

Nature eloquently utilizes hierarchical structures to form the world around us. Applying the hierarchical architecture paradigm to smart materials can provide a basis for a new genre of actuators which produce complex actuation motions. One promising example of cellular architecture—active knits—provides complex three-dimensional distributed actuation motions with expanded operational performance through a hierarchically organized structure. The hierarchical structure arranges a single fiber of active material, such as shape memory alloys (SMAs), into a cellular network of interlacing adjacent loops according to a knitting grid. This paper defines a four-level hierarchical classification of knit structures: the basic knit loop, knit patterns, grid patterns, and restructured grids. Each level of the hierarchy provides increased architectural complexity, resulting in expanded kinematic actuation motions of active knits. The range of kinematic actuation motions are displayed through experimental examples of different SMA active knits. The results from this paper illustrate and classify the ways in which each level of the hierarchical knit architecture leverages the performance of the base smart material to generate unique actuation motions, providing necessary insight to best exploit this new actuation paradigm. (paper)

Bayesian Networks An Introduction

CERN Document Server

Koski, Timo

2009-01-01

Bayesian Networks: An Introduction provides a self-contained introduction to the theory and applications of Bayesian networks, a topic of interest and importance for statisticians, computer scientists and those involved in modelling complex data sets. The material has been extensively tested in classroom teaching and assumes a basic knowledge of probability, statistics and mathematics. All notions are carefully explained and feature exercises throughout. Features include:.: An introduction to Dirichlet Distribution, Exponential Families and their applications.; A detailed description of learni

A default Bayesian hypothesis test for mediation.

Science.gov (United States)

Nuijten, Michèle B; Wetzels, Ruud; Matzke, Dora; Dolan, Conor V; Wagenmakers, Eric-Jan

2015-03-01

In order to quantify the relationship between multiple variables, researchers often carry out a mediation analysis. In such an analysis, a mediator (e.g., knowledge of a healthy diet) transmits the effect from an independent variable (e.g., classroom instruction on a healthy diet) to a dependent variable (e.g., consumption of fruits and vegetables). Almost all mediation analyses in psychology use frequentist estimation and hypothesis-testing techniques. A recent exception is Yuan and MacKinnon (Psychological Methods, 14, 301-322, 2009), who outlined a Bayesian parameter estimation procedure for mediation analysis. Here we complete the Bayesian alternative to frequentist mediation analysis by specifying a default Bayesian hypothesis test based on the Jeffreys-Zellner-Siow approach. We further extend this default Bayesian test by allowing a comparison to directional or one-sided alternatives, using Markov chain Monte Carlo techniques implemented in JAGS. All Bayesian tests are implemented in the R package BayesMed (Nuijten, Wetzels, Matzke, Dolan, & Wagenmakers, 2014).

Nested and Hierarchical Archimax copulas

KAUST Repository

Hofert, Marius

2017-07-03

The class of Archimax copulas is generalized to nested and hierarchical Archimax copulas in several ways. First, nested extreme-value copulas or nested stable tail dependence functions are introduced to construct nested Archimax copulas based on a single frailty variable. Second, a hierarchical construction of d-norm generators is presented to construct hierarchical stable tail dependence functions and thus hierarchical extreme-value copulas. Moreover, one can, by itself or additionally, introduce nested frailties to extend Archimax copulas to nested Archimax copulas in a similar way as nested Archimedean copulas extend Archimedean copulas. Further results include a general formula for the density of Archimax copulas.

Nested and Hierarchical Archimax copulas

KAUST Repository

Hofert, Marius; Huser, Raphaë l; Prasad, Avinash

2017-01-01

The class of Archimax copulas is generalized to nested and hierarchical Archimax copulas in several ways. First, nested extreme-value copulas or nested stable tail dependence functions are introduced to construct nested Archimax copulas based on a single frailty variable. Second, a hierarchical construction of d-norm generators is presented to construct hierarchical stable tail dependence functions and thus hierarchical extreme-value copulas. Moreover, one can, by itself or additionally, introduce nested frailties to extend Archimax copulas to nested Archimax copulas in a similar way as nested Archimedean copulas extend Archimedean copulas. Further results include a general formula for the density of Archimax copulas.

A Bayesian model for binary Markov chains

Directory of Open Access Journals (Sweden)

Belkheir Essebbar

2004-02-01

Full Text Available This note is concerned with Bayesian estimation of the transition probabilities of a binary Markov chain observed from heterogeneous individuals. The model is founded on the Jeffreys' prior which allows for transition probabilities to be correlated. The Bayesian estimator is approximated by means of Monte Carlo Markov chain (MCMC techniques. The performance of the Bayesian estimates is illustrated by analyzing a small simulated data set.

Inference in hybrid Bayesian networks

DEFF Research Database (Denmark)

Lanseth, Helge; Nielsen, Thomas Dyhre; Rumí, Rafael

2009-01-01

Since the 1980s, Bayesian Networks (BNs) have become increasingly popular for building statistical models of complex systems. This is particularly true for boolean systems, where BNs often prove to be a more efficient modelling framework than traditional reliability-techniques (like fault trees...... decade's research on inference in hybrid Bayesian networks. The discussions are linked to an example model for estimating human reliability....

Regulator Loss Functions and Hierarchical Modeling for Safety Decision Making.

Science.gov (United States)

Hatfield, Laura A; Baugh, Christine M; Azzone, Vanessa; Normand, Sharon-Lise T

2017-07-01

Regulators must act to protect the public when evidence indicates safety problems with medical devices. This requires complex tradeoffs among risks and benefits, which conventional safety surveillance methods do not incorporate. To combine explicit regulator loss functions with statistical evidence on medical device safety signals to improve decision making. In the Hospital Cost and Utilization Project National Inpatient Sample, we select pediatric inpatient admissions and identify adverse medical device events (AMDEs). We fit hierarchical Bayesian models to the annual hospital-level AMDE rates, accounting for patient and hospital characteristics. These models produce expected AMDE rates (a safety target), against which we compare the observed rates in a test year to compute a safety signal. We specify a set of loss functions that quantify the costs and benefits of each action as a function of the safety signal. We integrate the loss functions over the posterior distribution of the safety signal to obtain the posterior (Bayes) risk; the preferred action has the smallest Bayes risk. Using simulation and an analysis of AMDE data, we compare our minimum-risk decisions to a conventional Z score approach for classifying safety signals. The 2 rules produced different actions for nearly half of hospitals (45%). In the simulation, decisions that minimize Bayes risk outperform Z score-based decisions, even when the loss functions or hierarchical models are misspecified. Our method is sensitive to the choice of loss functions; eliciting quantitative inputs to the loss functions from regulators is challenging. A decision-theoretic approach to acting on safety signals is potentially promising but requires careful specification of loss functions in consultation with subject matter experts.

Bayesian Nonparametric Estimation of Targeted Agent Effects on Biomarker Change to Predict Clinical Outcome

Science.gov (United States)

Graziani, Rebecca; Guindani, Michele; Thall, Peter F.

2015-01-01

Summary The effect of a targeted agent on a cancer patient's clinical outcome putatively is mediated through the agent's effect on one or more early biological events. This is motivated by pre-clinical experiments with cells or animals that identify such events, represented by binary or quantitative biomarkers. When evaluating targeted agents in humans, central questions are whether the distribution of a targeted biomarker changes following treatment, the nature and magnitude of this change, and whether it is associated with clinical outcome. Major difficulties in estimating these effects are that a biomarker's distribution may be complex, vary substantially between patients, and have complicated relationships with clinical outcomes. We present a probabilistically coherent framework for modeling and estimation in this setting, including a hierarchical Bayesian nonparametric mixture model for biomarkers that we use to define a functional profile of pre-versus-post treatment biomarker distribution change. The functional is similar to the receiver operating characteristic used in diagnostic testing. The hierarchical model yields clusters of individual patient biomarker profile functionals, and we use the profile as a covariate in a regression model for clinical outcome. The methodology is illustrated by analysis of a dataset from a clinical trial in prostate cancer using imatinib to target platelet-derived growth factor, with the clinical aim to improve progression-free survival time. PMID:25319212

Universal Darwinism As a Process of Bayesian Inference.

Science.gov (United States)

Campbell, John O

2016-01-01

Many of the mathematical frameworks describing natural selection are equivalent to Bayes' Theorem, also known as Bayesian updating. By definition, a process of Bayesian Inference is one which involves a Bayesian update, so we may conclude that these frameworks describe natural selection as a process of Bayesian inference. Thus, natural selection serves as a counter example to a widely-held interpretation that restricts Bayesian Inference to human mental processes (including the endeavors of statisticians). As Bayesian inference can always be cast in terms of (variational) free energy minimization, natural selection can be viewed as comprising two components: a generative model of an "experiment" in the external world environment, and the results of that "experiment" or the "surprise" entailed by predicted and actual outcomes of the "experiment." Minimization of free energy implies that the implicit measure of "surprise" experienced serves to update the generative model in a Bayesian manner. This description closely accords with the mechanisms of generalized Darwinian process proposed both by Dawkins, in terms of replicators and vehicles, and Campbell, in terms of inferential systems. Bayesian inference is an algorithm for the accumulation of evidence-based knowledge. This algorithm is now seen to operate over a wide range of evolutionary processes, including natural selection, the evolution of mental models and cultural evolutionary processes, notably including science itself. The variational principle of free energy minimization may thus serve as a unifying mathematical framework for universal Darwinism, the study of evolutionary processes operating throughout nature.

Chemical purity using quantitative "1H-nuclear magnetic resonance: a hierarchical Bayesian approach for traceable calibrations

International Nuclear Information System (INIS)

Toman, Blaza; Nelson, Michael A.; Lippa, Katrice A.

2016-01-01

Chemical purity assessment using quantitative "1H-nuclear magnetic resonance spectroscopy is a method based on ratio references of mass and signal intensity of the analyte species to that of chemical standards of known purity. As such, it is an example of a calculation using a known measurement equation with multiple inputs. Though multiple samples are often analyzed during purity evaluations in order to assess measurement repeatability, the uncertainty evaluation must also account for contributions from inputs to the measurement equation. Furthermore, there may be other uncertainty components inherent in the experimental design, such as independent implementation of multiple calibration standards. As such, the uncertainty evaluation is not purely bottom up (based on the measurement equation) or top down (based on the experimental design), but inherently contains elements of both. This hybrid form of uncertainty analysis is readily implemented with Bayesian statistical analysis. In this article we describe this type of analysis in detail and illustrate it using data from an evaluation of chemical purity and its uncertainty for a folic acid material. (authors)

A bayesian approach to inferring the genetic population structure of sugarcane accessions from INTA (Argentina

Directory of Open Access Journals (Sweden)

Mariana Inés Pocovi

2015-06-01

Full Text Available Understanding the population structure and genetic diversity in sugarcane (Saccharum officinarum L. accessions from INTA germplasm bank (Argentina will be of great importance for germplasm collection and breeding improvement as it will identify diverse parental combinations to create segregating progenies with maximum genetic variability for further selection. A Bayesian approach, ordination methods (PCoA, Principal Coordinate Analysis and clustering analysis (UPGMA, Unweighted Pair Group Method with Arithmetic Mean were applied to this purpose. Sixty three INTA sugarcane hybrids were genotyped for 107 Simple Sequence Repeat (SSR and 136 Amplified Fragment Length Polymorphism (AFLP loci. Given the low probability values found with AFLP for individual assignment (4.7%, microsatellites seemed to perform better (54% for STRUCTURE analysis that revealed the germplasm to exist in five optimum groups with partly corresponding to their origin. However clusters shown high degree of admixture, F ST values confirmed the existence of differences among groups. Dissimilarity coefficients ranged from 0.079 to 0.651. PCoA separated sugarcane in groups that did not agree with those identified by STRUCTURE. The clustering including all genotypes neither showed resemblance to populations find by STRUCTURE, but clustering performed considering only individuals displaying a proportional membership > 0.6 in their primary population obtained with STRUCTURE showed close similarities. The Bayesian method indubitably brought more information on cultivar origins than classical PCoA and hierarchical clustering method.

A top-down approach for fabricating free-standing bio-carbon supercapacitor electrodes with a hierarchical structure.

Science.gov (United States)

Li, Yingzhi; Zhang, Qinghua; Zhang, Junxian; Jin, Lei; Zhao, Xin; Xu, Ting

2015-09-23

Biomass has delicate hierarchical structures, which inspired us to develop a cost-effective route to prepare electrode materials with rational nanostructures for use in high-performance storage devices. Here, we demonstrate a novel top-down approach for fabricating bio-carbon materials with stable structures and excellent diffusion pathways; this approach is based on carbonization with controlled chemical activation. The developed free-standing bio-carbon electrode exhibits a high specific capacitance of 204 F g(-1) at 1 A g(-1); good rate capability, as indicated by the residual initial capacitance of 85.5% at 10 A g(-1); and a long cycle life. These performance characteristics are attributed to the outstanding hierarchical structures of the electrode material. Appropriate carbonization conditions enable the bio-carbon materials to inherit the inherent hierarchical texture of the original biomass, thereby facilitating effective channels for fast ion transfer. The macropores and mesopores that result from chemical activation significantly increase the specific surface area and also play the role of temporary ion-buffering reservoirs, further shortening the ionic diffusion distance.

Daniel Goodman’s empirical approach to Bayesian statistics

Science.gov (United States)

Gerrodette, Tim; Ward, Eric; Taylor, Rebecca L.; Schwarz, Lisa K.; Eguchi, Tomoharu; Wade, Paul; Himes Boor, Gina

2016-01-01

Bayesian statistics, in contrast to classical statistics, uses probability to represent uncertainty about the state of knowledge. Bayesian statistics has often been associated with the idea that knowledge is subjective and that a probability distribution represents a personal degree of belief. Dr. Daniel Goodman considered this viewpoint problematic for issues of public policy. He sought to ground his Bayesian approach in data, and advocated the construction of a prior as an empirical histogram of “similar” cases. In this way, the posterior distribution that results from a Bayesian analysis combined comparable previous data with case-specific current data, using Bayes’ formula. Goodman championed such a data-based approach, but he acknowledged that it was difficult in practice. If based on a true representation of our knowledge and uncertainty, Goodman argued that risk assessment and decision-making could be an exact science, despite the uncertainties. In his view, Bayesian statistics is a critical component of this science because a Bayesian analysis produces the probabilities of future outcomes. Indeed, Goodman maintained that the Bayesian machinery, following the rules of conditional probability, offered the best legitimate inference from available data. We give an example of an informative prior in a recent study of Steller sea lion spatial use patterns in Alaska.

Hierarchical porous carbon/MnO2 hybrids as supercapacitor electrodes.

Science.gov (United States)

Lee, Min Eui; Yun, Young Soo; Jin, Hyoung-Joon

2014-12-01

Hybrid electrodes of hierarchical porous carbon (HPC) and manganese oxide (MnO2) were synthesized using a fast surface redox reaction of potassium permanganate under facile immersion methods. The HPC/MnO2 hybrids had a number of micropores and macropores and the MnO2 nanoparticles acted as a pseudocapacitive material. The synergistic effects of electric double-layer capacitor (EDLC)-induced capacitance and pseudocapacitance brought about a better electrochemical performance of the HPC/MnO2 hybrid electrodes compared to that obtained with a single component. The hybrids showed a specific capacitance of 228 F g(-1) and good cycle stability over 1000 cycles.

Approximation methods for efficient learning of Bayesian networks

CERN Document Server

Riggelsen, C

2008-01-01

This publication offers and investigates efficient Monte Carlo simulation methods in order to realize a Bayesian approach to approximate learning of Bayesian networks from both complete and incomplete data. For large amounts of incomplete data when Monte Carlo methods are inefficient, approximations are implemented, such that learning remains feasible, albeit non-Bayesian. The topics discussed are: basic concepts about probabilities, graph theory and conditional independence; Bayesian network learning from data; Monte Carlo simulation techniques; and, the concept of incomplete data. In order to provide a coherent treatment of matters, thereby helping the reader to gain a thorough understanding of the whole concept of learning Bayesian networks from (in)complete data, this publication combines in a clarifying way all the issues presented in the papers with previously unpublished work.

Bayesian community detection

DEFF Research Database (Denmark)

Mørup, Morten; Schmidt, Mikkel N

2012-01-01

Many networks of scientific interest naturally decompose into clusters or communities with comparatively fewer external than internal links; however, current Bayesian models of network communities do not exert this intuitive notion of communities. We formulate a nonparametric Bayesian model...... for community detection consistent with an intuitive definition of communities and present a Markov chain Monte Carlo procedure for inferring the community structure. A Matlab toolbox with the proposed inference procedure is available for download. On synthetic and real networks, our model detects communities...... consistent with ground truth, and on real networks, it outperforms existing approaches in predicting missing links. This suggests that community structure is an important structural property of networks that should be explicitly modeled....

Inverse Problems in a Bayesian Setting

KAUST Repository

Matthies, Hermann G.

2016-02-13

In a Bayesian setting, inverse problems and uncertainty quantification (UQ)—the propagation of uncertainty through a computational (forward) model—are strongly connected. In the form of conditional expectation the Bayesian update becomes computationally attractive. We give a detailed account of this approach via conditional approximation, various approximations, and the construction of filters. Together with a functional or spectral approach for the forward UQ there is no need for time-consuming and slowly convergent Monte Carlo sampling. The developed sampling-free non-linear Bayesian update in form of a filter is derived from the variational problem associated with conditional expectation. This formulation in general calls for further discretisation to make the computation possible, and we choose a polynomial approximation. After giving details on the actual computation in the framework of functional or spectral approximations, we demonstrate the workings of the algorithm on a number of examples of increasing complexity. At last, we compare the linear and nonlinear Bayesian update in form of a filter on some examples.

Inverse Problems in a Bayesian Setting

KAUST Repository

Matthies, Hermann G.; Zander, Elmar; Rosić, Bojana V.; Litvinenko, Alexander; Pajonk, Oliver

2016-01-01

In a Bayesian setting, inverse problems and uncertainty quantification (UQ)—the propagation of uncertainty through a computational (forward) model—are strongly connected. In the form of conditional expectation the Bayesian update becomes computationally attractive. We give a detailed account of this approach via conditional approximation, various approximations, and the construction of filters. Together with a functional or spectral approach for the forward UQ there is no need for time-consuming and slowly convergent Monte Carlo sampling. The developed sampling-free non-linear Bayesian update in form of a filter is derived from the variational problem associated with conditional expectation. This formulation in general calls for further discretisation to make the computation possible, and we choose a polynomial approximation. After giving details on the actual computation in the framework of functional or spectral approximations, we demonstrate the workings of the algorithm on a number of examples of increasing complexity. At last, we compare the linear and nonlinear Bayesian update in form of a filter on some examples.

Implementing the Bayesian paradigm in risk analysis

International Nuclear Information System (INIS)

Aven, T.; Kvaloey, J.T.

2002-01-01

The Bayesian paradigm comprises a unified and consistent framework for analyzing and expressing risk. Yet, we see rather few examples of applications where the full Bayesian setting has been adopted with specifications of priors of unknown parameters. In this paper, we discuss some of the practical challenges of implementing Bayesian thinking and methods in risk analysis, emphasizing the introduction of probability models and parameters and associated uncertainty assessments. We conclude that there is a need for a pragmatic view in order to 'successfully' apply the Bayesian approach, such that we can do the assignments of some of the probabilities without adopting the somewhat sophisticated procedure of specifying prior distributions of parameters. A simple risk analysis example is presented to illustrate ideas

Interactive Instruction in Bayesian Inference

DEFF Research Database (Denmark)

Khan, Azam; Breslav, Simon; Hornbæk, Kasper

2018-01-01

An instructional approach is presented to improve human performance in solving Bayesian inference problems. Starting from the original text of the classic Mammography Problem, the textual expression is modified and visualizations are added according to Mayer’s principles of instruction. These pri......An instructional approach is presented to improve human performance in solving Bayesian inference problems. Starting from the original text of the classic Mammography Problem, the textual expression is modified and visualizations are added according to Mayer’s principles of instruction....... These principles concern coherence, personalization, signaling, segmenting, multimedia, spatial contiguity, and pretraining. Principles of self-explanation and interactivity are also applied. Four experiments on the Mammography Problem showed that these principles help participants answer the questions...... that an instructional approach to improving human performance in Bayesian inference is a promising direction....

Universal Darwinism as a process of Bayesian inference

Directory of Open Access Journals (Sweden)

John Oberon Campbell

2016-06-01

Full Text Available Many of the mathematical frameworks describing natural selection are equivalent to Bayes’ Theorem, also known as Bayesian updating. By definition, a process of Bayesian Inference is one which involves a Bayesian update, so we may conclude that these frameworks describe natural selection as a process of Bayesian inference. Thus natural selection serves as a counter example to a widely-held interpretation that restricts Bayesian Inference to human mental processes (including the endeavors of statisticians. As Bayesian inference can always be cast in terms of (variational free energy minimization, natural selection can be viewed as comprising two components: a generative model of an ‘experiment’ in the external world environment, and the results of that 'experiment' or the 'surprise' entailed by predicted and actual outcomes of the ‘experiment’. Minimization of free energy implies that the implicit measure of 'surprise' experienced serves to update the generative model in a Bayesian manner. This description closely accords with the mechanisms of generalized Darwinian process proposed both by Dawkins, in terms of replicators and vehicles, and Campbell, in terms of inferential systems. Bayesian inference is an algorithm for the accumulation of evidence-based knowledge. This algorithm is now seen to operate over a wide range of evolutionary processes, including natural selection, the evolution of mental models and cultural evolutionary processes, notably including science itself. The variational principle of free energy minimization may thus serve as a unifying mathematical framework for universal Darwinism, the study of evolutionary processes operating throughout nature.

Bayesian analysis of magnetic island dynamics

International Nuclear Information System (INIS)

Preuss, R.; Maraschek, M.; Zohm, H.; Dose, V.

2003-01-01

We examine a first order differential equation with respect to time used to describe magnetic islands in magnetically confined plasmas. The free parameters of this equation are obtained by employing Bayesian probability theory. Additionally, a typical Bayesian change point is solved in the process of obtaining the data

Hierarchical statistical modeling of xylem vulnerability to cavitation.

Science.gov (United States)

Ogle, Kiona; Barber, Jarrett J; Willson, Cynthia; Thompson, Brenda

2009-01-01

Cavitation of xylem elements diminishes the water transport capacity of plants, and quantifying xylem vulnerability to cavitation is important to understanding plant function. Current approaches to analyzing hydraulic conductivity (K) data to infer vulnerability to cavitation suffer from problems such as the use of potentially unrealistic vulnerability curves, difficulty interpreting parameters in these curves, a statistical framework that ignores sampling design, and an overly simplistic view of uncertainty. This study illustrates how two common curves (exponential-sigmoid and Weibull) can be reparameterized in terms of meaningful parameters: maximum conductivity (k(sat)), water potential (-P) at which percentage loss of conductivity (PLC) =X% (P(X)), and the slope of the PLC curve at P(X) (S(X)), a 'sensitivity' index. We provide a hierarchical Bayesian method for fitting the reparameterized curves to K(H) data. We illustrate the method using data for roots and stems of two populations of Juniperus scopulorum and test for differences in k(sat), P(X), and S(X) between different groups. Two important results emerge from this study. First, the Weibull model is preferred because it produces biologically realistic estimates of PLC near P = 0 MPa. Second, stochastic embolisms contribute an important source of uncertainty that should be included in such analyses.

Self-Reconstructed Formation of a One-Dimensional Hierarchical Porous Nanostructure Assembled by Ultrathin TiO2 Nanobelts for Fast and Stable Lithium Storage.

Science.gov (United States)

Liu, Yuan; Yan, Xiaodong; Xu, Bingqing; Lan, Jinle; Yu, Yunhua; Yang, Xiaoping; Lin, Yuanhua; Nan, Cewen

2018-06-06

Owing to their unique structural advantages, TiO 2 hierarchical nanostructures assembled by low-dimensional (LD) building blocks have been extensively used in the energy-storage/-conversion field. However, it is still a big challenge to produce such advanced structures by current synthetic techniques because of the harsh conditions needed to generate primary LD subunits. Herein, a novel one-dimensional (1D) TiO 2 hierarchical porous fibrous nanostructure constructed by TiO 2 nanobelts is synthesized by combining a room-temperature aqueous solution growth mechanism with the electrospinning technology. The nanobelt-constructed 1D hierarchical nanoarchitecture is evolves directly from the amorphous TiO 2 /SiO 2 composite fibers in alkaline solutions at ambient conditions without any catalyst and other reactant. Benefiting from the unique structural features such as 1D nanoscale building blocks, large surface area, and numerous interconnected pores, as well as mixed phase anatase-TiO 2 (B), the optimum 1D TiO 2 hierarchical porous nanostructure shows a remarkable high-rate performance when tested as an anode material for lithium-ion batteries (107 mA h g -1 at ∼10 A g -1 ) and can be used in a hybrid lithium-ion supercapacitor with very stable lithium-storage performance (a capacity retention of ∼80% after 3000 cycles at 2 A g -1 ). The current work presents a scalable and cost-effective method for the synthesis of advanced TiO 2 hierarchical materials for high-power and stable energy-storage/-conversion devices.

Bayesian ensemble refinement by replica simulations and reweighting

Science.gov (United States)

Hummer, Gerhard; Köfinger, Jürgen

2015-12-01

We describe different Bayesian ensemble refinement methods, examine their interrelation, and discuss their practical application. With ensemble refinement, the properties of dynamic and partially disordered (bio)molecular structures can be characterized by integrating a wide range of experimental data, including measurements of ensemble-averaged observables. We start from a Bayesian formulation in which the posterior is a functional that ranks different configuration space distributions. By maximizing this posterior, we derive an optimal Bayesian ensemble distribution. For discrete configurations, this optimal distribution is identical to that obtained by the maximum entropy "ensemble refinement of SAXS" (EROS) formulation. Bayesian replica ensemble refinement enhances the sampling of relevant configurations by imposing restraints on averages of observables in coupled replica molecular dynamics simulations. We show that the strength of the restraints should scale linearly with the number of replicas to ensure convergence to the optimal Bayesian result in the limit of infinitely many replicas. In the "Bayesian inference of ensembles" method, we combine the replica and EROS approaches to accelerate the convergence. An adaptive algorithm can be used to sample directly from the optimal ensemble, without replicas. We discuss the incorporation of single-molecule measurements and dynamic observables such as relaxation parameters. The theoretical analysis of different Bayesian ensemble refinement approaches provides a basis for practical applications and a starting point for further investigations.

Bayesian Decision Theoretical Framework for Clustering

Science.gov (United States)

Chen, Mo

2011-01-01

In this thesis, we establish a novel probabilistic framework for the data clustering problem from the perspective of Bayesian decision theory. The Bayesian decision theory view justifies the important questions: what is a cluster and what a clustering algorithm should optimize. We prove that the spectral clustering (to be specific, the…

Quantum-Like Representation of Non-Bayesian Inference

Science.gov (United States)

Asano, M.; Basieva, I.; Khrennikov, A.; Ohya, M.; Tanaka, Y.

2013-01-01

This research is related to the problem of "irrational decision making or inference" that have been discussed in cognitive psychology. There are some experimental studies, and these statistical data cannot be described by classical probability theory. The process of decision making generating these data cannot be reduced to the classical Bayesian inference. For this problem, a number of quantum-like coginitive models of decision making was proposed. Our previous work represented in a natural way the classical Bayesian inference in the frame work of quantum mechanics. By using this representation, in this paper, we try to discuss the non-Bayesian (irrational) inference that is biased by effects like the quantum interference. Further, we describe "psychological factor" disturbing "rationality" as an "environment" correlating with the "main system" of usual Bayesian inference.

Correct Bayesian and frequentist intervals are similar

International Nuclear Information System (INIS)

Atwood, C.L.

1986-01-01

This paper argues that Bayesians and frequentists will normally reach numerically similar conclusions, when dealing with vague data or sparse data. It is shown that both statistical methodologies can deal reasonably with vague data. With sparse data, in many important practical cases Bayesian interval estimates and frequentist confidence intervals are approximately equal, although with discrete data the frequentist intervals are somewhat longer. This is not to say that the two methodologies are equally easy to use: The construction of a frequentist confidence interval may require new theoretical development. Bayesians methods typically require numerical integration, perhaps over many variables. Also, Bayesian can easily fall into the trap of over-optimism about their amount of prior knowledge. But in cases where both intervals are found correctly, the two intervals are usually not very different. (orig.)

Using consensus bayesian network to model the reactive oxygen species regulatory pathway.

Directory of Open Access Journals (Sweden)

Liangdong Hu

Full Text Available Bayesian network is one of the most successful graph models for representing the reactive oxygen species regulatory pathway. With the increasing number of microarray measurements, it is possible to construct the bayesian network from microarray data directly. Although large numbers of bayesian network learning algorithms have been developed, when applying them to learn bayesian networks from microarray data, the accuracies are low due to that the databases they used to learn bayesian networks contain too few microarray data. In this paper, we propose a consensus bayesian network which is constructed by combining bayesian networks from relevant literatures and bayesian networks learned from microarray data. It would have a higher accuracy than the bayesian networks learned from one database. In the experiment, we validated the bayesian network combination algorithm on several classic machine learning databases and used the consensus bayesian network to model the Escherichia coli's ROS pathway.

Bayesian analysis of rare events

Energy Technology Data Exchange (ETDEWEB)

Straub, Daniel, E-mail: straub@tum.de; Papaioannou, Iason; Betz, Wolfgang

2016-06-01

In many areas of engineering and science there is an interest in predicting the probability of rare events, in particular in applications related to safety and security. Increasingly, such predictions are made through computer models of physical systems in an uncertainty quantification framework. Additionally, with advances in IT, monitoring and sensor technology, an increasing amount of data on the performance of the systems is collected. This data can be used to reduce uncertainty, improve the probability estimates and consequently enhance the management of rare events and associated risks. Bayesian analysis is the ideal method to include the data into the probabilistic model. It ensures a consistent probabilistic treatment of uncertainty, which is central in the prediction of rare events, where extrapolation from the domain of observation is common. We present a framework for performing Bayesian updating of rare event probabilities, termed BUS. It is based on a reinterpretation of the classical rejection-sampling approach to Bayesian analysis, which enables the use of established methods for estimating probabilities of rare events. By drawing upon these methods, the framework makes use of their computational efficiency. These methods include the First-Order Reliability Method (FORM), tailored importance sampling (IS) methods and Subset Simulation (SuS). In this contribution, we briefly review these methods in the context of the BUS framework and investigate their applicability to Bayesian analysis of rare events in different settings. We find that, for some applications, FORM can be highly efficient and is surprisingly accurate, enabling Bayesian analysis of rare events with just a few model evaluations. In a general setting, BUS implemented through IS and SuS is more robust and flexible.

Hierarchical porous Co3O4 films with size-adjustable pores as Li ion battery anodes with excellent rate performances

International Nuclear Information System (INIS)

Zhao, Guangyu; Xu, Zhanming; Zhang, Li; Sun, Kening

2013-01-01

Highlights: •Template-free synthesis of hierarchical porous Co 3 O 4 films on Ni foams. •Hierarchical porous Co 3 O 4 films with size-adjustable pores. •Excellent rate performances (650 mAh g −1 at 30 C) as Li ion battery anodes. -- Abstract: Constructing hierarchical porous structures on the current collectors is an attractive strategy for improving the rate performance of the Li ion battery electrodes. However, preparing hierarchical porous structures normally requires hard or soft templates to create hollows or pores in different sizes. Rigorous preparation conditions are needed to control the size (especially nanosize) and size distribution of the pores obtained by conventional methods. Herein, we describe a template-free two-step synthesis process to prepare hierarchical porous Co 3 O 4 films on Ni foam substrates. In this synthesis process, free-standing mesoporous precursor flakes are deposited on Ni foams by an electrochemical method. Subsequently, the meosporous precursor flake arrays are calcined to obtain hierarchical porous Co 3 O 4 films. More strikingly, the size of the mesopores in the flakes can be adjusted by altering the calcination temperature. The structure and morphology of the samples are characterized by scanning electron microscopy, transmission electron microscopy and Brunauer–Emmett–Teller measurements. The relationship of the in-flake-pore size and the calcinations temperature is proposed here. Electrochemical tests have revealed that the hierarchical porous Co 3 O 4 films demonstrate excellent rate performances (650 mAh g −1 at 30 C) as Li ion battery anodes due to the hierarchical porous structure, which endows fast ion transmission

Treatment strategies for coronary in-stent restenosis: systematic review and hierarchical Bayesian network meta-analysis of 24 randomised trials and 4880 patients

Science.gov (United States)

Giacoppo, Daniele; Gargiulo, Giuseppe; Aruta, Patrizia; Capranzano, Piera; Tamburino, Corrado

2015-01-01

Study question What is the most safe and effective interventional treatment for coronary in-stent restenosis? Methods In a hierarchical Bayesian network meta-analysis, PubMed, Embase, Scopus, Cochrane Library, Web of Science, ScienceDirect, and major scientific websites were screened up to 10 August 2015. Randomised controlled trials of patients with any type of coronary in-stent restenosis (either of bare metal stents or drug eluting stents; and either first or recurrent instances) were included. Trials including multiple treatments at the same time in the same group or comparing variants of the same intervention were excluded. Primary endpoints were target lesion revascularisation and late lumen loss, both at six to 12 months. The main analysis was complemented by network subanalyses, standard pairwise comparisons, and subgroup and sensitivity analyses. Study answer and limitations Twenty four trials (4880 patients), including seven interventional treatments, were identified. Compared with plain balloons, bare metal stents, brachytherapy, rotational atherectomy, and cutting balloons, drug coated balloons and drug eluting stents were associated with a reduced risk of target lesion revascularisation and major adverse cardiac events, and with reduced late lumen loss. Treatment ranking indicated that drug eluting stents had the highest probability (61.4%) of being the most effective for target lesion vascularisation; drug coated balloons were similarly indicated as the most effective treatment for late lumen loss (probability 70.3%). The comparative efficacy of drug coated balloons and drug eluting stents was similar for target lesion revascularisation (summary odds ratio 1.10, 95% credible interval 0.59 to 2.01) and late lumen loss reduction (mean difference in minimum lumen diameter 0.04 mm, 95% credible interval −0.20 to 0.10). Risks of death, myocardial infarction, and stent thrombosis were comparable across all treatments, but these analyses were limited by a

Bayesian modeling of consumer behavior in the presence of anonymous visits

Science.gov (United States)

Novak, Julie Esther

Tailoring content to consumers has become a hallmark of marketing and digital media, particularly as it has become easier to identify customers across usage or purchase occasions. However, across a wide variety of contexts, companies find that customers do not consistently identify themselves, leaving a substantial fraction of anonymous visits. We develop a Bayesian hierarchical model that allows us to probabilistically assign anonymous sessions to users. These probabilistic assignments take into account a customer's demographic information, frequency of visitation, activities taken when visiting, and times of arrival. We present two studies, one with synthetic and one with real data, where we demonstrate improved performance over two popular practices (nearest-neighbor matching and deleting the anonymous visits) due to increased efficiency and reduced bias driven by the non-ignorability of which types of events are more likely to be anonymous. Using our proposed model, we avoid potential bias in understanding the effect of a firm's marketing on its customers, improve inference about the total number of customers in the dataset, and provide more precise targeted marketing to both previously observed and unobserved customers.

Bayesian models a statistical primer for ecologists

CERN Document Server

Hobbs, N Thompson

2015-01-01

Bayesian modeling has become an indispensable tool for ecological research because it is uniquely suited to deal with complexity in a statistically coherent way. This textbook provides a comprehensive and accessible introduction to the latest Bayesian methods-in language ecologists can understand. Unlike other books on the subject, this one emphasizes the principles behind the computations, giving ecologists a big-picture understanding of how to implement this powerful statistical approach. Bayesian Models is an essential primer for non-statisticians. It begins with a definition of probabili

Direct large-scale synthesis of 3D hierarchical mesoporous NiO microspheres as high-performance anode materials for lithium ion batteries.

Science.gov (United States)

bai, Zhongchao; Ju, Zhicheng; Guo, Chunli; Qian, Yitai; Tang, Bin; Xiong, Shenglin

2014-03-21

Hierarchically porous materials are an ideal material platform for constructing high performance Li-ion batteries (LIBs), offering great advantages such as large contact area between the electrode and the electrolyte, fast and flexible transport pathways for the electrolyte ions and the space for buffering the strain caused by repeated Li insertion/extraction. In this work, NiO microspheres with hierarchically porous structures have been synthesized via a facile thermal decomposition method by only using a simple precursor. The superstructures are composed of nanocrystals with high specific surface area, large pore volume, and broad pore size distribution. The electrochemical properties of 3D hierarchical mesoporous NiO microspheres were examined by cyclic voltammetry and galvanostatic charge-discharge studies. The results demonstrate that the as-prepared NiO nanospheres are excellent electrode materials in LIBs with high specific capacity, good retention and rate performance. The 3D hierarchical mesoporous NiO microspheres can retain a reversible capacity of 800.2 mA h g(-1) after 100 cycles at a high current density of 500 mA g(-1).

Hierarchical Load Tracking Control of a Grid-Connected Solid Oxide Fuel Cell for Maximum Electrical Efficiency Operation

Directory of Open Access Journals (Sweden)

Yonghui Li

2015-03-01

Full Text Available Based on the benchmark solid oxide fuel cell (SOFC dynamic model for power system studies and the analysis of the SOFC operating conditions, the nonlinear programming (NLP optimization method was used to determine the maximum electrical efficiency of the grid-connected SOFC subject to the constraints of fuel utilization factor, stack temperature and output active power. The optimal operating conditions of the grid-connected SOFC were obtained by solving the NLP problem considering the power consumed by the air compressor. With the optimal operating conditions of the SOFC for the maximum efficiency operation obtained at different active power output levels, a hierarchical load tracking control scheme for the grid-connected SOFC was proposed to realize the maximum electrical efficiency operation with the stack temperature bounded. The hierarchical control scheme consists of a fast active power control and a slower stack temperature control. The active power control was developed by using a decentralized control method. The efficiency of the proposed hierarchical control scheme was demonstrated by case studies using the benchmark SOFC dynamic model.

Robust Bayesian detection of unmodelled bursts

International Nuclear Information System (INIS)

Searle, Antony C; Sutton, Patrick J; Tinto, Massimo; Woan, Graham

2008-01-01

We develop a Bayesian treatment of the problem of detecting unmodelled gravitational wave bursts using the new global network of interferometric detectors. We also compare this Bayesian treatment with existing coherent methods, and demonstrate that the existing methods make implicit assumptions on the distribution of signals that make them sub-optimal for realistic signal populations

Two-Level Control for Fast Electrical Vehicle Charging Stations with Multi Flywheel Energy Storage System