Applied Bayesian Hierarchical Methods
Congdon, Peter D
2010-01-01
Bayesian methods facilitate the analysis of complex models and data structures. Emphasizing data applications, alternative modeling specifications, and computer implementation, this book provides a practical overview of methods for Bayesian analysis of hierarchical models.
Bayesian hierarchical modeling of drug stability data.
Chen, Jie; Zhong, Jinglin; Nie, Lei
2008-06-15
Stability data are commonly analyzed using linear fixed or random effect model. The linear fixed effect model does not take into account the batch-to-batch variation, whereas the random effect model may suffer from the unreliable shelf-life estimates due to small sample size. Moreover, both methods do not utilize any prior information that might have been available. In this article, we propose a Bayesian hierarchical approach to modeling drug stability data. Under this hierarchical structure, we first use Bayes factor to test the poolability of batches. Given the decision on poolability of batches, we then estimate the shelf-life that applies to all batches. The approach is illustrated with two example data sets and its performance is compared in simulation studies with that of the commonly used frequentist methods. (c) 2008 John Wiley & Sons, Ltd.
A Hierarchical Bayesian Model for Crowd Emotions
Urizar, Oscar J.; Baig, Mirza S.; Barakova, Emilia I.; Regazzoni, Carlo S.; Marcenaro, Lucio; Rauterberg, Matthias
2016-01-01
Estimation of emotions is an essential aspect in developing intelligent systems intended for crowded environments. However, emotion estimation in crowds remains a challenging problem due to the complexity in which human emotions are manifested and the capability of a system to perceive them in such conditions. This paper proposes a hierarchical Bayesian model to learn in unsupervised manner the behavior of individuals and of the crowd as a single entity, and explore the relation between behavior and emotions to infer emotional states. Information about the motion patterns of individuals are described using a self-organizing map, and a hierarchical Bayesian network builds probabilistic models to identify behaviors and infer the emotional state of individuals and the crowd. This model is trained and tested using data produced from simulated scenarios that resemble real-life environments. The conducted experiments tested the efficiency of our method to learn, detect and associate behaviors with emotional states yielding accuracy levels of 74% for individuals and 81% for the crowd, similar in performance with existing methods for pedestrian behavior detection but with novel concepts regarding the analysis of crowds. PMID:27458366
Hierarchical Bayesian inference in the visual cortex
Lee, Tai Sing; Mumford, David
2003-07-01
Traditional views of visual processing suggest that early visual neurons in areas V1 and V2 are static spatiotemporal filters that extract local features from a visual scene. The extracted information is then channeled through a feedforward chain of modules in successively higher visual areas for further analysis. Recent electrophysiological recordings from early visual neurons in awake behaving monkeys reveal that there are many levels of complexity in the information processing of the early visual cortex, as seen in the long-latency responses of its neurons. These new findings suggest that activity in the early visual cortex is tightly coupled and highly interactive with the rest of the visual system. They lead us to propose a new theoretical setting based on the mathematical framework of hierarchical Bayesian inference for reasoning about the visual system. In this framework, the recurrent feedforward/feedback loops in the cortex serve to integrate top-down contextual priors and bottom-up observations so as to implement concurrent probabilistic inference along the visual hierarchy. We suggest that the algorithms of particle filtering and Bayesian-belief propagation might model these interactive cortical computations. We review some recent neurophysiological evidences that support the plausibility of these ideas. 2003 Optical Society of America
Hierarchical Bayesian sparse image reconstruction with application to MRFM
Dobigeon, Nicolas; Tourneret, Jean-Yves
2008-01-01
This paper presents a hierarchical Bayesian model to reconstruct sparse images when the observations are obtained from linear transformations and corrupted by an additive white Gaussian noise. Our hierarchical Bayes model is well suited to such naturally sparse image applications as it seamlessly accounts for properties such as sparsity and positivity of the image via appropriate Bayes priors. We propose a prior that is based on a weighted mixture of a positive exponential distribution and a mass at zero. The prior has hyperparameters that are tuned automatically by marginalization over the hierarchical Bayesian model. To overcome the complexity of the posterior distribution, a Gibbs sampling strategy is proposed. The Gibbs samples can be used to estimate the image to be recovered, e.g. by maximizing the estimated posterior distribution. In our fully Bayesian approach the posteriors of all the parameters are available. Thus our algorithm provides more information than other previously proposed sparse reconstr...
Directory of Open Access Journals (Sweden)
Dongsheng Chen
2016-01-01
Full Text Available Accurate biomass estimations are important for assessing and monitoring forest carbon storage. Bayesian theory has been widely applied to tree biomass models. Recently, a hierarchical Bayesian approach has received increasing attention for improving biomass models. In this study, tree biomass data were obtained by sampling 310 trees from 209 permanent sample plots from larch plantations in six regions across China. Non-hierarchical and hierarchical Bayesian approaches were used to model allometric biomass equations. We found that the total, root, stem wood, stem bark, branch and foliage biomass model relationships were statistically significant (p-values < 0.001 for both the non-hierarchical and hierarchical Bayesian approaches, but the hierarchical Bayesian approach increased the goodness-of-fit statistics over the non-hierarchical Bayesian approach. The R2 values of the hierarchical approach were higher than those of the non-hierarchical approach by 0.008, 0.018, 0.020, 0.003, 0.088 and 0.116 for the total tree, root, stem wood, stem bark, branch and foliage models, respectively. The hierarchical Bayesian approach significantly improved the accuracy of the biomass model (except for the stem bark and can reflect regional differences by using random parameters to improve the regional scale model accuracy.
Bayesian Hierarchical Models to Augment the Mediterranean Forecast System
2016-06-07
year. Our goal is to develop an ensemble ocean forecast methodology, using Bayesian Hierarchical Modelling (BHM) tools . The ocean ensemble forecast...from above); i.e. we assume Ut ~ Z Λt1/2. WORK COMPLETED The prototype MFS-Wind-BHM was designed and implemented based on stochastic...coding refinements we implemented on the prototype surface wind BHM. A DWF event in February 2005, in the Gulf of Lions, was identified for reforecast
Prediction of road accidents: A Bayesian hierarchical approach
DEFF Research Database (Denmark)
Deublein, Markus; Schubert, Matthias; Adey, Bryan T.;
2013-01-01
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...
Road network safety evaluation using Bayesian hierarchical joint model.
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.
Spatial Bayesian hierarchical modelling of extreme sea states
Clancy, Colm; O'Sullivan, John; Sweeney, Conor; Dias, Frédéric; Parnell, Andrew C.
2016-11-01
A Bayesian hierarchical framework is used to model extreme sea states, incorporating a latent spatial process to more effectively capture the spatial variation of the extremes. The model is applied to a 34-year hindcast of significant wave height off the west coast of Ireland. The generalised Pareto distribution is fitted to declustered peaks over a threshold given by the 99.8th percentile of the data. Return levels of significant wave height are computed and compared against those from a model based on the commonly-used maximum likelihood inference method. The Bayesian spatial model produces smoother maps of return levels. Furthermore, this approach greatly reduces the uncertainty in the estimates, thus providing information on extremes which is more useful for practical applications.
[A medical image semantic modeling based on hierarchical Bayesian networks].
Lin, Chunyi; Ma, Lihong; Yin, Junxun; Chen, Jianyu
2009-04-01
A semantic modeling approach for medical image semantic retrieval based on hierarchical Bayesian networks was proposed, in allusion to characters of medical images. It used GMM (Gaussian mixture models) to map low-level image features into object semantics with probabilities, then it captured high-level semantics through fusing these object semantics using a Bayesian network, so that it built a multi-layer medical image semantic model, aiming to enable automatic image annotation and semantic retrieval by using various keywords at different semantic levels. As for the validity of this method, we have built a multi-level semantic model from a small set of astrocytoma MRI (magnetic resonance imaging) samples, in order to extract semantics of astrocytoma in malignant degree. Experiment results show that this is a superior approach.
Bayesian hierarchical modelling of weak lensing - the golden goal
Heavens, Alan; Jaffe, Andrew; Hoffmann, Till; Kiessling, Alina; Wandelt, Benjamin
2016-01-01
To accomplish correct Bayesian inference from weak lensing shear data requires a complete statistical description of the data. The natural framework to do this is a Bayesian Hierarchical Model, which divides the chain of reasoning into component steps. Starting with a catalogue of shear estimates in tomographic bins, we build a model that allows us to sample simultaneously from the the underlying tomographic shear fields and the relevant power spectra (E-mode, B-mode, and E-B, for auto- and cross-power spectra). The procedure deals easily with masked data and intrinsic alignments. Using Gibbs sampling and messenger fields, we show with simulated data that the large (over 67000-)dimensional parameter space can be efficiently sampled and the full joint posterior probability density function for the parameters can feasibly be obtained. The method correctly recovers the underlying shear fields and all of the power spectra, including at levels well below the shot noise.
Constructive Epistemic Modeling: A Hierarchical Bayesian Model Averaging Method
Tsai, F. T. C.; Elshall, A. S.
2014-12-01
Constructive epistemic modeling is the idea that our understanding of a natural system through a scientific model is a mental construct that continually develops through learning about and from the model. Using the hierarchical Bayesian model averaging (HBMA) method [1], this study shows that segregating different uncertain model components through a BMA tree of posterior model probabilities, model prediction, within-model variance, between-model variance and total model variance serves as a learning tool [2]. First, the BMA tree of posterior model probabilities permits the comparative evaluation of the candidate propositions of each uncertain model component. Second, systemic model dissection is imperative for understanding the individual contribution of each uncertain model component to the model prediction and variance. Third, the hierarchical representation of the between-model variance facilitates the prioritization of the contribution of each uncertain model component to the overall model uncertainty. We illustrate these concepts using the groundwater modeling of a siliciclastic aquifer-fault system. The sources of uncertainty considered are from geological architecture, formation dip, boundary conditions and model parameters. The study shows that the HBMA analysis helps in advancing knowledge about the model rather than forcing the model to fit a particularly understanding or merely averaging several candidate models. [1] Tsai, F. T.-C., and A. S. Elshall (2013), Hierarchical Bayesian model averaging for hydrostratigraphic modeling: Uncertainty segregation and comparative evaluation. Water Resources Research, 49, 5520-5536, doi:10.1002/wrcr.20428. [2] Elshall, A.S., and F. T.-C. Tsai (2014). Constructive epistemic modeling of groundwater flow with geological architecture and boundary condition uncertainty under Bayesian paradigm, Journal of Hydrology, 517, 105-119, doi: 10.1016/j.jhydrol.2014.05.027.
Hierarchical Bayesian spatial models for multispecies conservation planning and monitoring.
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
Introduction to Hierarchical Bayesian Modeling for Ecological Data
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
Bayesian hierarchical modeling for detecting safety signals in clinical trials.
Xia, H Amy; Ma, Haijun; Carlin, Bradley P
2011-09-01
Detection of safety signals from clinical trial adverse event data is critical in drug development, but carries a challenging statistical multiplicity problem. Bayesian hierarchical mixture modeling is appealing for its ability to borrow strength across subgroups in the data, as well as moderate extreme findings most likely due merely to chance. We implement such a model for subject incidence (Berry and Berry, 2004 ) using a binomial likelihood, and extend it to subject-year adjusted incidence rate estimation under a Poisson likelihood. We use simulation to choose a signal detection threshold, and illustrate some effective graphics for displaying the flagged signals.
Technique for fast and efficient hierarchical clustering
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 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...
Bayesian hierarchical grouping: Perceptual grouping as mixture estimation.
Froyen, Vicky; Feldman, Jacob; Singh, Manish
2015-10-01
We propose a novel framework for perceptual grouping based on the idea of mixture models, called Bayesian hierarchical grouping (BHG). In BHG, we assume that the configuration of image elements is generated by a mixture of distinct objects, each of which generates image elements according to some generative assumptions. Grouping, in this framework, means estimating the number and the parameters of the mixture components that generated the image, including estimating which image elements are "owned" by which objects. We present a tractable implementation of the framework, based on the hierarchical clustering approach of Heller and Ghahramani (2005). We illustrate it with examples drawn from a number of classical perceptual grouping problems, including dot clustering, contour integration, and part decomposition. Our approach yields an intuitive hierarchical representation of image elements, giving an explicit decomposition of the image into mixture components, along with estimates of the probability of various candidate decompositions. We show that BHG accounts well for a diverse range of empirical data drawn from the literature. Because BHG provides a principled quantification of the plausibility of grouping interpretations over a wide range of grouping problems, we argue that it provides an appealing unifying account of the elusive Gestalt notion of Prägnanz.
Unsupervised Transient Light Curve Analysis Via Hierarchical Bayesian Inference
Sanders, Nathan; Soderberg, Alicia
2014-01-01
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 photometr...
Inferring on the intentions of others by hierarchical Bayesian learning.
Directory of Open Access Journals (Sweden)
Andreea O Diaconescu
2014-09-01
Full Text Available 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.
Inferring on the intentions of others by hierarchical Bayesian learning.
Diaconescu, Andreea O; Mathys, Christoph; Weber, Lilian A E; Daunizeau, Jean; Kasper, Lars; Lomakina, Ekaterina I; Fehr, Ernst; Stephan, Klaas E
2014-09-01
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.
Bayesian structural equation modeling method for hierarchical model validation
Energy Technology Data Exchange (ETDEWEB)
Jiang Xiaomo [Department of Civil and Environmental Engineering, Vanderbilt University, Box 1831-B, Nashville, TN 37235 (United States)], E-mail: xiaomo.jiang@vanderbilt.edu; Mahadevan, Sankaran [Department of Civil and Environmental Engineering, Vanderbilt University, Box 1831-B, Nashville, TN 37235 (United States)], E-mail: sankaran.mahadevan@vanderbilt.edu
2009-04-15
A building block approach to model validation may proceed through various levels, such as material to component to subsystem to system, comparing model predictions with experimental observations at each level. Usually, experimental data becomes scarce as one proceeds from lower to higher levels. This paper presents a structural equation modeling approach to make use of the lower-level data for higher-level model validation under uncertainty, integrating several components: lower-level data, higher-level data, computational model, and latent variables. The method proposed in this paper uses latent variables to model two sets of relationships, namely, the computational model to system-level data, and lower-level data to system-level data. A Bayesian network with Markov chain Monte Carlo simulation is applied to represent the two relationships and to estimate the influencing factors between them. Bayesian hypothesis testing is employed to quantify the confidence in the predictive model at the system level, and the role of lower-level data in the model validation assessment at the system level. The proposed methodology is implemented for hierarchical assessment of three validation problems, using discrete observations and time-series data.
Prediction of road accidents: A Bayesian hierarchical approach.
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
HDDM: Hierarchical Bayesian estimation of the Drift-Diffusion Model in Python.
Wiecki, Thomas V; Sofer, Imri; Frank, Michael J
2013-01-01
The diffusion model is a commonly used tool to infer latent psychological processes underlying decision-making, and to link them to neural mechanisms based on response times. Although efficient open source software has been made available to quantitatively fit the model to data, current estimation methods require an abundance of response time measurements to recover meaningful parameters, and only provide point estimates of each parameter. In contrast, hierarchical Bayesian parameter estimation methods are useful for enhancing statistical power, allowing for simultaneous estimation of individual subject parameters and the group distribution that they are drawn from, while also providing measures of uncertainty in these parameters in the posterior distribution. Here, we present a novel Python-based toolbox called HDDM (hierarchical drift diffusion model), which allows fast and flexible estimation of the the drift-diffusion model and the related linear ballistic accumulator model. HDDM requires fewer data per subject/condition than non-hierarchical methods, allows for full Bayesian data analysis, and can handle outliers in the data. Finally, HDDM supports the estimation of how trial-by-trial measurements (e.g., fMRI) influence decision-making parameters. This paper will first describe the theoretical background of the drift diffusion model and Bayesian inference. We then illustrate usage of the toolbox on a real-world data set from our lab. Finally, parameter recovery studies show that HDDM beats alternative fitting methods like the χ(2)-quantile method as well as maximum likelihood estimation. The software and documentation can be downloaded at: http://ski.clps.brown.edu/hddm_docs/
HDDM: Hierarchical Bayesian estimation of the Drift-Diffusion Model in Python
Directory of Open Access Journals (Sweden)
Thomas V Wiecki
2013-08-01
Full Text Available The diffusion model is a commonly used tool to infer latent psychological processes underlying decision making, and to link them to neural mechanisms based on reaction times. Although efficient open source software has been made available to quantitatively fit the model to data, current estimation methods require an abundance of reaction time measurements to recover meaningful parameters, and only provide point estimates of each parameter. In contrast, hierarchical Bayesian parameter estimation methods are useful for enhancing statistical power, allowing for simultaneous estimation of individual subject parameters and the group distribution that they are drawn from, while also providing measures of uncertainty in these parameters in the posterior distribution. Here, we present a novel Python-based toolbox called HDDM (hierarchical drift diffusion model, which allows fast and flexible estimation of the the drift-diffusion model and the related linear ballistic accumulator model. HDDM requires fewer data per subject / condition than non-hierarchical method, allows for full Bayesian data analysis, and can handle outliers in the data. Finally, HDDM supports the estimation of how trial-by-trial measurements (e.g. fMRI influence decision making parameters. This paper will first describe the theoretical background of drift-diffusion model and Bayesian inference. We then illustrate usage of the toolbox on a real-world data set from our lab. Finally, parameter recovery studies show that HDDM beats alternative fitting methods like the chi-quantile method as well as maximum likelihood estimation. The software and documentation can be downloaded at: http://ski.clps.brown.edu/hddm_docs
Bayesian Hierarchical Modeling for Big Data Fusion in Soil Hydrology
Mohanty, B.; Kathuria, D.; Katzfuss, M.
2016-12-01
Soil moisture datasets from remote sensing (RS) platforms (such as SMOS and SMAP) and reanalysis products from land surface models are typically available on a coarse spatial granularity of several square km. Ground based sensors on the other hand provide observations on a finer spatial scale (meter scale or less) but are sparsely available. Soil moisture is affected by high variability due to complex interactions between geologic, topographic, vegetation and atmospheric variables. Hydrologic processes usually occur at a scale of 1 km or less and therefore spatially ubiquitous and temporally periodic soil moisture products at this scale are required to aid local decision makers in agriculture, weather prediction and reservoir operations. Past literature has largely focused on downscaling RS soil moisture for a small extent of a field or a watershed and hence the applicability of such products has been limited. The present study employs a spatial Bayesian Hierarchical Model (BHM) to derive soil moisture products at a spatial scale of 1 km for the state of Oklahoma by fusing point scale Mesonet data and coarse scale RS data for soil moisture and its auxiliary covariates such as precipitation, topography, soil texture and vegetation. It is seen that the BHM model handles change of support problems easily while performing accurate uncertainty quantification arising from measurement errors and imperfect retrieval algorithms. The computational challenge arising due to the large number of measurements is tackled by utilizing basis function approaches and likelihood approximations. The BHM model can be considered as a complex Bayesian extension of traditional geostatistical prediction methods (such as Kriging) for large datasets in the presence of uncertainties.
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.
Spatial Hierarchical Bayesian Analysis of the Historical Extreme Streamflow
Najafi, M. R.; Moradkhani, H.
2012-04-01
Analysis of the climate change impact on extreme hydro-climatic events is crucial for future hydrologic/hydraulic designs and water resources decision making. The purpose of this study is to investigate the changes of the extreme value distribution parameters with respect to time to reflect upon the impact of climate change. We develop a statistical model using the observed streamflow data of the Columbia River Basin in USA to estimate the changes of high flows as a function of time as well as other variables. Generalized Pareto Distribution (GPD) is used to model the upper 95% flows during December through March for 31 gauge stations. In the process layer of the model the covariates including time, latitude, longitude, elevation and basin area are considered to assess the sensitivity of the model to each variable. Markov Chain Monte Carlo (MCMC) method is used to estimate the parameters. The Spatial Hierarchical Bayesian technique models the GPD parameters spatially and borrows strength from other locations by pooling data together, while providing an explicit estimation of the uncertainties in all stages of modeling.
A Bayesian hierarchical model for wind gust prediction
Friederichs, Petra; Oesting, Marco; Schlather, Martin
2014-05-01
A postprocessing method for ensemble wind gust forecasts given by a mesoscale limited area numerical weather prediction (NWP) model is presented, which is based on extreme value theory. A process layer for the parameters of a generalized extreme value distribution (GEV) is introduced using a Bayesian hierarchical model (BHM). Incorporating the information of the COMSO-DE forecasts, the process parameters model the spatial response surfaces of the GEV parameters as Gaussian random fields. The spatial BHM provides area wide forecasts of wind gusts in terms of a conditional GEV. It models the marginal distribution of the spatial gust process and provides not only forecasts of the conditional GEV at locations without observations, but also uncertainty information about the estimates. A disadvantages of BHM model is that it assumes conditional independent observations. In order to incorporate the dependence between gusts at neighboring locations as well as the spatial random fields of observed and forecasted maximal wind gusts, we propose to model them jointly by a bivariate Brown-Resnick process.
An agglomerative hierarchical approach to visualization in Bayesian clustering problems.
Dawson, K J; Belkhir, K
2009-07-01
Clustering problems (including the clustering of individuals into outcrossing populations, hybrid generations, full-sib families and selfing lines) have recently received much attention in population genetics. In these clustering problems, the parameter of interest is a partition of the set of sampled individuals--the sample partition. In a fully Bayesian approach to clustering problems of this type, our knowledge about the sample partition is represented by a probability distribution on the space of possible sample partitions. As the number of possible partitions grows very rapidly with the sample size, we cannot visualize this probability distribution in its entirety, unless the sample is very small. As a solution to this visualization problem, we recommend using an agglomerative hierarchical clustering algorithm, which we call the exact linkage algorithm. This algorithm is a special case of the maximin clustering algorithm that we introduced previously. The exact linkage algorithm is now implemented in our software package PartitionView. The exact linkage algorithm takes the posterior co-assignment probabilities as input and yields as output a rooted binary tree, or more generally, a forest of such trees. Each node of this forest defines a set of individuals, and the node height is the posterior co-assignment probability of this set. This provides a useful visual representation of the uncertainty associated with the assignment of individuals to categories. It is also a useful starting point for a more detailed exploration of the posterior distribution in terms of the co-assignment probabilities.
A Bayesian hierarchical model for accident and injury surveillance.
MacNab, Ying C
2003-01-01
This article presents a recent study which applies Bayesian hierarchical methodology to model and analyse accident and injury surveillance data. A hierarchical Poisson random effects spatio-temporal model is introduced and an analysis of inter-regional variations and regional trends in hospitalisations due to motor vehicle accident injuries to boys aged 0-24 in the province of British Columbia, Canada, is presented. The objective of this article is to illustrate how the modelling technique can be implemented as part of an accident and injury surveillance and prevention system where transportation and/or health authorities may routinely examine accidents, injuries, and hospitalisations to target high-risk regions for prevention programs, to evaluate prevention strategies, and to assist in health planning and resource allocation. The innovation of the methodology is its ability to uncover and highlight important underlying structure of the data. Between 1987 and 1996, British Columbia hospital separation registry registered 10,599 motor vehicle traffic injury related hospitalisations among boys aged 0-24 who resided in British Columbia, of which majority (89%) of the injuries occurred to boys aged 15-24. The injuries were aggregated by three age groups (0-4, 5-14, and 15-24), 20 health regions (based of place-of-residence), and 10 calendar years (1987 to 1996) and the corresponding mid-year population estimates were used as 'at risk' population. An empirical Bayes inference technique using penalised quasi-likelihood estimation was implemented to model both rates and counts, with spline smoothing accommodating non-linear temporal effects. The results show that (a) crude rates and ratios at health region level are unstable, (b) the models with spline smoothing enable us to explore possible shapes of injury trends at both the provincial level and the regional level, and (c) the fitted models provide a wealth of information about the patterns (both over space and time
Eadie, Gwendolyn; Harris, William
2016-01-01
We present a hierarchical Bayesian method for estimating the total mass and mass profile of the Milky Way Galaxy. The new hierarchical Bayesian approach further improves the framework presented by Eadie, Harris, & Widrow (2015) and Eadie & Harris (2016) and builds upon the preliminary reports by Eadie et al (2015a,c). The method uses a distribution function $f(\\mathcal{E},L)$ to model the galaxy and kinematic data from satellite objects such as globular clusters to trace the Galaxy's gravitational potential. A major advantage of the method is that it not only includes complete and incomplete data simultaneously in the analysis, but also incorporates measurement uncertainties in a coherent and meaningful way. We first test the hierarchical Bayesian framework, which includes measurement uncertainties, using the same data and power-law model assumed in Eadie & Harris (2016), and find the results are similar but more strongly constrained. Next, we take advantage of the new statistical framework and in...
A Bayesian hierarchical diffusion model decomposition of performance in Approach-Avoidance Tasks.
Krypotos, Angelos-Miltiadis; Beckers, Tom; Kindt, Merel; Wagenmakers, Eric-Jan
2015-01-01
Common methods for analysing response time (RT) tasks, frequently used across different disciplines of psychology, suffer from a number of limitations such as the failure to directly measure the underlying latent processes of interest and the inability to take into account the uncertainty associated with each individual's point estimate of performance. Here, we discuss a Bayesian hierarchical diffusion model and apply it to RT data. This model allows researchers to decompose performance into meaningful psychological processes and to account optimally for individual differences and commonalities, even with relatively sparse data. We highlight the advantages of the Bayesian hierarchical diffusion model decomposition by applying it to performance on Approach-Avoidance Tasks, widely used in the emotion and psychopathology literature. Model fits for two experimental data-sets demonstrate that the model performs well. The Bayesian hierarchical diffusion model overcomes important limitations of current analysis procedures and provides deeper insight in latent psychological processes of interest.
Poor-data and data-poor species stock assessment using a Bayesian hierarchical approach.
Jiao, Yan; Cortés, Enric; Andrews, Kate; Guo, Feng
2011-10-01
Appropriate inference for stocks or species with low-quality data (poor data) or limited data (data poor) is extremely important. Hierarchical Bayesian methods are especially applicable to small-area, small-sample-size estimation problems because they allow poor-data species to borrow strength from species with good-quality data. We used a hammerhead shark complex as an example to investigate the advantages of using hierarchical Bayesian models in assessing the status of poor-data and data-poor exploited species. The hammerhead shark complex (Sphyrna spp.) along the Atlantic and Gulf of Mexico coasts of the United States is composed of three species: the scalloped hammerhead (S. lewini), the great hammerhead (S. mokarran), and the smooth hammerhead (S. zygaena) sharks. The scalloped hammerhead comprises 70-80% of the catch and has catch and relative abundance data of good quality, whereas great and smooth hammerheads have relative abundance indices that are both limited and of low quality presumably because of low stock density and limited sampling. Four hierarchical Bayesian state-space surplus production models were developed to simulate variability in population growth rates, carrying capacity, and catchability of the species. The results from the hierarchical Bayesian models were considerably more robust than those of the nonhierarchical models. The hierarchical Bayesian approach represents an intermediate strategy between traditional models that assume different population parameters for each species and those that assume all species share identical parameters. Use of the hierarchical Bayesian approach is suggested for future hammerhead shark stock assessments and for modeling fish complexes with species-specific data, because the poor-data species can borrow strength from the species with good data, making the estimation more stable and robust.
Qian, Song S; Craig, J Kevin; Baustian, Melissa M; Rabalais, Nancy N
2009-12-01
We introduce the Bayesian hierarchical modeling approach for analyzing observational data from marine ecological studies using a data set intended for inference on the effects of bottom-water hypoxia on macrobenthic communities in the northern Gulf of Mexico off the coast of Louisiana, USA. We illustrate (1) the process of developing a model, (2) the use of the hierarchical model results for statistical inference through innovative graphical presentation, and (3) a comparison to the conventional linear modeling approach (ANOVA). Our results indicate that the Bayesian hierarchical approach is better able to detect a "treatment" effect than classical ANOVA while avoiding several arbitrary assumptions necessary for linear models, and is also more easily interpreted when presented graphically. These results suggest that the hierarchical modeling approach is a better alternative than conventional linear models and should be considered for the analysis of observational field data from marine systems.
A Hierarchical Bayesian Model to Predict Self-Thinning Line for Chinese Fir in Southern China.
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Xiongqing Zhang
Full Text Available Self-thinning is a dynamic equilibrium between forest growth and mortality at full site occupancy. Parameters of the self-thinning lines are often confounded by differences across various stand and site conditions. For overcoming the problem of hierarchical and repeated measures, we used hierarchical Bayesian method to estimate the self-thinning line. The results showed that the self-thinning line for Chinese fir (Cunninghamia lanceolata (Lamb.Hook. plantations was not sensitive to the initial planting density. The uncertainty of model predictions was mostly due to within-subject variability. The simulation precision of hierarchical Bayesian method was better than that of stochastic frontier function (SFF. Hierarchical Bayesian method provided a reasonable explanation of the impact of other variables (site quality, soil type, aspect, etc. on self-thinning line, which gave us the posterior distribution of parameters of self-thinning line. The research of self-thinning relationship could be benefit from the use of hierarchical Bayesian method.
Fast, Linear Time Hierarchical Clustering using the Baire Metric
Contreras, Pedro
2011-01-01
The Baire metric induces an ultrametric on a dataset and is of linear computational complexity, contrasted with the standard quadratic time agglomerative hierarchical clustering algorithm. In this work we evaluate empirically this new approach to hierarchical clustering. We compare hierarchical clustering based on the Baire metric with (i) agglomerative hierarchical clustering, in terms of algorithm properties; (ii) generalized ultrametrics, in terms of definition; and (iii) fast clustering through k-means partititioning, in terms of quality of results. For the latter, we carry out an in depth astronomical study. We apply the Baire distance to spectrometric and photometric redshifts from the Sloan Digital Sky Survey using, in this work, about half a million astronomical objects. We want to know how well the (more costly to determine) spectrometric redshifts can predict the (more easily obtained) photometric redshifts, i.e. we seek to regress the spectrometric on the photometric redshifts, and we use clusterwi...
Wei Wu; James Clark; James Vose
2010-01-01
Hierarchical Bayesian (HB) modeling allows for multiple sources of uncertainty by factoring complex relationships into conditional distributions that can be used to draw inference and make predictions. We applied an HB model to estimate the parameters and state variables of a parsimonious hydrological model â GR4J â by coherently assimilating the uncertainties from the...
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 Hierarchical Bayesian M/EEG Imaging Method Correcting for Incomplete Spatio-Temporal Priors
DEFF Research Database (Denmark)
Stahlhut, Carsten; Attias, Hagai T.; Sekihara, Kensuke;
2013-01-01
In this paper we present a hierarchical Bayesian model, to tackle the highly ill-posed problem that follows with MEG and EEG source imaging. Our model promotes spatiotemporal patterns through the use of both spatial and temporal basis functions. While in contrast to most previous spatio-temporal ...
Osei, Frank B.; Duker, Alfred A.; Stein, Alfred
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
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Moritz eBoos
2016-05-01
Full Text Available Cognitive determinants of probabilistic inference were examined using hierarchical Bayesian modelling techniques. A classic urn-ball paradigm served as experimental strategy, involving a factorial two (prior probabilities by two (likelihoods design. Five computational models of cognitive processes were compared with the observed behaviour. Parameter-free Bayesian posterior probabilities and parameter-free base rate neglect provided inadequate models of probabilistic inference. The introduction of distorted subjective probabilities yielded more robust and generalizable results. A general class of (inverted S-shaped probability weighting functions had been proposed; however, the possibility of large differences in probability distortions not only across experimental conditions, but also across individuals, seems critical for the model’s success. It also seems advantageous to consider individual differences in parameters of probability weighting as being sampled from weakly informative prior distributions of individual parameter values. Thus, the results from hierarchical Bayesian modelling converge with previous results in revealing that probability weighting parameters show considerable task dependency and individual differences. Methodologically, this work exemplifies the usefulness of hierarchical Bayesian modelling techniques for cognitive psychology. Theoretically, human probabilistic inference might be best described as the application of individualized strategic policies for Bayesian belief revision.
Boos, Moritz; Seer, Caroline; Lange, Florian; Kopp, Bruno
2016-01-01
Cognitive determinants of probabilistic inference were examined using hierarchical Bayesian modeling techniques. A classic urn-ball paradigm served as experimental strategy, involving a factorial two (prior probabilities) by two (likelihoods) design. Five computational models of cognitive processes were compared with the observed behavior. Parameter-free Bayesian posterior probabilities and parameter-free base rate neglect provided inadequate models of probabilistic inference. The introduction of distorted subjective probabilities yielded more robust and generalizable results. A general class of (inverted) S-shaped probability weighting functions had been proposed; however, the possibility of large differences in probability distortions not only across experimental conditions, but also across individuals, seems critical for the model's success. It also seems advantageous to consider individual differences in parameters of probability weighting as being sampled from weakly informative prior distributions of individual parameter values. Thus, the results from hierarchical Bayesian modeling converge with previous results in revealing that probability weighting parameters show considerable task dependency and individual differences. Methodologically, this work exemplifies the usefulness of hierarchical Bayesian modeling techniques for cognitive psychology. Theoretically, human probabilistic inference might be best described as the application of individualized strategic policies for Bayesian belief revision.
Scheibehenne, Benjamin; Pachur, Thorsten
2015-04-01
To be useful, cognitive models with fitted parameters should show generalizability across time and allow accurate predictions of future observations. It has been proposed that hierarchical procedures yield better estimates of model parameters than do nonhierarchical, independent approaches, because the formers' estimates for individuals within a group can mutually inform each other. Here, we examine Bayesian hierarchical approaches to evaluating model generalizability in the context of two prominent models of risky choice-cumulative prospect theory (Tversky & Kahneman, 1992) and the transfer-of-attention-exchange model (Birnbaum & Chavez, 1997). Using empirical data of risky choices collected for each individual at two time points, we compared the use of hierarchical versus independent, nonhierarchical Bayesian estimation techniques to assess two aspects of model generalizability: parameter stability (across time) and predictive accuracy. The relative performance of hierarchical versus independent estimation varied across the different measures of generalizability. The hierarchical approach improved parameter stability (in terms of a lower absolute discrepancy of parameter values across time) and predictive accuracy (in terms of deviance; i.e., likelihood). With respect to test-retest correlations and posterior predictive accuracy, however, the hierarchical approach did not outperform the independent approach. Further analyses suggested that this was due to strong correlations between some parameters within both models. Such intercorrelations make it difficult to identify and interpret single parameters and can induce high degrees of shrinkage in hierarchical models. Similar findings may also occur in the context of other cognitive models of choice.
Fast Bayesian inference of optical trap stiffness and particle diffusion
Bera, Sudipta; Paul, Shuvojit; Singh, Rajesh; Ghosh, Dipanjan; Kundu, Avijit; Banerjee, Ayan; Adhikari, R.
2017-01-01
Bayesian inference provides a principled way of estimating the parameters of a stochastic process that is observed discretely in time. The overdamped Brownian motion of a particle confined in an optical trap is generally modelled by the Ornstein-Uhlenbeck process and can be observed directly in experiment. Here we present Bayesian methods for inferring the parameters of this process, the trap stiffness and the particle diffusion coefficient, that use exact likelihoods and sufficient statistics to arrive at simple expressions for the maximum a posteriori estimates. This obviates the need for Monte Carlo sampling and yields methods that are both fast and accurate. We apply these to experimental data and demonstrate their advantage over commonly used non-Bayesian fitting methods.
Fast Bayesian inference of optical trap stiffness and particle diffusion
Bera, Sudipta; Singh, Rajesh; Ghosh, Dipanjan; Kundu, Avijit; Banerjee, Ayan; Adhikari, R
2016-01-01
Bayesian inference provides a principled way of estimating the parameters of a stochastic process that is observed discretely in time. The overdamped Brownian motion of a particle confined in an optical trap is generally modelled by the Ornstein-Uhlenbeck process and can be observed directly in experiment. Here we present Bayesian methods for inferring the parameters of this process, the trap stiffness and the particle diffusion coefficient, that use exact likelihoods and sufficient statistics to arrive at simple expressions for the maximum a posteriori estimates. This obviates the need for Monte Carlo sampling and yields methods that are both fast and accurate. We apply these to experimental data and demonstrate their advantage over commonly used non-Bayesian fitting methods.
Using hierarchical Bayesian methods to examine the tools of decision-making
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Michael D. Lee
2011-12-01
Full Text Available Hierarchical Bayesian methods offer a principled and comprehensive way to relate psychological models to data. Here we use them to model the patterns of information search, stopping and deciding in a simulated binary comparison judgment task. The simulation involves 20 subjects making 100 forced choice comparisons about the relative magnitudes of two objects (which of two German cities has more inhabitants. Two worked-examples show how hierarchical models can be developed to account for and explain the diversity of both search and stopping rules seen across the simulated individuals. We discuss how the results provide insight into current debates in the literature on heuristic decision making and argue that they demonstrate the power and flexibility of hierarchical Bayesian methods in modeling human decision-making.
Sparse Event Modeling with Hierarchical Bayesian Kernel Methods
2016-01-05
the kernel function which depends on the application and the model user. This research uses the most popular kernel function, the radial basis...an important role in the nation’s economy. Unfortunately, the system’s reliability is declining due to the aging components of the network [Grier...kernel function. Gaussian Bayesian kernel models became very popular recently and were extended and applied to a number of classification problems. An
Determining the Bayesian optimal sampling strategy in a hierarchical system.
Energy Technology Data Exchange (ETDEWEB)
Grace, Matthew D.; Ringland, James T.; Boggs, Paul T.; Pebay, Philippe Pierre
2010-09-01
Consider a classic hierarchy tree as a basic model of a 'system-of-systems' network, where each node represents a component system (which may itself consist of a set of sub-systems). For this general composite system, we present a technique for computing the optimal testing strategy, which is based on Bayesian decision analysis. In previous work, we developed a Bayesian approach for computing the distribution of the reliability of a system-of-systems structure that uses test data and prior information. This allows for the determination of both an estimate of the reliability and a quantification of confidence in the estimate. Improving the accuracy of the reliability estimate and increasing the corresponding confidence require the collection of additional data. However, testing all possible sub-systems may not be cost-effective, feasible, or even necessary to achieve an improvement in the reliability estimate. To address this sampling issue, we formulate a Bayesian methodology that systematically determines the optimal sampling strategy under specified constraints and costs that will maximally improve the reliability estimate of the composite system, e.g., by reducing the variance of the reliability distribution. This methodology involves calculating the 'Bayes risk of a decision rule' for each available sampling strategy, where risk quantifies the relative effect that each sampling strategy could have on the reliability estimate. A general numerical algorithm is developed and tested using an example multicomponent system. The results show that the procedure scales linearly with the number of components available for testing.
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Brodjol Sutijo Supri Ulama
2012-01-01
Full Text Available Problem statement: Household expenditure analysis was highly demanding for government in order to formulate its policy. Since household data was viewed as hierarchical structure with household nested in its regional residence which varies inter region, the contextual welfare analysis was needed. This study proposed to develop a hierarchical model for estimating household expenditure in an attempt to measure the effect of regional diversity by taking into account district characteristics and household attributes using a Bayesian approach. Approach: Due to the variation of household expenditure data which was captured by the three parameters of Log-Normal (LN3 distribution, the model was developed based on LN3 distribution. Data used in this study was household expenditure data in Central Java, Indonesia. Since, data were unbalanced and hierarchical models using a classical approach work well for balanced data, thus the estimation process was done by using Bayesian method with MCMC and Gibbs sampling. Results: The hierarchical Bayesian model based on LN3 distribution could be implemented to explain the variation of household expenditure using district characteristics and household attributes. Conclusion: The model shows that districts characteristics which include demographic and economic conditions of districts and the availability of public facilities which are strongly associated with a dimension of human development index, i.e., economic, education and health, do affect to household expenditure through its household attributes."
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Guillaume Marrelec
Full Text Available The use of mutual information as a similarity measure in agglomerative hierarchical clustering (AHC raises an important issue: some correction needs to be applied for the dimensionality of variables. In this work, we formulate the decision of merging dependent multivariate normal variables in an AHC procedure as a Bayesian model comparison. We found that the Bayesian formulation naturally shrinks the empirical covariance matrix towards a matrix set a priori (e.g., the identity, provides an automated stopping rule, and corrects for dimensionality using a term that scales up the measure as a function of the dimensionality of the variables. Also, the resulting log Bayes factor is asymptotically proportional to the plug-in estimate of mutual information, with an additive correction for dimensionality in agreement with the Bayesian information criterion. We investigated the behavior of these Bayesian alternatives (in exact and asymptotic forms to mutual information on simulated and real data. An encouraging result was first derived on simulations: the hierarchical clustering based on the log Bayes factor outperformed off-the-shelf clustering techniques as well as raw and normalized mutual information in terms of classification accuracy. On a toy example, we found that the Bayesian approaches led to results that were similar to those of mutual information clustering techniques, with the advantage of an automated thresholding. On real functional magnetic resonance imaging (fMRI datasets measuring brain activity, it identified clusters consistent with the established outcome of standard procedures. On this application, normalized mutual information had a highly atypical behavior, in the sense that it systematically favored very large clusters. These initial experiments suggest that the proposed Bayesian alternatives to mutual information are a useful new tool for hierarchical clustering.
Marrelec, Guillaume; Messé, Arnaud; Bellec, Pierre
2015-01-01
The use of mutual information as a similarity measure in agglomerative hierarchical clustering (AHC) raises an important issue: some correction needs to be applied for the dimensionality of variables. In this work, we formulate the decision of merging dependent multivariate normal variables in an AHC procedure as a Bayesian model comparison. We found that the Bayesian formulation naturally shrinks the empirical covariance matrix towards a matrix set a priori (e.g., the identity), provides an automated stopping rule, and corrects for dimensionality using a term that scales up the measure as a function of the dimensionality of the variables. Also, the resulting log Bayes factor is asymptotically proportional to the plug-in estimate of mutual information, with an additive correction for dimensionality in agreement with the Bayesian information criterion. We investigated the behavior of these Bayesian alternatives (in exact and asymptotic forms) to mutual information on simulated and real data. An encouraging result was first derived on simulations: the hierarchical clustering based on the log Bayes factor outperformed off-the-shelf clustering techniques as well as raw and normalized mutual information in terms of classification accuracy. On a toy example, we found that the Bayesian approaches led to results that were similar to those of mutual information clustering techniques, with the advantage of an automated thresholding. On real functional magnetic resonance imaging (fMRI) datasets measuring brain activity, it identified clusters consistent with the established outcome of standard procedures. On this application, normalized mutual information had a highly atypical behavior, in the sense that it systematically favored very large clusters. These initial experiments suggest that the proposed Bayesian alternatives to mutual information are a useful new tool for hierarchical clustering.
Application of Bayesian Hierarchical Prior Modeling to Sparse Channel Estimation
DEFF Research Database (Denmark)
Pedersen, Niels Lovmand; Manchón, Carles Navarro; Shutin, Dmitriy
2012-01-01
. The estimators result as an application of the variational message-passing algorithm on the factor graph representing the signal model extended with the hierarchical prior models. Numerical results demonstrate the superior performance of our channel estimators as compared to traditional and state......Existing methods for sparse channel estimation typically provide an estimate computed as the solution maximizing an objective function defined as the sum of the log-likelihood function and a penalization term proportional to the l1-norm of the parameter of interest. However, other penalization......-of-the-art sparse methods....
A hierarchical Bayesian framework for force field selection in molecular dynamics simulations.
Wu, S; Angelikopoulos, P; Papadimitriou, C; Moser, R; Koumoutsakos, P
2016-02-13
We present a hierarchical Bayesian framework for the selection of force fields in molecular dynamics (MD) simulations. The framework associates the variability of the optimal parameters of the MD potentials under different environmental conditions with the corresponding variability in experimental data. The high computational cost associated with the hierarchical Bayesian framework is reduced by orders of magnitude through a parallelized Transitional Markov Chain Monte Carlo method combined with the Laplace Asymptotic Approximation. The suitability of the hierarchical approach is demonstrated by performing MD simulations with prescribed parameters to obtain data for transport coefficients under different conditions, which are then used to infer and evaluate the parameters of the MD model. We demonstrate the selection of MD models based on experimental data and verify that the hierarchical model can accurately quantify the uncertainty across experiments; improve the posterior probability density function estimation of the parameters, thus, improve predictions on future experiments; identify the most plausible force field to describe the underlying structure of a given dataset. The framework and associated software are applicable to a wide range of nanoscale simulations associated with experimental data with a hierarchical structure.
Bayesian site selection for fast Gaussian process regression
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.
Fast Gibbs sampling for high-dimensional Bayesian inversion
Lucka, Felix
2016-11-01
Solving ill-posed inverse problems by Bayesian inference has recently attracted considerable attention. Compared to deterministic approaches, the probabilistic representation of the solution by the posterior distribution can be exploited to explore and quantify its uncertainties. In applications where the inverse solution is subject to further analysis procedures can be a significant advantage. Alongside theoretical progress, various new computational techniques allow us to sample very high dimensional posterior distributions: in (Lucka 2012 Inverse Problems 28 125012), and a Markov chain Monte Carlo posterior sampler was developed for linear inverse problems with {{\\ell }}1-type priors. In this article, we extend this single component (SC) Gibbs-type sampler to a wide range of priors used in Bayesian inversion, such as general {{\\ell }}pq priors with additional hard constraints. In addition, a fast computation of the conditional, SC densities in an explicit, parameterized form, a fast, robust and exact sampling from these one-dimensional densities is key to obtain an efficient algorithm. We demonstrate that a generalization of slice sampling can utilize their specific structure for this task and illustrate the performance of the resulting slice-within-Gibbs samplers by different computed examples. These new samplers allow us to perform sample-based Bayesian inference in high-dimensional scenarios with certain priors for the first time, including the inversion of computed tomography data with the popular isotropic total variation prior.
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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.
Wu, Stephen; Angelikopoulos, Panagiotis; Tauriello, Gerardo; Papadimitriou, Costas; Koumoutsakos, Petros
2016-12-28
We propose a hierarchical Bayesian framework to systematically integrate heterogeneous data for the calibration of force fields in Molecular Dynamics (MD) simulations. Our approach enables the fusion of diverse experimental data sets of the physico-chemical properties of a system at different thermodynamic conditions. We demonstrate the value of this framework for the robust calibration of MD force-fields for water using experimental data of its diffusivity, radial distribution function, and density. In order to address the high computational cost associated with the hierarchical Bayesian models, we develop a novel surrogate model based on the empirical interpolation method. Further computational savings are achieved by implementing a highly parallel transitional Markov chain Monte Carlo technique. The present method bypasses possible subjective weightings of the experimental data in identifying MD force-field parameters.
Sensor Network Data Fault Detection using Hierarchical Bayesian Space-Time Modeling
Ni, Kevin; Pottie, G J
2009-01-01
We present a new application of hierarchical Bayesian space-time (HBST) modeling: data fault detection in sensor networks primarily used in environmental monitoring situations. To show the effectiveness of HBST modeling, we develop a rudimentary tagging system to mark data that does not fit with given models. Using this, we compare HBST modeling against first order linear autoregressive (AR) modeling, which is a commonly used alternative due to its simplicity. We show that while HBST is mo...
Eadie, Gwendolyn M.; Springford, Aaron; Harris, William E.
2017-02-01
We present a hierarchical Bayesian method for estimating the total mass and mass profile of the Milky Way Galaxy. The new hierarchical Bayesian approach further improves the framework presented by Eadie et al. and Eadie and Harris and builds upon the preliminary reports by Eadie et al. The method uses a distribution function f({ E },L) to model the Galaxy and kinematic data from satellite objects, such as globular clusters (GCs), to trace the Galaxy’s gravitational potential. A major advantage of the method is that it not only includes complete and incomplete data simultaneously in the analysis, but also incorporates measurement uncertainties in a coherent and meaningful way. We first test the hierarchical Bayesian framework, which includes measurement uncertainties, using the same data and power-law model assumed in Eadie and Harris and find the results are similar but more strongly constrained. Next, we take advantage of the new statistical framework and incorporate all possible GC data, finding a cumulative mass profile with Bayesian credible regions. This profile implies a mass within 125 kpc of 4.8× {10}11{M}ȯ with a 95% Bayesian credible region of (4.0{--}5.8)× {10}11{M}ȯ . Our results also provide estimates of the true specific energies of all the GCs. By comparing these estimated energies to the measured energies of GCs with complete velocity measurements, we observe that (the few) remote tracers with complete measurements may play a large role in determining a total mass estimate of the Galaxy. Thus, our study stresses the need for more remote tracers with complete velocity measurements.
Shetty, Rahul; Bigiel, Frank
2012-01-01
We develop a Bayesian linear regression method which rigorously treats measurement uncertainties, and accounts for hierarchical data structure for investigating the relationship between the star formation rate and gas surface density. The method simultaneously estimates the intercept, slope, and scatter about the regression line of each individual subject (e.g. a galaxy) and the population (e.g. an ensemble of galaxies). Using synthetic datasets, we demonstrate that the Bayesian method accurately recovers the parameters of both the individuals and the population, especially when compared to commonly employed least squares methods, such as the bisector. We apply the Bayesian method to estimate the Kennicutt-Schmidt (KS) parameters of a sample of spiral galaxies compiled by Bigiel et al. (2008). We find significant variation in the KS parameters, indicating that no single KS relationship holds for all galaxies. This suggests that the relationship between molecular gas and star formation differs between galaxies...
Hierarchical Bayesian Analysis of Biased Beliefs and Distributional Other-Regarding Preferences
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Jeroen Weesie
2013-02-01
Full Text Available This study investigates the relationship between an actor’s beliefs about others’ other-regarding (social preferences and her own other-regarding preferences, using an “avant-garde” hierarchical Bayesian method. We estimate two distributional other-regarding preference parameters, α and β, of actors using incentivized choice data in binary Dictator Games. Simultaneously, we estimate the distribution of actors’ beliefs about others α and β, conditional on actors’ own α and β, with incentivized belief elicitation. We demonstrate the benefits of the Bayesian method compared to it’s hierarchical frequentist counterparts. Results show a positive association between an actor’s own (α; β and her beliefs about average(α; β in the population. The association between own preferences and the variance in beliefs about others’ preferences in the population, however, is curvilinear for α and insignificant for β. These results are partially consistent with the cone effect [1,2] which is described in detail below. Because in the Bayesian-Nash equilibrium concept, beliefs and own preferences are assumed to be independent, these results cast doubt on the application of the Bayesian-Nash equilibrium concept to experimental data.
Progress on Bayesian Inference of the Fast Ion Distribution Function
DEFF Research Database (Denmark)
Stagner, L.; Heidbrink, W.W,; Chen, X.;
2013-01-01
The fast-ion distribution function (DF) has a complicated dependence on several phase-space variables. The standard analysis procedure in energetic particle research is to compute the DF theoretically, use that DF in forward modeling to predict diagnostic signals, then compare with measured data...... 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...
Application of Bayesian hierarchical models for phase I/II clinical trials in oncology.
Yada, Shinjo; Hamada, Chikuma
2017-03-01
Treatment during cancer clinical trials sometimes involves the combination of multiple drugs. In addition, in recent years there has been a trend toward phase I/II trials in which a phase I and a phase II trial are combined into a single trial to accelerate drug development. Methods for the seamless combination of phases I and II parts are currently under investigation. In the phase II part, adaptive randomization on the basis of patient efficacy outcomes allocates more patients to the dose combinations considered to have higher efficacy. Patient toxicity outcomes are used for determining admissibility to each dose combination and are not used for selection of the dose combination itself. In cases where the objective is not to find the optimum dose combination solely for efficacy but regarding both toxicity and efficacy, the need exists to allocate patients to dose combinations with consideration of the balance of existing trade-offs between toxicity and efficacy. We propose a Bayesian hierarchical model and an adaptive randomization with consideration for the relationship with toxicity and efficacy. Using the toxicity and efficacy outcomes of patients, the Bayesian hierarchical model is used to estimate the toxicity probability and efficacy probability in each of the dose combinations. Here, we use Bayesian moving-reference adaptive randomization on the basis of desirability computed from the obtained estimator. Computer simulations suggest that the proposed method will likely recommend a higher percentage of target dose combinations than a previously proposed method.
Learning emergent behaviours for a hierarchical Bayesian framework for active robotic perception.
Ferreira, João Filipe; Tsiourti, Christiana; Dias, Jorge
2012-08-01
In this research work, we contribute with a behaviour learning process for a hierarchical Bayesian framework for multimodal active perception, devised to be emergent, scalable and adaptive. This framework is composed by models built upon a common spatial configuration for encoding perception and action that is naturally fitting for the integration of readings from multiple sensors, using a Bayesian approach devised in previous work. The proposed learning process is shown to reproduce goal-dependent human-like active perception behaviours by learning model parameters (referred to as "attentional sets") for different free-viewing and active search tasks. Learning was performed by presenting several 3D audiovisual virtual scenarios using a head-mounted display, while logging the spatial distribution of fixations of the subject (in 2D, on left and right images, and in 3D space), data which are consequently used as the training set for the framework. As a consequence, the hierarchical Bayesian framework adequately implements high-level behaviour resulting from low-level interaction of simpler building blocks by using the attentional sets learned for each task, and is able to change these attentional sets "on the fly," allowing the implementation of goal-dependent behaviours (i.e., top-down influences).
Risk Assessment for Mobile Systems Through a Multilayered Hierarchical Bayesian Network.
Li, Shancang; Tryfonas, Theo; Russell, Gordon; Andriotis, Panagiotis
2016-08-01
Mobile systems are facing a number of application vulnerabilities that can be combined together and utilized to penetrate systems with devastating impact. When assessing the overall security of a mobile system, it is important to assess the security risks posed by each mobile applications (apps), thus gaining a stronger understanding of any vulnerabilities present. This paper aims at developing a three-layer framework that assesses the potential risks which apps introduce within the Android mobile systems. A Bayesian risk graphical model is proposed to evaluate risk propagation in a layered risk architecture. By integrating static analysis, dynamic analysis, and behavior analysis in a hierarchical framework, the risks and their propagation through each layer are well modeled by the Bayesian risk graph, which can quantitatively analyze risks faced to both apps and mobile systems. The proposed hierarchical Bayesian risk graph model offers a novel way to investigate the security risks in mobile environment and enables users and administrators to evaluate the potential risks. This strategy allows to strengthen both app security as well as the security of the entire system.
Analysis of household data on influenza epidemic with Bayesian hierarchical model.
Hsu, C Y; Yen, A M F; Chen, L S; Chen, H H
2015-03-01
Data used for modelling the household transmission of infectious diseases, such as influenza, have inherent multilevel structures and correlated property, which make the widely used conventional infectious disease transmission models (including the Greenwood model and the Reed-Frost model) not directly applicable within the context of a household (due to the crowded domestic condition or socioeconomic status of the household). Thus, at the household level, the effects resulting from individual-level factors, such as vaccination, may be confounded or modified in some way. We proposed the Bayesian hierarchical random-effects (random intercepts and random slopes) model under the context of generalised linear model to capture heterogeneity and variation on the individual, generation, and household levels. It was applied to empirical surveillance data on the influenza epidemic in Taiwan. The parameters of interest were estimated by using the Markov chain Monte Carlo method in conjunction with the Bayesian directed acyclic graphical models. Comparisons between models were made using the deviance information criterion. Based on the result of the random-slope Bayesian hierarchical method under the context of the Reed-Frost transmission model, the regression coefficient regarding the protective effect of vaccination varied statistically significantly from household to household. The result of such a heterogeneity was robust to the use of different prior distributions (including non-informative, sceptical, and enthusiastic ones). By integrating out the uncertainty of the parameters of the posterior distribution, the predictive distribution was computed to forecast the number of influenza cases allowing for random-household effect.
Gas turbine engine prognostics using Bayesian hierarchical models: A variational approach
Zaidan, Martha A.; Mills, Andrew R.; Harrison, Robert F.; Fleming, Peter J.
2016-03-01
Prognostics is an emerging requirement of modern health monitoring that aims to increase the fidelity of failure-time predictions by the appropriate use of sensory and reliability information. In the aerospace industry it is a key technology to reduce life-cycle costs, improve reliability and asset availability for a diverse fleet of gas turbine engines. In this work, a Bayesian hierarchical model is selected to utilise fleet data from multiple assets to perform probabilistic estimation of remaining useful life (RUL) for civil aerospace gas turbine engines. The hierarchical formulation allows Bayesian updates of an individual predictive model to be made, based upon data received asynchronously from a fleet of assets with different in-service lives and for the entry of new assets into the fleet. In this paper, variational inference is applied to the hierarchical formulation to overcome the computational and convergence concerns that are raised by the numerical sampling techniques needed for inference in the original formulation. The algorithm is tested on synthetic data, where the quality of approximation is shown to be satisfactory with respect to prediction performance, computational speed, and ease of use. A case study of in-service gas turbine engine data demonstrates the value of integrating fleet data for accurately predicting degradation trajectories of assets.
Fast empirical Bayesian LASSO for multiple quantitative trait locus mapping
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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.
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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.
Yu, Rongjie; Abdel-Aty, Mohamed
2013-07-01
The Bayesian inference method has been frequently adopted to develop safety performance functions. One advantage of the Bayesian inference is that prior information for the independent variables can be included in the inference procedures. However, there are few studies that discussed how to formulate informative priors for the independent variables and evaluated the effects of incorporating informative priors in developing safety performance functions. This paper addresses this deficiency by introducing four approaches of developing informative priors for the independent variables based on historical data and expert experience. Merits of these informative priors have been tested along with two types of Bayesian hierarchical models (Poisson-gamma and Poisson-lognormal models). Deviance information criterion (DIC), R-square values, and coefficients of variance for the estimations were utilized as evaluation measures to select the best model(s). Comparison across the models indicated that the Poisson-gamma model is superior with a better model fit and it is much more robust with the informative priors. Moreover, the two-stage Bayesian updating informative priors provided the best goodness-of-fit and coefficient estimation accuracies. Furthermore, informative priors for the inverse dispersion parameter have also been introduced and tested. Different types of informative priors' effects on the model estimations and goodness-of-fit have been compared and concluded. Finally, based on the results, recommendations for future research topics and study applications have been made.
Bayesian Uncertainty Quantification for Subsurface Inversion Using a Multiscale Hierarchical Model
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.
Bayesian methods for estimating the reliability in complex hierarchical networks (interim report).
Energy Technology Data Exchange (ETDEWEB)
Marzouk, Youssef M.; Zurn, Rena M.; Boggs, Paul T.; Diegert, Kathleen V. (Sandia National Laboratories, Albuquerque, NM); Red-Horse, John Robert (Sandia National Laboratories, Albuquerque, NM); Pebay, Philippe Pierre
2007-05-01
Current work on the Integrated Stockpile Evaluation (ISE) project is evidence of Sandia's commitment to maintaining the integrity of the nuclear weapons stockpile. In this report, we undertake a key element in that process: development of an analytical framework for determining the reliability of the stockpile in a realistic environment of time-variance, inherent uncertainty, and sparse available information. This framework is probabilistic in nature and is founded on a novel combination of classical and computational Bayesian analysis, Bayesian networks, and polynomial chaos expansions. We note that, while the focus of the effort is stockpile-related, it is applicable to any reasonably-structured hierarchical system, including systems with feedback.
A Bayesian Hierarchical Model for Relating Multiple SNPs within Multiple Genes to Disease Risk
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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.
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X. Chen
2013-09-01
Full Text Available A Hierarchal Bayesian model for forecasting regional summer rainfall and streamflow season-ahead using exogenous climate variables for East Central China is presented. The model provides estimates of the posterior forecasted probability distribution for 12 rainfall and 2 streamflow stations considering parameter uncertainty, and cross-site correlation. The model has a multilevel structure with regression coefficients modeled from a common multivariate normal distribution results in partial-pooling of information across multiple stations and better representation of parameter and posterior distribution uncertainty. Covariance structure of the residuals across stations is explicitly modeled. Model performance is tested under leave-10-out cross-validation. Frequentist and Bayesian performance metrics used include Receiver Operating Characteristic, Reduction of Error, Coefficient of Efficiency, Rank Probability Skill Scores, and coverage by posterior credible intervals. The ability of the model to reliably forecast regional summer rainfall and streamflow season-ahead offers potential for developing adaptive water risk management strategies.
Improved Estimates of the Milky Way's Disk Scale Length From Hierarchical Bayesian Techniques
Licquia, Timothy C
2016-01-01
The exponential scale length ($L_d$) of the Milky Way's (MW's) disk is a critical parameter for describing the global physical size of our Galaxy, important both for interpreting other Galactic measurements and helping us to understand how our Galaxy fits into extragalactic contexts. Unfortunately, current estimates span a wide range of values and often are statistically incompatible with one another. Here, we aim to determine an improved, aggregate estimate for $L_d$ by utilizing a hierarchical Bayesian (HB) meta-analysis technique that accounts for the possibility that any one measurement has not properly accounted for all statistical or systematic errors. Within this machinery we explore a variety of ways of modeling the nature of problematic measurements, and then use a Bayesian model averaging technique to derive net posterior distributions that incorporate any model-selection uncertainty. Our meta-analysis combines 29 different (15 visible and 14 infrared) photometric measurements of $L_d$ available in ...
Siwek, M; Finocchiaro, R; Curik, I; Portolano, B
2011-02-01
Genetic structure and relationship amongst the main goat populations in Sicily (Girgentana, Derivata di Siria, Maltese and Messinese) were analysed using information from 19 microsatellite markers genotyped on 173 individuals. A posterior Bayesian approach implemented in the program STRUCTURE revealed a hierarchical structure with two clusters at the first level (Girgentana vs. Messinese, Derivata di Siria and Maltese), explaining 4.8% of variation (amovaФ(ST) estimate). Seven clusters nested within these first two clusters (further differentiations of Girgentana, Derivata di Siria and Maltese), explaining 8.5% of variation (amovaФ(SC) estimate). The analyses and methods applied in this study indicate their power to detect subtle population structure.
Xu, Lizhen; Paterson, Andrew D; Xu, Wei
2017-04-01
Motivated by the multivariate nature of microbiome data with hierarchical taxonomic clusters, counts that are often skewed and zero inflated, and repeated measures, we propose a Bayesian latent variable methodology to jointly model multiple operational taxonomic units within a single taxonomic cluster. This novel method can incorporate both negative binomial and zero-inflated negative binomial responses, and can account for serial and familial correlations. We develop a Markov chain Monte Carlo algorithm that is built on a data augmentation scheme using Pólya-Gamma random variables. Hierarchical centering and parameter expansion techniques are also used to improve the convergence of the Markov chain. We evaluate the performance of our proposed method through extensive simulations. We also apply our method to a human microbiome study.
A fast quad-tree based two dimensional hierarchical clustering.
Rajadurai, Priscilla; Sankaranarayanan, Swamynathan
2012-01-01
Recently, microarray technologies have become a robust technique in the area of genomics. An important step in the analysis of gene expression data is the identification of groups of genes disclosing analogous expression patterns. Cluster analysis partitions a given dataset into groups based on specified features. Euclidean distance is a widely used similarity measure for gene expression data that considers the amount of changes in gene expression. However, the huge number of genes and the intricacy of biological networks have highly increased the challenges of comprehending and interpreting the resulting group of data, increasing processing time. The proposed technique focuses on a QT based fast 2-dimensional hierarchical clustering algorithm to perform clustering. The construction of the closest pair data structure is an each level is an important time factor, which determines the processing time of clustering. The proposed model reduces the processing time and improves analysis of gene expression data.
Prion Amplification and Hierarchical Bayesian Modeling Refine Detection of Prion Infection
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.
A hierarchical bayesian model to quantify uncertainty of stream water temperature forecasts.
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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.
A hierarchical Bayesian-MAP approach to inverse problems in imaging
Raj, Raghu G.
2016-07-01
We present a novel approach to inverse problems in imaging based on a hierarchical Bayesian-MAP (HB-MAP) formulation. In this paper we specifically focus on the difficult and basic inverse problem of multi-sensor (tomographic) imaging wherein the source object of interest is viewed from multiple directions by independent sensors. Given the measurements recorded by these sensors, the problem is to reconstruct the image (of the object) with a high degree of fidelity. We employ a probabilistic graphical modeling extension of the compound Gaussian distribution as a global image prior into a hierarchical Bayesian inference procedure. Since the prior employed by our HB-MAP algorithm is general enough to subsume a wide class of priors including those typically employed in compressive sensing (CS) algorithms, HB-MAP algorithm offers a vehicle to extend the capabilities of current CS algorithms to include truly global priors. After rigorously deriving the regression algorithm for solving our inverse problem from first principles, we demonstrate the performance of the HB-MAP algorithm on Monte Carlo trials and on real empirical data (natural scenes). In all cases we find that our algorithm outperforms previous approaches in the literature including filtered back-projection and a variety of state-of-the-art CS algorithms. We conclude with directions of future research emanating from this work.
fastRESOLVE: fast Bayesian imaging for aperture synthesis in radio astronomy
Greiner, Maksim; Junklewitz, Henrik; Enßlin, Torsten A
2016-01-01
The standard imaging algorithm for interferometric radio data, CLEAN, is optimal for point source observations, but suboptimal for diffuse emission. Recently, RESOLVE, a new Bayesian algorithm has been developed, which is ideal for extended source imaging. Unfortunately, RESOLVE is computationally very expensive. In this paper we present fastRESOLVE, a modification of RESOLVE based on an approximation of the interferometric likelihood that allows us to avoid expensive gridding routines and consequently gain a factor of roughly 100 in computation time. Furthermore, we include a Bayesian estimation of the measurement uncertainty of the visibilities into the imaging, a procedure not applied in aperture synthesis before. The algorithm requires little to no user input compared to the standard method CLEAN while being superior for extended and faint emission. We apply the algorithm to VLA data of Abell 2199 and show that it resolves more detailed structures.
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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.
A Bayesian Hierarchical Model for Reconstructing Sea Levels: From Raw Data to Rates of Change
Cahill, Niamh; Horton, Benjamin P; Parnell, Andrew C
2015-01-01
We present a holistic Bayesian hierarchical model for reconstructing the continuous and dynamic evolution of relative sea-level (RSL) change with fully quantified uncertainty. The reconstruction is produced from biological (foraminifera) and geochemical ({\\delta}13C) sea-level indicators preserved in dated cores of salt-marsh sediment. Our model is comprised of three modules: (1) A Bayesian transfer function for the calibration of foraminifera into tidal elevation, which is flexible enough to formally accommodate additional proxies (in this case bulk-sediment {\\delta}13C values); (2) A chronology developed from an existing Bchron age-depth model, and (3) An existing errors-in-variables integrated Gaussian process (EIV-IGP) model for estimating rates of sea-level change. We illustrate our approach using a case study of Common Era sea-level variability from New Jersey, U.S.A. We develop a new Bayesian transfer function (B-TF), with and without the {\\delta}13C proxy and compare our results to those from a widely...
A hierarchical Bayesian GEV model for improving local and regional flood quantile estimates
Lima, Carlos H. R.; Lall, Upmanu; Troy, Tara; Devineni, Naresh
2016-10-01
We estimate local and regional Generalized Extreme Value (GEV) distribution parameters for flood frequency analysis in a multilevel, hierarchical Bayesian framework, to explicitly model and reduce uncertainties. As prior information for the model, we assume that the GEV location and scale parameters for each site come from independent log-normal distributions, whose mean parameter scales with the drainage area. From empirical and theoretical arguments, the shape parameter for each site is shrunk towards a common mean. Non-informative prior distributions are assumed for the hyperparameters and the MCMC method is used to sample from the joint posterior distribution. The model is tested using annual maximum series from 20 streamflow gauges located in an 83,000 km2 flood prone basin in Southeast Brazil. The results show a significant reduction of uncertainty estimates of flood quantile estimates over the traditional GEV model, particularly for sites with shorter records. For return periods within the range of the data (around 50 years), the Bayesian credible intervals for the flood quantiles tend to be narrower than the classical confidence limits based on the delta method. As the return period increases beyond the range of the data, the confidence limits from the delta method become unreliable and the Bayesian credible intervals provide a way to estimate satisfactory confidence bands for the flood quantiles considering parameter uncertainties and regional information. In order to evaluate the applicability of the proposed hierarchical Bayesian model for regional flood frequency analysis, we estimate flood quantiles for three randomly chosen out-of-sample sites and compare with classical estimates using the index flood method. The posterior distributions of the scaling law coefficients are used to define the predictive distributions of the GEV location and scale parameters for the out-of-sample sites given only their drainage areas and the posterior distribution of the
Lowman, L.; Barros, A. P.
2014-12-01
Computational modeling of surface erosion processes is inherently difficult because of the four-dimensional nature of the problem and the multiple temporal and spatial scales that govern individual mechanisms. Landscapes are modified via surface and fluvial erosion and exhumation, each of which takes place over a range of time scales. Traditional field measurements of erosion/exhumation rates are scale dependent, often valid for a single point-wise location or averaging over large aerial extents and periods with intense and mild erosion. We present a method of remotely estimating erosion rates using a Bayesian hierarchical model based upon the stream power erosion law (SPEL). A Bayesian approach allows for estimating erosion rates using the deterministic relationship given by the SPEL and data on channel slopes and precipitation at the basin and sub-basin scale. The spatial scale associated with this framework is the elevation class, where each class is characterized by distinct morphologic behavior observed through different modes in the distribution of basin outlet elevations. Interestingly, the distributions of first-order outlets are similar in shape and extent to the distribution of precipitation events (i.e. individual storms) over a 14-year period between 1998-2011. We demonstrate an application of the Bayesian hierarchical modeling framework for five basins and one intermontane basin located in the central Andes between 5S and 20S. Using remotely sensed data of current annual precipitation rates from the Tropical Rainfall Measuring Mission (TRMM) and topography from a high resolution (3 arc-seconds) digital elevation map (DEM), our erosion rate estimates are consistent with decadal-scale estimates based on landslide mapping and sediment flux observations and 1-2 orders of magnitude larger than most millennial and million year timescale estimates from thermochronology and cosmogenic nuclides.
Probabilistic daily ILI syndromic surveillance with a spatio-temporal Bayesian hierarchical model.
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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.
Cahill, Niamh; Kemp, Andrew C.; Horton, Benjamin P.; Parnell, Andrew C.
2016-02-01
We present a Bayesian hierarchical model for reconstructing the continuous and dynamic evolution of relative sea-level (RSL) change with quantified uncertainty. The reconstruction is produced from biological (foraminifera) and geochemical (δ13C) sea-level indicators preserved in dated cores of salt-marsh sediment. Our model is comprised of three modules: (1) a new Bayesian transfer (B-TF) function for the calibration of biological indicators into tidal elevation, which is flexible enough to formally accommodate additional proxies; (2) an existing chronology developed using the Bchron age-depth model, and (3) an existing Errors-In-Variables integrated Gaussian process (EIV-IGP) model for estimating rates of sea-level change. Our approach is illustrated using a case study of Common Era sea-level variability from New Jersey, USA We develop a new B-TF using foraminifera, with and without the additional (δ13C) proxy and compare our results to those from a widely used weighted-averaging transfer function (WA-TF). The formal incorporation of a second proxy into the B-TF model results in smaller vertical uncertainties and improved accuracy for reconstructed RSL. The vertical uncertainty from the multi-proxy B-TF is ˜ 28 % smaller on average compared to the WA-TF. When evaluated against historic tide-gauge measurements, the multi-proxy B-TF most accurately reconstructs the RSL changes observed in the instrumental record (mean square error = 0.003 m2). The Bayesian hierarchical model provides a single, unifying framework for reconstructing and analyzing sea-level change through time. This approach is suitable for reconstructing other paleoenvironmental variables (e.g., temperature) using biological proxies.
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 Random Intercept Model Based on Three Parameter Gamma Distribution
Wirawati, Ika; Iriawan, Nur; Irhamah
2017-06-01
Hierarchical data structures are common throughout many areas of research. Beforehand, the existence of this type of data was less noticed in the analysis. The appropriate statistical analysis to handle this type of data is the hierarchical linear model (HLM). This article will focus only on random intercept model (RIM), as a subclass of HLM. This model assumes that the intercept of models in the lowest level are varied among those models, and their slopes are fixed. The differences of intercepts were suspected affected by some variables in the upper level. These intercepts, therefore, are regressed against those upper level variables as predictors. The purpose of this paper would demonstrate a proven work of the proposed two level RIM of the modeling on per capita household expenditure in Maluku Utara, which has five characteristics in the first level and three characteristics of districts/cities in the second level. The per capita household expenditure data in the first level were captured by the three parameters Gamma distribution. The model, therefore, would be more complex due to interaction of many parameters for representing the hierarchical structure and distribution pattern of the data. To simplify the estimation processes of parameters, the computational Bayesian method couple with Markov Chain Monte Carlo (MCMC) algorithm and its Gibbs Sampling are employed.
Brochu, Eric; de Freitas, Nando
2010-01-01
We present a tutorial on Bayesian optimization, a method of finding the maximum of expensive cost functions. Bayesian optimization employs the Bayesian technique of setting a prior over the objective function and combining it with evidence to get a posterior function. This permits a utility-based selection of the next observation to make on the objective function, which must take into account both exploration (sampling from areas of high uncertainty) and exploitation (sampling areas likely to offer improvement over the current best observation). We also present two detailed extensions of Bayesian optimization, with experiments---active user modelling with preferences, and hierarchical reinforcement learning---and a discussion of the pros and cons of Bayesian optimization based on our experiences.
Fast Bayesian optimal experimental design for seismic source inversion
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 L
Fast Bayesian Optimal Experimental Design for Seismic Source Inversion
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.
Towards Bayesian Inference of the Fast-Ion Distribution Function
DEFF Research Database (Denmark)
Stagner, L.; Heidbrink, W.W.; Salewski, Mirko
2012-01-01
. 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, 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...
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, ...
Dries, M; Koopmans, L V E
2016-01-01
Recent studies based on the integrated light of distant galaxies suggest that the initial mass function (IMF) might not be universal. Variations of the IMF with galaxy type and/or formation time may have important consequences for our understanding of galaxy evolution. We have developed a new stellar population synthesis (SPS) code specifically designed to reconstruct the IMF. We implement a novel approach combining regularization with hierarchical Bayesian inference. Within this approach we use a parametrized IMF prior to regulate a direct inference of the IMF. This direct inference gives more freedom to the IMF and allows the model to deviate from parametrized models when demanded by the data. We use Markov Chain Monte Carlo sampling techniques to reconstruct the best parameters for the IMF prior, the age, and the metallicity of a single stellar population. We present our code and apply our model to a number of mock single stellar populations with different ages, metallicities, and IMFs. When systematic unc...
Hierarchical Bayesian Model for Simultaneous EEG Source and Forward Model Reconstruction (SOFOMORE)
DEFF Research Database (Denmark)
Stahlhut, Carsten; Mørup, Morten; Winther, Ole;
2009-01-01
In this paper we propose an approach to handle forward model uncertainty for EEG source reconstruction. A stochastic forward model is motivated by the many uncertain contributions that form the forward propagation model including the tissue conductivity distribution, the cortical surface, and ele......In this paper we propose an approach to handle forward model uncertainty for EEG source reconstruction. A stochastic forward model is motivated by the many uncertain contributions that form the forward propagation model including the tissue conductivity distribution, the cortical surface......, and electrode positions. We first present a hierarchical Bayesian framework for EEG source localization that jointly performs source and forward model reconstruction (SOFOMORE). Secondly, we evaluate the SOFOMORE model by comparison with source reconstruction methods that use fixed forward models. Simulated...... and real EEG data demonstrate that invoking a stochastic forward model leads to improved source estimates....
A spectral-spatial-dynamic hierarchical Bayesian (SSD-HB) model for estimating soybean yield
Kazama, Yoriko; Kujirai, Toshihiro
2014-10-01
A method called a "spectral-spatial-dynamic hierarchical-Bayesian (SSD-HB) model," which can deal with many parameters (such as spectral and weather information all together) by reducing the occurrence of multicollinearity, is proposed. Experiments conducted on soybean yields in Brazil fields with a RapidEye satellite image indicate that the proposed SSD-HB model can predict soybean yield with a higher degree of accuracy than other estimation methods commonly used in remote-sensing applications. In the case of the SSD-HB model, the mean absolute error between estimated yield of the target area and actual yield is 0.28 t/ha, compared to 0.34 t/ha when conventional PLS regression was applied, showing the potential effectiveness of the proposed model.
Sánchez Gil, M. Carmen; Berihuete, Angel; Alfaro, Emilio J.; Pérez, Enrique; Sarro, Luis M.
2015-09-01
One of the fundamental goals of modern Astronomy is to estimate the physical parameters of galaxies from images in different spectral bands. We present a hierarchical Bayesian model for obtaining age maps from images in the Ha line (taken with Taurus Tunable Filter (TTF)), ultraviolet band (far UV or FUV, from GALEX) and infrared bands (24, 70 and 160 microns (μm), from Spitzer). As shown in [1], we present the burst ages for young stellar populations in the nearby and nearly face on galaxy M74. As it is shown in the previous work, the Hα to FUV flux ratio gives a good relative indicator of very recent star formation history (SFH). As a nascent star-forming region evolves, the Ha line emission declines earlier than the UV continuum, leading to a decrease in the HαFUV ratio. Through a specific star-forming galaxy model (Starburst 99, SB99), we can obtain the corresponding theoretical ratio Hα / FUV to compare with our observed flux ratios, and thus to estimate the ages of the observed regions. Due to the nature of the problem, it is necessary to propose a model of high complexity to take into account the mean uncertainties, and the interrelationship between parameters when the Hα / FUV flux ratio mentioned above is obtained. To address the complexity of the model, we propose a Bayesian hierarchical model, where a joint probability distribution is defined to determine the parameters (age, metallicity, IMF), from the observed data, in this case the observed flux ratios Hα / FUV. The joint distribution of the parameters is described through an i.i.d. (independent and identically distributed random variables), generated through MCMC (Markov Chain Monte Carlo) techniques.
Directory of Open Access Journals (Sweden)
C Elizabeth McCarron
Full Text Available BACKGROUND: Bayesian hierarchical models have been proposed to combine evidence from different types of study designs. However, when combining evidence from randomised and non-randomised controlled studies, imbalances in patient characteristics between study arms may bias the results. The objective of this study was to assess the performance of a proposed Bayesian approach to adjust for imbalances in patient level covariates when combining evidence from both types of study designs. METHODOLOGY/PRINCIPAL FINDINGS: Simulation techniques, in which the truth is known, were used to generate sets of data for randomised and non-randomised studies. Covariate imbalances between study arms were introduced in the non-randomised studies. The performance of the Bayesian hierarchical model adjusted for imbalances was assessed in terms of bias. The data were also modelled using three other Bayesian approaches for synthesising evidence from randomised and non-randomised studies. The simulations considered six scenarios aimed at assessing the sensitivity of the results to changes in the impact of the imbalances and the relative number and size of studies of each type. For all six scenarios considered, the Bayesian hierarchical model adjusted for differences within studies gave results that were unbiased and closest to the true value compared to the other models. CONCLUSIONS/SIGNIFICANCE: Where informed health care decision making requires the synthesis of evidence from randomised and non-randomised study designs, the proposed hierarchical Bayesian method adjusted for differences in patient characteristics between study arms may facilitate the optimal use of all available evidence leading to unbiased results compared to unadjusted analyses.
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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.
Dries, M.; Trager, S. C.; Koopmans, L. V. E.
2016-11-01
Recent studies based on the integrated light of distant galaxies suggest that the initial mass function (IMF) might not be universal. Variations of the IMF with galaxy type and/or formation time may have important consequences for our understanding of galaxy evolution. We have developed a new stellar population synthesis (SPS) code specifically designed to reconstruct the IMF. We implement a novel approach combining regularization with hierarchical Bayesian inference. Within this approach, we use a parametrized IMF prior to regulate a direct inference of the IMF. This direct inference gives more freedom to the IMF and allows the model to deviate from parametrized models when demanded by the data. We use Markov chain Monte Carlo sampling techniques to reconstruct the best parameters for the IMF prior, the age and the metallicity of a single stellar population. We present our code and apply our model to a number of mock single stellar populations with different ages, metallicities and IMFs. When systematic uncertainties are not significant, we are able to reconstruct the input parameters that were used to create the mock populations. Our results show that if systematic uncertainties do play a role, this may introduce a bias on the results. Therefore, it is important to objectively compare different ingredients of SPS models. Through its Bayesian framework, our model is well suited for this.
Hierarchical Bayesian methods for estimation of parameters in a longitudinal HIV dynamic system.
Huang, Yangxin; Liu, Dacheng; Wu, Hulin
2006-06-01
HIV dynamics studies have significantly contributed to the understanding of HIV infection and antiviral treatment strategies. But most studies are limited to short-term viral dynamics due to the difficulty of establishing a relationship of antiviral response with multiple treatment factors such as drug exposure and drug susceptibility during long-term treatment. In this article, a mechanism-based dynamic model is proposed for characterizing long-term viral dynamics with antiretroviral therapy, described by a set of nonlinear differential equations without closed-form solutions. In this model we directly incorporate drug concentration, adherence, and drug susceptibility into a function of treatment efficacy, defined as an inhibition rate of virus replication. We investigate a Bayesian approach under the framework of hierarchical Bayesian (mixed-effects) models for estimating unknown dynamic parameters. In particular, interest focuses on estimating individual dynamic parameters. The proposed methods not only help to alleviate the difficulty in parameter identifiability, but also flexibly deal with sparse and unbalanced longitudinal data from individual subjects. For illustration purposes, we present one simulation example to implement the proposed approach and apply the methodology to a data set from an AIDS clinical trial. The basic concept of the longitudinal HIV dynamic systems and the proposed methodologies are generally applicable to any other biomedical dynamic systems.
Busschaert, P; Geeraerd, A H; Uyttendaele, M; Van Impe, J F
2011-06-01
Microbiological contamination data often is censored because of the presence of non-detects or because measurement outcomes are known only to be smaller than, greater than, or between certain boundary values imposed by the laboratory procedures. Therefore, it is not straightforward to fit distributions that summarize contamination data for use in quantitative microbiological risk assessment, especially when variability and uncertainty are to be characterized separately. In this paper, distributions are fit using Bayesian analysis, and results are compared to results obtained with a methodology based on maximum likelihood estimation and the non-parametric bootstrap method. The Bayesian model is also extended hierarchically to estimate the effects of the individual elements of a covariate such as, for example, on a national level, the food processing company where the analyzed food samples were processed, or, on an international level, the geographical origin of contamination data. Including this extra information allows a risk assessor to differentiate between several scenario's and increase the specificity of the estimate of risk of illness, or compare different scenario's to each other. Furthermore, inference is made on the predictive importance of several different covariates while taking into account uncertainty, allowing to indicate which covariates are influential factors determining contamination.
Directory of Open Access Journals (Sweden)
J. P. Werner
2014-12-01
Full Text Available Reconstructions of late-Holocene climate rely heavily upon proxies that are assumed to be accurately dated by layer counting, such as measurement on tree rings, ice cores, and varved lake sediments. Considerable advances may be achievable if time uncertain proxies could 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 to accounting for time uncertainty are generally limited to repeating the reconstruction using each 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, while 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 climate reconstruction, 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 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 hierarchical clustering for studying cancer gene expression data with unknown statistics.
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Korsuk Sirinukunwattana
Full Text Available Clustering analysis is an important tool in studying gene expression data. The Bayesian hierarchical clustering (BHC algorithm can automatically infer the number of clusters and uses Bayesian model selection to improve clustering quality. In this paper, we present an extension of the BHC algorithm. Our Gaussian BHC (GBHC algorithm represents data as a mixture of Gaussian distributions. It uses normal-gamma distribution as a conjugate prior on the mean and precision of each of the Gaussian components. We tested GBHC over 11 cancer and 3 synthetic datasets. The results on cancer datasets show that in sample clustering, GBHC on average produces a clustering partition that is more concordant with the ground truth than those obtained from other commonly used algorithms. Furthermore, GBHC frequently infers the number of clusters that is often close to the ground truth. In gene clustering, GBHC also produces a clustering partition that is more biologically plausible than several other state-of-the-art methods. This suggests GBHC as an alternative tool for studying gene expression data. The implementation of GBHC is available at https://sites.google.com/site/gaussianbhc/
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.
Improving water quality assessments through a hierarchical Bayesian analysis of variability.
Gronewold, Andrew D; Borsuk, Mark E
2010-10-15
Water quality measurement error and variability, while well-documented in laboratory-scale studies, is rarely acknowledged or explicitly resolved in most model-based water body assessments, including those conducted in compliance with the United States Environmental Protection Agency (USEPA) Total Maximum Daily Load (TMDL) program. Consequently, proposed pollutant loading reductions in TMDLs and similar water quality management programs may be biased, resulting in either slower-than-expected rates of water quality restoration and designated use reinstatement or, in some cases, overly conservative management decisions. To address this problem, we present a hierarchical Bayesian approach for relating actual in situ or model-predicted pollutant concentrations to multiple sampling and analysis procedures, each with distinct sources of variability. We apply this method to recently approved TMDLs to investigate whether appropriate accounting for measurement error and variability will lead to different management decisions. We find that required pollutant loading reductions may in fact vary depending not only on how measurement variability is addressed but also on which water quality analysis procedure is used to assess standard compliance. As a general strategy, our Bayesian approach to quantifying variability may represent an alternative to the common practice of addressing all forms of uncertainty through an arbitrary margin of safety (MOS).
A Bayesian hierarchical nonhomogeneous hidden Markov model for multisite streamflow reconstructions
Bracken, C.; Rajagopalan, B.; Woodhouse, C.
2016-10-01
In many complex water supply systems, the next generation of water resources planning models will require simultaneous probabilistic streamflow inputs at multiple locations on an interconnected network. To make use of the valuable multicentury records provided by tree-ring data, reconstruction models must be able to produce appropriate multisite inputs. Existing streamflow reconstruction models typically focus on one site at a time, not addressing intersite dependencies and potentially misrepresenting uncertainty. To this end, we develop a model for multisite streamflow reconstruction with the ability to capture intersite correlations. The proposed model is a hierarchical Bayesian nonhomogeneous hidden Markov model (NHMM). A NHMM is fit to contemporary streamflow at each location using lognormal component distributions. Leading principal components of tree rings are used as covariates to model nonstationary transition probabilities and the parameters of the lognormal component distributions. Spatial dependence between sites is captured with a Gaussian elliptical copula. Parameters of the model are estimated in a fully Bayesian framework, in that marginal posterior distributions of all the parameters are obtained. The model is applied to reconstruct flows at 20 sites in the Upper Colorado River Basin (UCRB) from 1473 to 1906. Many previous reconstructions are available for this basin, making it ideal for testing this new method. The results show some improvements over regression-based methods in terms of validation statistics. Key advantages of the Bayesian NHMM over traditional approaches are a dynamic representation of uncertainty and the ability to make long multisite simulations that capture at-site statistics and spatial correlations between sites.
Mustac, M.; Kim, S.; Tkalcic, H.; Rhie, J.; Chen, Y.; Ford, S. R.; Sebastian, N.
2015-12-01
Conventional approaches to inverse problems suffer from non-linearity and non-uniqueness in estimations of seismic structures and source properties. Estimated results and associated uncertainties are often biased by applied regularizations and additional constraints, which are commonly introduced to solve such problems. Bayesian methods, however, provide statistically meaningful estimations of models and their uncertainties constrained by data information. In addition, hierarchical and trans-dimensional (trans-D) techniques are inherently implemented in the Bayesian framework to account for involved error statistics and model parameterizations, and, in turn, allow more rigorous estimations of the same. Here, we apply Bayesian methods throughout the entire inference process to estimate seismic structures and source properties in Northeast Asia including east China, the Korean peninsula, and the Japanese islands. Ambient noise analysis is first performed to obtain a base three-dimensional (3-D) heterogeneity model using continuous broadband waveforms from more than 300 stations. As for the tomography of surface wave group and phase velocities in the 5-70 s band, we adopt a hierarchical and trans-D Bayesian inversion method using Voronoi partition. The 3-D heterogeneity model is further improved by joint inversions of teleseismic receiver functions and dispersion data using a newly developed high-efficiency Bayesian technique. The obtained model is subsequently used to prepare 3-D structural Green's functions for the source characterization. A hierarchical Bayesian method for point source inversion using regional complete waveform data is applied to selected events from the region. The seismic structure and source characteristics with rigorously estimated uncertainties from the novel Bayesian methods provide enhanced monitoring and discrimination of seismic events in northeast Asia.
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.
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.
Application of hierarchical Bayesian unmixing models in river sediment source apportionment
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
Extreme Rainfall Analysis using Bayesian Hierarchical Modeling in the Willamette River Basin, Oregon
Love, C. A.; Skahill, B. E.; AghaKouchak, A.; Karlovits, G. S.; England, J. F.; Duren, A. M.
2016-12-01
We present preliminary results of ongoing research directed at evaluating the worth of including various covariate data to support extreme rainfall analysis in the Willamette River basin using Bayesian hierarchical modeling (BHM). We also compare the BHM derived extreme rainfall estimates with their respective counterparts obtained from a traditional regional frequency analysis (RFA) using the same set of rain gage extreme rainfall data. The U.S. Army Corps of Engineers (USACE) Portland District operates thirteen dams in 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. Extreme rainfall estimates are required to support risk-informed hydrologic analyses for these projects as part of the USACE Dam Safety Program. We analyze daily annual rainfall 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 rainfall by return level. Our intent is to profile for the USACE an alternate methodology to a RFA which was developed in 2008 due to the lack of an official NOAA Atlas 14 update for the state of Oregon. Unlike RFA, the advantage of a BHM-based analysis of hydrometeorological extremes is its ability to account for non-stationarity while providing robust estimates of uncertainty. BHM also allows for the inclusion of geographical and climatological factors which we show for the WRB influence regional rainfall extremes. Moreover, the Bayesian framework permits one to combine additional data types into the analysis; for example, information derived via elicitation and causal information expansion data, both being additional opportunities for future related research.
Wynton, Sarah K A; Anglim, Jeromy
2017-04-10
While researchers have often sought to understand the learning curve in terms of multiple component processes, few studies have measured and mathematically modeled these processes on a complex task. In particular, there remains a need to reconcile how abrupt changes in strategy use can co-occur with gradual changes in task completion time. Thus, the current study aimed to assess the degree to which strategy change was abrupt or gradual, and whether strategy aggregation could partially explain gradual performance change. It also aimed to show how Bayesian methods could be used to model the effect of practice on strategy use. To achieve these aims, 162 participants completed 15 blocks of practice on a complex computer-based task-the Wynton-Anglim booking (WAB) task. The task allowed for multiple component strategies (i.e., memory retrieval, information reduction, and insight) that could also be aggregated to a global measure of strategy use. Bayesian hierarchical models were used to compare abrupt and gradual functions of component and aggregate strategy use. Task completion time was well-modeled by a power function, and global strategy use explained substantial variance in performance. Change in component strategy use tended to be abrupt, whereas change in global strategy use was gradual and well-modeled by a power function. Thus, differential timing of component strategy shifts leads to gradual changes in overall strategy efficiency, and this provides one reason for why smooth learning curves can co-occur with abrupt changes in strategy use. (PsycINFO Database Record (c) 2017 APA, all rights reserved).
Jin, Ick Hoon; Yuan, Ying; Bandyopadhyay, Dipankar
2016-01-01
Research in dental caries generates data with two levels of hierarchy: that of a tooth overall and that of the different surfaces of the tooth. The outcomes often exhibit spatial referencing among neighboring teeth and surfaces, i.e., the disease status of a tooth or surface might be influenced by the status of a set of proximal teeth/surfaces. Assessments of dental caries (tooth decay) at the tooth level yield binary outcomes indicating the presence/absence of teeth, and trinary outcomes at the surface level indicating healthy, decayed, or filled surfaces. The presence of these mixed discrete responses complicates the data analysis under a unified framework. To mitigate complications, we develop a Bayesian two-level hierarchical model under suitable (spatial) Markov random field assumptions that accommodates the natural hierarchy within the mixed responses. At the first level, we utilize an autologistic model to accommodate the spatial dependence for the tooth-level binary outcomes. For the second level and conditioned on a tooth being non-missing, we utilize a Potts model to accommodate the spatial referencing for the surface-level trinary outcomes. The regression models at both levels were controlled for plausible covariates (risk factors) of caries, and remain connected through shared parameters. To tackle the computational challenges in our Bayesian estimation scheme caused due to the doubly-intractable normalizing constant, we employ a double Metropolis-Hastings sampler. We compare and contrast our model performances to the standard non-spatial (naive) model using a small simulation study, and illustrate via an application to a clinical dataset on dental caries. PMID:27807470
Full Bayesian hierarchical light curve modeling of core-collapse supernova populations
Sanders, Nathan; Betancourt, Michael; Soderberg, Alicia Margarita
2016-06-01
While wide field surveys have yielded remarkable quantities of photometry of transient objects, including supernovae, light curves reconstructed from this data suffer from several characteristic problems. Because most transients are discovered near the detection limit, signal to noise is generally poor; because coverage is limited to the observing season, light curves are often incomplete; and because temporal sampling can be uneven across filters, these problems can be exacerbated at any one wavelength. While the prevailing approach of modeling individual light curves independently is successful at recovering inferences for the objects with the highest quality observations, it typically neglects a substantial portion of the data and can introduce systematic biases. Joint modeling of the light curves of transient populations enables direct inference on population-level characteristics as well as superior measurements for individual objects. We present a new hierarchical Bayesian model for supernova light curves, where information inferred from observations of every individual light curve in a sample is partially pooled across objects to constrain population-level hyperparameters. Using an efficient Hamiltonian Monte Carlo sampling technique, the model posterior can be explored to enable marginalization over weakly-identified hyperparameters through full Bayesian inference. We demonstrate our technique on the Pan-STARRS1 (PS1) Type IIP supernova light curve sample published by Sanders et al. (2015), consisting of nearly 20,000 individual photometric observations of more than 70 supernovae in five photometric filters. We discuss the Stan probabilistic programming language used to implement the model, computational challenges, and prospects for future work including generalization to multiple supernova types. We also discuss scientific results from the PS1 dataset including a new relation between the peak magnitude and decline rate of SNe IIP, a new perspective on the
A Tool for Fast Development of Modular and Hierarchic Neural Network-based Systems
Directory of Open Access Journals (Sweden)
Francisco Reinaldo
2006-08-01
Full Text Available This paper presents PyramidNet tool as a fast and easy way to develop Modular and Hierarchic Neural Network-based Systems. This tool facilitates the fast emergence of autonomous behaviors in agents because it uses a hierarchic and modular control methodology of heterogeneous learning modules: the pyramid. Using the graphical resources of PyramidNet the user is able to specify a behavior system even having little understanding of artificial neural networks. Experimental tests have shown that a very significant speedup is attained in the development of modular and hierarchic neural network-based systems by using this tool.
Directory of Open Access Journals (Sweden)
Meyer Christopher P
2008-11-01
Full Text Available Abstract Background Marine allopatric speciation is an enigma because pelagic larval dispersal can potentially connect disjunct populations thereby preventing reproductive and morphological divergence. Here we present a new hierarchical approximate Bayesian computation model (HABC that tests two hypotheses of marine allopatric speciation: 1. "soft vicariance", where a speciation involves fragmentation of a large widespread ancestral species range that was previously connected by long distance gene flow; and 2. peripatric colonization, where speciations in peripheral archipelagos emerge from sweepstakes colonizations from central source regions. The HABC approach analyzes all the phylogeographic datasets at once in order to make across taxon-pair inferences about biogeographic processes while explicitly allowing for uncertainty in the demographic differences within each taxon-pair. Our method uses comparative phylogeographic data that consists of single locus mtDNA sequences from multiple co-distributed taxa containing pairs of central and peripheral populations. We use the method on two comparative phylogeographic data sets consisting of cowrie gastropod endemics co-distributed in the Hawaiian (11 taxon-pairs and Marquesan archipelagos (7 taxon-pairs. Results Given the Marquesan data, we find strong evidence of simultaneous colonization across all seven cowrie gastropod endemics co-distributed in the Marquesas. In contrast, the lower sample sizes in the Hawaiian data lead to greater uncertainty associated with the Hawaiian estimates. Although, the hyper-parameter estimates point to soft vicariance in a subset of the 11 Hawaiian taxon-pairs, the hyper-prior and hyper-posterior are too similar to make a definitive conclusion. Both results are not inconsistent with what is known about the geologic history of the archipelagos. Simulations verify that our method can successfully distinguish these two histories across a wide range of conditions given
A method of spherical harmonic analysis in the geosciences via hierarchical Bayesian inference
Muir, J. B.; Tkalčić, H.
2015-11-01
The problem of decomposing irregular data on the sphere into a set of spherical harmonics is common in many fields of geosciences where it is necessary to build a quantitative understanding of a globally varying field. For example, in global seismology, a compressional or shear wave speed that emerges from tomographic images is used to interpret current state and composition of the mantle, and in geomagnetism, secular variation of magnetic field intensity measured at the surface is studied to better understand the changes in the Earth's core. Optimization methods are widely used for spherical harmonic analysis of irregular data, but they typically do not treat the dependence of the uncertainty estimates on the imposed regularization. This can cause significant difficulties in interpretation, especially when the best-fit model requires more variables as a result of underestimating data noise. Here, with the above limitations in mind, the problem of spherical harmonic expansion of irregular data is treated within the hierarchical Bayesian framework. The hierarchical approach significantly simplifies the problem by removing the need for regularization terms and user-supplied noise estimates. The use of the corrected Akaike Information Criterion for picking the optimal maximum degree of spherical harmonic expansion and the resulting spherical harmonic analyses are first illustrated on a noisy synthetic data set. Subsequently, the method is applied to two global data sets sensitive to the Earth's inner core and lowermost mantle, consisting of PKPab-df and PcP-P differential traveltime residuals relative to a spherically symmetric Earth model. The posterior probability distributions for each spherical harmonic coefficient are calculated via Markov Chain Monte Carlo sampling; the uncertainty obtained for the coefficients thus reflects the noise present in the real data and the imperfections in the spherical harmonic expansion.
Approximate Bayesian Computation by Subset Simulation using hierarchical state-space models
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
DEFF Research Database (Denmark)
Kristensen, Anders Ringgaard; Søllested, Thomas Algot
2004-01-01
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...... estimated at herd level. It is argued that the multi-level formulation and the standard software comprise a flexible tool and a shortcut to working prototypes...
2013-01-01
This paper proposes a hierarchical Bayesian framework for modeling the life cycle of marine exploited fish with a spatial perspective. The application was developed for a nursery-dependent fish species, the common sole (Solea solea), on the Eastern Channel population (Western Europe). The approach combined processes of different natures and various sources of observations within an integrated framework for life-cycle modeling: (1) outputs of an individual-based model for larval drift and surv...
Energy Technology Data Exchange (ETDEWEB)
Kelly, Brandon C.; Goodman, Alyssa A. [Harvard-Smithsonian Center for Astrophysics, 60 Garden Street, Cambridge, MA 02138 (United States); Shetty, Rahul [Zentrum fuer Astronomie der Universitaet Heidelberg, Institut fuer Theoretische Astrophysik, Albert-Ueberle-Str. 2, 69120 Heidelberg (Germany); Stutz, Amelia M.; Launhardt, Ralf [Max Planck Institut fuer Astronomie, Koenigstuhl 17, 69117 Heidelberg (Germany); Kauffmann, Jens [NASA JPL, 4800 Oak Grove Drive, Pasadena, CA 91109 (United States)
2012-06-10
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 {beta}. The traditional non-hierarchical approaches, typically based on {chi}{sup 2} minimization, are severely limited by this degeneracy, as it produces an artificial anti-correlation between T and {beta} 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 {chi}{sup 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 {beta} are weakly positively correlated-in contradiction with the {chi}{sup 2} fits, which indicate a T-{beta} anti-correlation from the same data set. Additionally, in comparison to the {chi}{sup 2} fits the Bayesian SED parameter estimates exhibit a reduced range in values.
Hu, Yi; Ward, Michael P; Xia, Congcong; Li, Rui; Sun, Liqian; Lynn, Henry; Gao, Fenghua; Wang, Qizhi; Zhang, Shiqing; Xiong, Chenglong; Zhang, Zhijie; Jiang, Qingwu
2016-04-07
Schistosomiasis remains a major public health problem and causes substantial economic impact in east China, particularly along the Yangtze River Basin. Disease forecasting and surveillance can assist in the development and implementation of more effective intervention measures to control disease. In this study, we applied a Bayesian hierarchical spatio-temporal model to describe trends in schistosomiasis risk in Anhui Province, China, using annual parasitological and environmental data for the period 1997-2010. A computationally efficient approach-Integrated Nested Laplace Approximation-was used for model inference. A zero-inflated, negative binomial model best described the spatio-temporal dynamics of schistosomiasis risk. It predicted that the disease risk would generally be low and stable except for some specific, local areas during the period 2011-2014. High-risk counties were identified in the forecasting maps: three in which the risk remained high, and two in which risk would become high. The results indicated that schistosomiasis risk has been reduced to consistently low levels throughout much of this region of China; however, some counties were identified in which progress in schistosomiasis control was less than satisfactory. Whilst maintaining overall control, specific interventions in the future should focus on these refractive counties as part of a strategy to eliminate schistosomiasis from this region.
Gil, M Carmen Sánchez; Alfaro, Emilio J; Pérez, Enrique; Sarro, Luis M
2015-01-01
One of the fundamental goals of modern Astronomy is to estimate the physical parameters of galaxies from images in different spectral bands. We present a hierarchical Bayesian model for obtaining age maps from images in the \\Ha\\ line (taken with Taurus Tunable Filter (TTF)), ultraviolet band (far UV or FUV, from GALEX) and infrared bands (24, 70 and 160 microns ($\\mu$m), from Spitzer). As shown in S\\'anchez-Gil et al. (2011), we present the burst ages for young stellar populations in the nearby and nearly face on galaxy M74. As it is shown in the previous work, the \\Ha\\ to FUV flux ratio gives a good relative indicator of very recent star formation history (SFH). As a nascent star-forming region evolves, the \\Ha\\ line emission declines earlier than the UV continuum, leading to a decrease in the \\Ha\\/FUV ratio. Through a specific star-forming galaxy model (Starburst 99, SB99), we can obtain the corresponding theoretical ratio \\Ha\\ / FUV to compare with our observed flux ratios, and thus to estimate the ages of...
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.
Snyder, Carolyn W.
2016-09-01
Statistical challenges often preclude comparisons among different sea surface temperature (SST) reconstructions over the past million years. Inadequate consideration of uncertainty can result in misinterpretation, overconfidence, and biased conclusions. Here I apply Bayesian hierarchical regressions to analyze local SST responsiveness to climate changes for 54 SST reconstructions from across the globe over the past million years. I develop methods to account for multiple sources of uncertainty, including the quantification of uncertainty introduced from absolute dating into interrecord comparisons. The estimates of local SST responsiveness explain 64% (62% to 77%, 95% interval) of the total variation within each SST reconstruction with a single number. There is remarkable agreement between SST proxy methods, with the exception of Mg/Ca proxy methods estimating muted responses at high latitudes. The Indian Ocean exhibits a muted response in comparison to other oceans. I find a stable estimate of the proposed "universal curve" of change in local SST responsiveness to climate changes as a function of sin2(latitude) over the past 400,000 years: SST change at 45°N/S is larger than the average tropical response by a factor of 1.9 (1.5 to 2.6, 95% interval) and explains 50% (35% to 58%, 95% interval) of the total variation between each SST reconstruction. These uncertainty and statistical methods are well suited for application across paleoclimate and environmental data series intercomparisons.
Merging information from multi-model flood projections in a hierarchical Bayesian framework
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.
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
Mapping brucellosis increases relative to elk density using hierarchical Bayesian models
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 Bayesian hierarchical model with novel prior specifications for estimating HIV testing rates
An, Qian; Kang, Jian; Song, Ruiguang; Hall, H. Irene
2016-01-01
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. PMID:26567891
Alsing, Justin; Jaffe, Andrew H
2016-01-01
We apply two Bayesian hierarchical inference schemes to infer shear power spectra, shear maps and cosmological parameters from the CFHTLenS weak lensing survey - the first application of this method to data. In the first approach, we sample the joint posterior distribution of the shear maps and power spectra by Gibbs sampling, with minimal model assumptions. In the second approach, we sample the joint posterior of the shear maps and cosmological parameters, providing a new, accurate and principled approach to cosmological parameter inference from cosmic shear data. As a first demonstration on data we perform a 2-bin tomographic analysis to constrain cosmological parameters and investigate the possibility of photometric redshift bias in the CFHTLenS data. Under the baseline $\\Lambda$CDM model we constrain $S_8 = \\sigma_8(\\Omega_\\mathrm{m}/0.3)^{0.5} = 0.67 ^{\\scriptscriptstyle+ 0.03 }_{\\scriptscriptstyle- 0.03 }$ $(68\\%)$, consistent with previous CFHTLenS analysis but in tension with Planck. Adding neutrino m...
Mandel, Kaisey S; Kirshner, Robert P
2014-01-01
We investigate the correlations between the peak intrinsic colors of Type Ia supernovae (SN Ia) and their expansion velocities at maximum light, measured from the Si II 6355 A spectral feature. We construct a new hierarchical Bayesian regression model and Gibbs sampler to estimate the dependence of the intrinsic colors of a SN Ia on its ejecta velocity, while accounting for the random effects of intrinsic scatter, measurement error, and reddening by host galaxy dust. The method is applied to the apparent color data from BVRI light curves and Si II velocity data for 79 nearby SN Ia. Comparison of the apparent color distributions of high velocity (HV) and normal velocity (NV) supernovae reveals significant discrepancies in 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. Under a linear m...
Bello, Nora M; Steibel, Juan P; Tempelman, Robert J
2010-06-01
Bivariate mixed effects models are often used to jointly infer upon covariance matrices for both random effects (u) and residuals (e) between two different phenotypes in order to investigate the architecture of their relationship. However, these (co)variances themselves may additionally depend upon covariates as well as additional sets of exchangeable random effects that facilitate borrowing of strength across a large number of clusters. We propose a hierarchical Bayesian extension of the classical bivariate mixed effects model by embedding additional levels of mixed effects modeling of reparameterizations of u-level and e-level (co)variances between two traits. These parameters are based upon a recently popularized square-root-free Cholesky decomposition and are readily interpretable, each conveniently facilitating a generalized linear model characterization. Using Markov Chain Monte Carlo methods, we validate our model based on a simulation study and apply it to a joint analysis of milk yield and calving interval phenotypes in Michigan dairy cows. This analysis indicates that the e-level relationship between the two traits is highly heterogeneous across herds and depends upon systematic herd management factors.
Xu, Lei; Johnson, Timothy D.; Nichols, Thomas E.; Nee, Derek E.
2010-01-01
Summary The aim of this work is to develop a spatial model for multi-subject fMRI data. There has been extensive work on univariate modeling of each voxel for single and multi-subject data, some work on spatial modeling of single-subject data, and some recent work on spatial modeling of multi-subject data. However, there has been no work on spatial models that explicitly account for inter-subject variability in activation locations. In this work, we use the idea of activation centers and model the inter-subject variability in activation locations directly. Our model is specified in a Bayesian hierarchical frame work which allows us to draw inferences at all levels: the population level, the individual level and the voxel level. We use Gaussian mixtures for the probability that an individual has a particular activation. This helps answer an important question which is not addressed by any of the previous methods: What proportion of subjects had a significant activity in a given region. Our approach incorporates the unknown number of mixture components into the model as a parameter whose posterior distribution is estimated by reversible jump Markov Chain Monte Carlo. We demonstrate our method with a fMRI study of resolving proactive interference and show dramatically better precision of localization with our method relative to the standard mass-univariate method. Although we are motivated by fMRI data, this model could easily be modified to handle other types of imaging data. PMID:19210732
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 Bayesian optimal experimental design and its applications
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.
Wasson, Anton P; Chiu, Grace S; Zwart, Alexander B; Binns, Timothy R
2017-01-01
Ensuring future food security for a growing population while climate change and urban sprawl put pressure on agricultural land will require sustainable intensification of current farming practices. For the crop breeder this means producing higher crop yields with less resources due to greater environmental stresses. While easy gains in crop yield have been made mostly "above ground," little progress has been made "below ground"; and yet it is these root system traits that can improve productivity and resistance to drought stress. Wheat pre-breeders use soil coring and core-break counts to phenotype root architecture traits, with data collected on rooting density for hundreds of genotypes in small increments of depth. The measured densities are both large datasets and highly variable even within the same genotype, hence, any rigorous, comprehensive statistical analysis of such complex field data would be technically challenging. Traditionally, most attributes of the field data are therefore discarded in favor of simple numerical summary descriptors which retain much of the high variability exhibited by the raw data. This poses practical challenges: although plant scientists have established that root traits do drive resource capture in crops, traits that are more randomly (rather than genetically) determined are difficult to breed for. In this paper we develop a hierarchical nonlinear mixed modeling approach that utilizes the complete field data for wheat genotypes to fit, under the Bayesian paradigm, an "idealized" relative intensity function for the root distribution over depth. Our approach was used to determine heritability: how much of the variation between field samples was purely random vs. being mechanistically driven by the plant genetics? Based on the genotypic intensity functions, the overall heritability estimate was 0.62 (95% Bayesian confidence interval was 0.52 to 0.71). Despite root count profiles that were statistically very noisy, our approach led
Jomelli, Vincent; Pavlova, Irina; Eckert, Nicolas; Grancher, Delphine; Brunstein, Daniel
2015-12-01
How can debris flow occurrences be modelled at regional scale and take both environmental and climatic conditions into account? And, of the two, which has the most influence on debris flow activity? In this paper, we try to answer these questions with an innovative Bayesian hierarchical probabilistic model that simultaneously accounts for how debris flows respond to environmental and climatic variables. In it, full decomposition of space and time effects in occurrence probabilities is assumed, revealing an environmental and a climatic trend shared by all years/catchments, respectively, clearly distinguished from residual "random" effects. The resulting regional and annual occurrence probabilities evaluated as functions of the covariates make it possible to weight the respective contribution of the different terms and, more generally, to check the model performances at different spatio-temporal scales. After suitable validation, the model can be used to make predictions at undocumented sites and could be used in further studies for predictions under future climate conditions. Also, the Bayesian paradigm easily copes with missing data, thus making it possible to account for events that may have been missed during surveys. As a case study, we extract 124 debris flow event triggered between 1970 and 2005 in 27 catchments located in the French Alps from the French national natural hazard survey and model their variability of occurrence considering environmental and climatic predictors at the same time. We document the environmental characteristics of each debris flow catchment (morphometry, lithology, land cover, and the presence of permafrost). We also compute 15 climate variables including mean temperature and precipitation between May and October and the number of rainy days with daily cumulative rainfall greater than 10/15/20/25/30/40 mm day- 1. Application of our model shows that the combination of environmental and climatic predictors explained 77% of the overall
Huang, Susie Shih-Yin; Strathe, Anders Bjerring; Hung, Silas S O; Boston, Raymond C; Fadel, James G
2012-03-01
The biological function of selenium (Se) is determined by its form and concentration. Selenium is an essential micronutrient for all vertebrates, however, at environmental levels, it is a potent toxin. In the San Francisco Bay-Delta, Se pollution threatens top predatory fish, including white sturgeon. A multi-compartmental Bayesian hierarchical model was developed to estimate the fractional rates of absorption, disposition, and elimination of selenocompounds, in white sturgeon, from tissue measurements obtained in a previous study (Huang et al., 2012). This modeling methodology allows for a population based approach to estimate kinetic physiological parameters in white sturgeon. Briefly, thirty juvenile white sturgeon (five per treatment) were orally intubated with a control (no selenium) or a single dose of Se (500 μg Se/kg body weight) in the form of one inorganic (Selenite) or four organic selenocompounds: selenocystine (SeCys), l-selenomethionine (SeMet), Se-methylseleno-l-cysteine (MSeCys), or selenoyeast (SeYeast). Blood and urine Se were measured at intervals throughout the 48h post intubation period and eight tissues were sampled at 48 h. The model is composed of four state variables, conceptually the gut (Q1), blood (Q2), and tissue (Q3); and urine (Q0), all in units of μg Se. Six kinetics parameters were estimated: the fractional rates [1/h] of absorption, tissue disposition, tissue release, and urinary elimination (k12, k23, k32, and k20), the proportion of the absorbed dose eliminated through the urine (f20), and the distribution blood volume (V; percent body weight, BW). The parameter k12 was higher in sturgeon given the organic Se forms, in the descending order of MSeCys > SeMet > SeCys > Selenite > SeYeast. The parameters k23 and k32 followed similar patterns, and f20 was lowest in fish given MSeCys. Selenium form did not affect k20 or V. The parameter differences observed can be attributed to the different mechanisms of transmucosal transport
Wasson, Anton P.; Chiu, Grace S.; Zwart, Alexander B.; Binns, Timothy R.
2017-01-01
Ensuring future food security for a growing population while climate change and urban sprawl put pressure on agricultural land will require sustainable intensification of current farming practices. For the crop breeder this means producing higher crop yields with less resources due to greater environmental stresses. While easy gains in crop yield have been made mostly “above ground,” little progress has been made “below ground”; and yet it is these root system traits that can improve productivity and resistance to drought stress. Wheat pre-breeders use soil coring and core-break counts to phenotype root architecture traits, with data collected on rooting density for hundreds of genotypes in small increments of depth. The measured densities are both large datasets and highly variable even within the same genotype, hence, any rigorous, comprehensive statistical analysis of such complex field data would be technically challenging. Traditionally, most attributes of the field data are therefore discarded in favor of simple numerical summary descriptors which retain much of the high variability exhibited by the raw data. This poses practical challenges: although plant scientists have established that root traits do drive resource capture in crops, traits that are more randomly (rather than genetically) determined are difficult to breed for. In this paper we develop a hierarchical nonlinear mixed modeling approach that utilizes the complete field data for wheat genotypes to fit, under the Bayesian paradigm, an “idealized” relative intensity function for the root distribution over depth. Our approach was used to determine heritability: how much of the variation between field samples was purely random vs. being mechanistically driven by the plant genetics? Based on the genotypic intensity functions, the overall heritability estimate was 0.62 (95% Bayesian confidence interval was 0.52 to 0.71). Despite root count profiles that were statistically very noisy, our
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
Indian Academy of Sciences (India)
Wayan Suparta; Gusrizal
2014-08-01
We implement a hierarchical Bayesian spatiotemporal (HBST) model to forecast the daily trapped particle flux distribution over the South Atlantic Anomaly (SAA) region. The National Oceanic and Atmospheric Administration (NOAA)-15 data from 1–30 March 2008 with particle energies as < 30 keV (mep0e1) and < 300 keV (mep0e3) for electrons and 80–240 keV (mep0p2) and < 6900 keV (mep0p6) for protons were used as the model input to forecast the flux values on 31 March 2008. Data were transformed into logarithmic values and gridded in a 5° × 5° longitude and latitude size to fulfill the modeling precondition. A Monte Carlo Markov chain (MCMC) was then performed to solve the HBST Gaussian Process (GP) model by using the Gibbs sampling method. The result for this model was interpolated by a Kriging technique to achieve the whole distribution figure over the SAA region. Statistical results of the root mean square error (RMSE), mean absolute percentage error (MAPE), and bias (BIAS) showed a good indicator of the HBST method. The statistical validation also indicated the high variability of particle flux values in the SAA core area. The visual validation showed a powerful combination of HBST-GP model with Kriging interpolation technique. The Kriging also produced a good quality of the distribution map of particle flux over the SAA region as indicated by its small variance value. This suggests that the model can be applied in the development of a Low Earth Orbit (LEO)-Equatorial satellite for monitoring trapped particle radiation hazard.
Directory of Open Access Journals (Sweden)
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.
Alsing, Justin; Heavens, Alan; Jaffe, Andrew H.
2017-04-01
We apply two Bayesian hierarchical inference schemes to infer shear power spectra, shear maps and cosmological parameters from the Canada-France-Hawaii Telescope (CFHTLenS) weak lensing survey - the first application of this method to data. In the first approach, we sample the joint posterior distribution of the shear maps and power spectra by Gibbs sampling, with minimal model assumptions. In the second approach, we sample the joint posterior of the shear maps and cosmological parameters, providing a new, accurate and principled approach to cosmological parameter inference from cosmic shear data. As a first demonstration on data, we perform a two-bin tomographic analysis to constrain cosmological parameters and investigate the possibility of photometric redshift bias in the CFHTLenS data. Under the baseline ΛCDM (Λ cold dark matter) model, we constrain S_8 = σ _8(Ω _m/0.3)^{0.5} = 0.67+0.03-0.03 (68 per cent), consistent with previous CFHTLenS analyses but in tension with Planck. Adding neutrino mass as a free parameter, we are able to constrain ∑mν linear redshift-dependent photo-z bias Δz = p2(z - p1), we find p_1=-0.25+0.53-0.60 and p_2 = -0.15+0.17-0.15, and tension with Planck is only alleviated under very conservative prior assumptions. Neither the non-minimal neutrino mass nor photo-z bias models are significantly preferred by the CFHTLenS (two-bin tomography) data.
Energy Technology Data Exchange (ETDEWEB)
Mandel, Kaisey S.; Kirshner, Robert P. [Harvard-Smithsonian Center for Astrophysics, 60 Garden Street, Cambridge, MA 02138 (United States); Foley, Ryan J., E-mail: kmandel@cfa.harvard.edu [Astronomy Department, University of Illinois at Urbana-Champaign, 1002 West Green Street, Urbana, IL 61801 (United States)
2014-12-20
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{sup 3} km s{sup –1}){sup –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{sub 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.
Grzegorczyk, Marco; Husmeier, Dirk
2013-01-01
To relax the homogeneity assumption of classical dynamic Bayesian networks (DBNs), various recent studies have combined DBNs with multiple changepoint processes. The underlying assumption is that the parameters associated with time series segments delimited by multiple changepoints are a priori inde
Hierarchical data visualization using a fast rectangle-packing algorithm.
Itoh, Takayuki; Yamaguchi, Yumi; Ikehata, Yuko; Kajinaga, Yasumasa
2004-01-01
This paper presents a technique for the representation of large-scale hierarchical data which aims to provide good overviews of complete structures and the content of the data in one display space. The technique represents the data by using nested rectangles. It first packs icons or thumbnails of the lowest-level data and then generates rectangular borders that enclose the packed data. It repeats the process of generating rectangles that enclose the lower-level rectangles until the highest-level rectangles are packed. This paper presents two rectangle-packing algorithms for placing items of hierarchical data onto display spaces. The algorithms refer to Delaunay triangular meshes connecting the centers of rectangles to find gaps where rectangles can be placed. The first algorithm places rectangles where they do not overlap each other and where the extension of the layout area is minimal. The second algorithm places rectangles by referring to templates describing the ideal positions for nodes of input data. It places rectangles where they do not overlap each other and where the combination of the layout area and the distances between the positions described in the template and the actual positions is minimal. It can smoothly represent time-varying data by referring to templates that describe previous layout results. It is also suitable for semantics-based or design-based data layout by generating templates according to the semantics or design.
Architecture of the parallel hierarchical network for fast image recognition
Timchenko, Leonid; Wójcik, Waldemar; Kokriatskaia, Natalia; Kutaev, Yuriy; Ivasyuk, Igor; Kotyra, Andrzej; Smailova, Saule
2016-09-01
Multistage integration of visual information in the brain allows humans to respond quickly to most significant stimuli while maintaining their ability to recognize small details in the image. Implementation of this principle in technical systems can lead to more efficient processing procedures. The multistage approach to image processing includes main types of cortical multistage convergence. The input images are mapped into a flexible hierarchy that reflects complexity of image data. Procedures of the temporal image decomposition and hierarchy formation are described in mathematical expressions. The multistage system highlights spatial regularities, which are passed through a number of transformational levels to generate a coded representation of the image that encapsulates a structure on different hierarchical levels in the image. At each processing stage a single output result is computed to allow a quick response of the system. The result is presented as an activity pattern, which can be compared with previously computed patterns on the basis of the closest match. With regard to the forecasting method, its idea lies in the following. In the results synchronization block, network-processed data arrive to the database where a sample of most correlated data is drawn using service parameters of the parallel-hierarchical network.
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...
Xia, Yongqiu; Weller, Donald E; Williams, Meghan N; Jordan, Thomas E; Yan, Xiaoyuan
2016-11-15
Export coefficient models (ECMs) are often used to predict nutrient sources and sinks in watersheds because ECMs can flexibly incorporate processes and have minimal data requirements. However, ECMs do not quantify uncertainties in model structure, parameters, or predictions; nor do they account for spatial and temporal variability in land characteristics, weather, and management practices. We applied Bayesian hierarchical methods to address these problems in ECMs used to predict nitrate concentration in streams. We compared four model formulations, a basic ECM and three models with additional terms to represent competing hypotheses about the sources of error in ECMs and about spatial and temporal variability of coefficients: an ADditive Error Model (ADEM), a SpatioTemporal Parameter Model (STPM), and a Dynamic Parameter Model (DPM). The DPM incorporates a first-order random walk to represent spatial correlation among parameters and a dynamic linear model to accommodate temporal correlation. We tested the modeling approach in a proof of concept using watershed characteristics and nitrate export measurements from watersheds in the Coastal Plain physiographic province of the Chesapeake Bay drainage. Among the four models, the DPM was the best--it had the lowest mean error, explained the most variability (R(2) = 0.99), had the narrowest prediction intervals, and provided the most effective tradeoff between fit complexity (its deviance information criterion, DIC, was 45.6 units lower than any other model, indicating overwhelming support for the DPM). The superiority of the DPM supports its underlying hypothesis that the main source of error in ECMs is their failure to account for parameter variability rather than structural error. Analysis of the fitted DPM coefficients for cropland export and instream retention revealed some of the factors controlling nitrate concentration: cropland nitrate exports were positively related to stream flow and watershed average slope
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 PM2.5 is a promising way to fill the areas that are not covered by ground PM2.5 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 PM2.5 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 PM2.5 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 PM2.5 estimates.
Kim, J.; Kwon, H. H.
2014-12-01
The existing regional frequency analysis has disadvantages in that it is difficult to consider geographical characteristics in estimating areal rainfall. In this regard, This study aims to develop a hierarchical Bayesian model based regional frequency analysis in that spatial patterns of the design rainfall with geographical information are explicitly incorporated. This study assumes that the parameters of Gumbel distribution are a function of geographical characteristics (e.g. altitude, latitude and longitude) within a general linear regression framework. Posterior distributions of the regression parameters are estimated by Bayesian Markov Chain Monte Calro (MCMC) method, and the identified functional relationship is used to spatially interpolate the parameters of the Gumbel distribution by using digital elevation models (DEM) as inputs. The proposed model is applied to derive design rainfalls over the entire Han-river watershed. It was found that the proposed Bayesian regional frequency analysis model showed similar results compared to L-moment based regional frequency analysis. In addition, the model showed an advantage in terms of quantifying uncertainty of the design rainfall and estimating the area rainfall considering geographical information. Acknowledgement: This research was supported by a grant (14AWMP-B079364-01) from Water Management Research Program funded by Ministry of Land, Infrastructure and Transport of Korean government.
Rodhouse, T.J.; Irvine, K.M.; Vierling, K.T.; Vierling, L.A.
2011-01-01
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.
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...
Yang, Yuqing; Chen, Ning; Chen, Ting
2017-01-25
The inference of associations between environmental factors and microbes and among microbes is critical to interpreting metagenomic data, but compositional bias, indirect associations resulting from common factors, and variance within metagenomic sequencing data limit the discovery of associations. To account for these problems, we propose metagenomic Lognormal-Dirichlet-Multinomial (mLDM), a hierarchical Bayesian model with sparsity constraints, to estimate absolute microbial abundance and simultaneously infer both conditionally dependent associations among microbes and direct associations between microbes and environmental factors. We empirically show the effectiveness of the mLDM model using synthetic data, data from the TARA Oceans project, and a colorectal cancer dataset. Finally, we apply mLDM to 16S sequencing data from the western English Channel and report several associations. Our model can be used on both natural environmental and human metagenomic datasets, promoting the understanding of associations in the microbial community.
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.
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.
Boedeker, Peter
2017-01-01
Hierarchical linear modeling (HLM) is a useful tool when analyzing data collected from groups. There are many decisions to be made when constructing and estimating a model in HLM including which estimation technique to use. Three of the estimation techniques available when analyzing data with HLM are maximum likelihood, restricted maximum…
Modeling hypoxia in the Chesapeake Bay: Ensemble estimation using a Bayesian hierarchical model
Stow, Craig A.; Scavia, Donald
2009-02-01
Quantifying parameter and prediction uncertainty in a rigorous framework can be an important component of model skill assessment. Generally, models with lower uncertainty will be more useful for prediction and inference than models with higher uncertainty. Ensemble estimation, an idea with deep roots in the Bayesian literature, can be useful to reduce model uncertainty. It is based on the idea that simultaneously estimating common or similar parameters among models can result in more precise estimates. We demonstrate this approach using the Streeter-Phelps dissolved oxygen sag model fit to 29 years of data from Chesapeake Bay. Chesapeake Bay has a long history of bottom water hypoxia and several models are being used to assist management decision-making in this system. The Bayesian framework is particularly useful in a decision context because it can combine both expert-judgment and rigorous parameter estimation to yield model forecasts and a probabilistic estimate of the forecast uncertainty.
Directory of Open Access Journals (Sweden)
Björn J. Döring
2013-12-01
Full Text Available A synthetic aperture radar (SAR system requires external absolute calibration so that radiometric measurements can be exploited in numerous scientific and commercial applications. Besides estimating a calibration factor, metrological standards also demand the derivation of a respective calibration uncertainty. This uncertainty is currently not systematically determined. Here for the first time it is proposed to use hierarchical modeling and Bayesian statistics as a consistent method for handling and analyzing the hierarchical data typically acquired during external calibration campaigns. Through the use of Markov chain Monte Carlo simulations, a joint posterior probability can be conveniently derived from measurement data despite the necessary grouping of data samples. The applicability of the method is demonstrated through a case study: The radar reflectivity of DLR’s new C-band Kalibri transponder is derived through a series of RADARSAT-2 acquisitions and a comparison with reference point targets (corner reflectors. The systematic derivation of calibration uncertainties is seen as an important step toward traceable radiometric calibration of synthetic aperture radars.
Ahn, Kuk-Hyun; Palmer, Richard; Steinschneider, Scott
2017-01-01
This study presents a regional, probabilistic framework for seasonal forecasts of extreme low summer flows in the northeastern United States conditioned on antecedent climate and hydrologic conditions. The model is developed to explore three innovations in hierarchical modeling for seasonal forecasting at ungaged sites: (1) predictive climate teleconnections are inferred directly from ocean fields instead of predefined climate indices, (2) a parsimonious modeling structure is introduced to allow climate teleconnections to vary spatially across streamflow gages, and (3) climate teleconnections and antecedent hydrologic conditions are considered jointly for regional forecast development. The proposed model is developed and calibrated in a hierarchical Bayesian framework to pool regional information across sites and enhance regionalization skill. The model is validated in a cross-validation framework along with five simpler nested formulations to test specific hypotheses embedded in the full model structure. Results indicate that each of the three innovations improve out-of-sample summer low-flow forecasts, with the greatest benefits derived from the spatially heterogeneous effect of climate teleconnections. We conclude with a discussion of possible model improvements from a better representation of antecedent hydrologic conditions at ungaged sites.
A New Enhanced Fast Handover Algorithm in Hierarchical Mobile IPv6 Network
Institute of Scientific and Technical Information of China (English)
XU Kai; JI Hong; YUE Guang-xin
2004-01-01
Hierarchical Mobile IPv6 (HMIPv6) can reduce the delay and the amount of signaling during handover compared with the basic mobile IPv6. However, the protocol still cannot meet the requirement for traffic that is delay sensitive, such as voice, especially in macro mobility handover. Duplicate address detection and the transmission time for the handover operation could cause high handover delay. This paper proposes a new mechanism to improve the fast handover algorithms efficiency in HMIPv6 network. And we present and analyze the performance testing for our proposal by comparing it with the traditional HMIPv6 fast handover algorithm. The results of simulation show that our scheme can reduce the handover delay much more than the traditional fast handover method for HMIPv6 network.
ESS-FH: Enhanced Security Scheme for Fast Handover in Hierarchical Mobile IPv6
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.
Singh, Gurmeet; Raj, Ashish; Kressler, Bryan; Nguyen, Thanh D.; Spincemaille, Pascal; Zabih, Ramin; Wang, Yi
2010-01-01
Among recent parallel MR imaging reconstruction advances, a Bayesian method called Edge-preserving Parallel Imaging with GRAph cut Minimization (EPIGRAM) has been demonstrated to significantly improve signal to noise ratio (SNR) compared to conventional regularized sensitivity encoding (SENSE) method. However, EPIGRAM requires a large number of iterations in proportion to the number of intensity labels in the image, making it computationally expensive for high dynamic range images. The objective of this study is to develop a Fast EPIGRAM reconstruction based on the efficient binary jump move algorithm that provides a logarithmic reduction in reconstruction time while maintaining image quality. Preliminary in vivo validation of the proposed algorithm is presented for 2D cardiac cine MR imaging and 3D coronary MR angiography at acceleration factors of 2-4. Fast EPIGRAM was found to provide similar image quality to EPIGRAM and maintain the previously reported SNR improvement over regularized SENSE, while reducing EPIGRAM reconstruction time by 25-50 times. PMID:20939095
Wheeler, David C; Hickson, Demarc A; Waller, Lance A
2010-06-01
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.
Directory of Open Access Journals (Sweden)
Fontez B.
2014-04-01
Full Text Available Back-calculation allows to increase available data on fish growth. The accuracy of back-calculation models is of paramount importance for growth analysis. Frequentist and Bayesian hierarchical approaches were used for regression between fish body size and scale size for the rare fish species Zingel asper. The Bayesian approach permits more reliable estimation of back-calculated size, taking into account biological information and cohort variability. This method greatly improves estimation of back-calculated length when sampling is uneven and/or small.
Bayesian inference with ecological applications
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...
Semmens, Brice X; Ward, Eric J; Moore, Jonathan W; Darimont, Chris T
2009-07-09
Variability in resource use defines the width of a trophic niche occupied by a population. Intra-population variability in resource use may occur across hierarchical levels of population structure from individuals to subpopulations. Understanding how levels of population organization contribute to population niche width is critical to ecology and evolution. Here we describe a hierarchical stable isotope mixing model that can simultaneously estimate both the prey composition of a consumer diet and the diet variability among individuals and across levels of population organization. By explicitly estimating variance components for multiple scales, the model can deconstruct the niche width of a consumer population into relevant levels of population structure. We apply this new approach to stable isotope data from a population of gray wolves from coastal British Columbia, and show support for extensive intra-population niche variability among individuals, social groups, and geographically isolated subpopulations. The analytic method we describe improves mixing models by accounting for diet variability, and improves isotope niche width analysis by quantitatively assessing the contribution of levels of organization to the niche width of a population.
Buscot, Marie-Jeanne; Wotherspoon, Simon S; Magnussen, Costan G; Juonala, Markus; Sabin, Matthew A; Burgner, David P; Lehtimäki, Terho; Viikari, Jorma S A; Hutri-Kähönen, Nina; Raitakari, Olli T; Thomson, Russell J
2017-06-06
Bayesian hierarchical piecewise regression (BHPR) modeling has not been previously formulated to detect and characterise the mechanism of trajectory divergence between groups of participants that have longitudinal responses with distinct developmental phases. These models are useful when participants in a prospective cohort study are grouped according to a distal dichotomous health outcome. Indeed, a refined understanding of how deleterious risk factor profiles develop across the life-course may help inform early-life interventions. Previous techniques to determine between-group differences in risk factors at each age may result in biased estimate of the age at divergence. We demonstrate the use of Bayesian hierarchical piecewise regression (BHPR) to generate a point estimate and credible interval for the age at which trajectories diverge between groups for continuous outcome measures that exhibit non-linear within-person response profiles over time. We illustrate our approach by modeling the divergence in childhood-to-adulthood body mass index (BMI) trajectories between two groups of adults with/without type 2 diabetes mellitus (T2DM) in the Cardiovascular Risk in Young Finns Study (YFS). Using the proposed BHPR approach, we estimated the BMI profiles of participants with T2DM diverged from healthy participants at age 16 years for males (95% credible interval (CI):13.5-18 years) and 21 years for females (95% CI: 19.5-23 years). These data suggest that a critical window for weight management intervention in preventing T2DM might exist before the age when BMI growth rate is naturally expected to decrease. Simulation showed that when using pairwise comparison of least-square means from categorical mixed models, smaller sample sizes tended to conclude a later age of divergence. In contrast, the point estimate of the divergence time is not biased by sample size when using the proposed BHPR method. BHPR is a powerful analytic tool to model long-term non
Walter, William D.; 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 modeling and Markov chain Monte Carlo sampling for tuning-curve analysis.
Cronin, Beau; Stevenson, Ian H; Sur, Mriganka; Körding, Konrad P
2010-01-01
A central theme of systems neuroscience is to characterize the tuning of neural responses to sensory stimuli or the production of movement. Statistically, we often want to estimate the parameters of the tuning curve, such as preferred direction, as well as the associated degree of uncertainty, characterized by error bars. Here we present a new sampling-based, Bayesian method that allows the estimation of tuning-curve parameters, the estimation of error bars, and hypothesis testing. This method also provides a useful way of visualizing which tuning curves are compatible with the recorded data. We demonstrate the utility of this approach using recordings of orientation and direction tuning in primary visual cortex, direction of motion tuning in primary motor cortex, and simulated data.
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Auvinen Petri
2008-01-01
Full Text Available We propose a method for improving the quality of signal from DNA microarrays by using several scans at varying scanner sen-sitivities. A Bayesian latent intensity model is introduced for the analysis of such data. The method improves the accuracy at which expressions can be measured in all ranges and extends the dynamic range of measured gene expression at the high end. Our method is generic and can be applied to data from any organism, for imaging with any scanner that allows varying the laser power, and for extraction with any image analysis software. Results from a self-self hybridization data set illustrate an improved precision in the estimation of the expression of genes compared to what can be achieved by applying standard methods and using only a single scan.
Contending non-double-couple source components with hierarchical Bayesian moment tensor inversion
Mustac, M.; Tkalcic, H.
2015-12-01
Seismic moment tensors can aid the discrimination between earthquakes and explosions. However, the isotropic component can be found in a large number of earthquakes simply as a consequence of earthquake location, poorly modeled structure or noise in the data. Recently, we have developed a method for moment tensor inversion, capable of retrieving parameter uncertainties together with their optimal values, using probabilistic Bayesian inference. It has been applied to data from a complex volcanic environment in the Long Valley Caldera (LVC), California, and confirmed a large isotropic source component. We now extend the application to two different environments where the existence of non-double-couple source components is likely. The method includes notable treatment of the noise, utilizing pre-event noise to estimate the noise covariance matrix. This is extended throughout the inversion, where noise variance is a "hyperparameter" that determines the level of data fit. On top of that, different noise parameters for each station are used as weights, naturally penalizing stations with noisy data. In the LVC case, this means increasing the amount of information from two stations at moderate distances, which results in a 1 km deeper estimate for the source location. This causes a change in the non-double-couple components in the inversions assuming a simple diagonal or exponential covariance matrix, but not in the inversion assuming a more complicated, attenuated cosine covariance matrix. Combining a sophisticated noise treatment with a powerful Bayesian inversion technique can give meaningful uncertainty estimates for long-period (20-50 s) data, provided an appropriate regional structure model.
Hoffman, Joseph J; Nelson, Amber M; Holland, Mark R; Miller, James G
2012-09-01
A Bayesian probability theory approach for separating overlapping ultrasonic fast and slow waves in cancellous bone has been previously introduced. The goals of this study were to investigate whether the fast and slow waves obtained from Bayesian separation of an apparently single mode signal individually correlate with porosity and to isolate the fast and slow waves from medial-lateral insonification of the calcaneus. The Bayesian technique was applied to trabecular bone data from eight human calcanei insonified in the medial-lateral direction. The phase velocity, slope of attenuation (nBUA), and amplitude were determined for both the fast and slow waves. The porosity was assessed by micro-computed tomography (microCT) and ranged from 78.7% to 94.1%. The method successfully separated the fast and slow waves from medial-lateral insonification of the calcaneus. The phase velocity for both the fast and slow wave modes showed an inverse correlation with porosity (R(2) = 0.73 and R(2) = 0.86, respectively). The slope of attenuation for both wave modes also had a negative correlation with porosity (fast wave: R(2) = 0.73, slow wave: R(2) = 0.53). The fast wave amplitude decreased with increasing porosity (R(2) = 0.66). Conversely, the slow wave amplitude modestly increased with increasing porosity (R(2) = 0.39).
Molnar, S.; Dettmer, J.; Steininger, G.; Dosso, S. E.; Cassidy, J. F.
2013-12-01
This paper applies hierarchical, trans-dimensional Bayesian models for earth and residual-error parametrizations to the inversion of microtremor array dispersion data for shear-wave velocity (Vs) structure. The earth is parametrized in terms of flat-lying, homogeneous layers and residual errors are parametrized with a first-order autoregressive data-error model. The inversion accounts for the limited knowledge of the optimal earth and residual error model parametrization (e.g. the number of layers in the Vs profile) in the resulting Vs parameter uncertainty estimates. The assumed earth model parametrization influences estimates of parameter values and uncertainties due to different parametrizations leading to different ranges of data predictions. The support of the data for a particular model is often non-unique and several parametrizations may be supported. A trans-dimensional formulation accounts for this non-uniqueness by including a model-indexing parameter as an unknown so that groups of models (identified by the index) are considered in the results. In addition, serial residual-error correlations are addressed by augmenting the geophysical forward model with a hierarchical autoregressive error model that can account for a wide range of error processes with a small number of parameters. Hence, the limited knowledge about the true statistical distribution of data errors is also accounted for in the earth model parameter estimates, resulting in more realistic uncertainties and parameter values. Hierarchical autoregressive error models do not rely on point estimates of the model vector to estimate residual-error statistics, and have no requirement for computing the inverse or determinant of a covariance matrix. This approach is particularly useful for trans-dimensional inverse problems, as point estimates may not be representative of the state space that spans multiple subspaces of different dimensions. The autoregressive process is restricted to first order and
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J.-J. Boreux
2009-10-01
Full Text Available One basic premise of dendroclimatology is that tree rings can be viewed as climate proxies, i.e. rings are assumed to contain some hidden information about past climate. From a statistical perspective, this extraction problem can be understood as the search of a hidden variable which represents the common signal within a collection of tree-ring width series. Classical average-based techniques used in dendrochronology have been applied to estimate the mean behavior of this latent variable. Still, depending on tree species, regional factors and statistical methods, a precise quantification of uncertainties associated to the hidden variable distribution is difficult to assess. To model the error propagation throughout the extraction procedure, we propose and study a Bayesian hierarchical model that focuses on extracting an inter-annual high frequency signal. Our method is applied to black spruce (Picea mariana tree-rings recorded in Northern Quebec and compared to a classical average-based techniques used by dendrochronologists (Cook and Kairiukstis, 1992.
Zarekarizi, M.; Moradkhani, H.
2015-12-01
Extreme events are proven to be affected by climate change, influencing hydrologic simulations for which stationarity is usually a main assumption. Studies have discussed that this assumption would lead to large bias in model estimations and higher flood hazard consequently. Getting inspired by the importance of non-stationarity, we determined how the exceedance probabilities have changed over time in Johnson Creek River, Oregon. This could help estimate the probability of failure of a structure that was primarily designed to resist less likely floods according to common practice. Therefore, we built a climate informed Bayesian hierarchical model and non-stationarity was considered in modeling framework. Principle component analysis shows that North Atlantic Oscillation (NAO), Western Pacific Index (WPI) and Eastern Asia (EA) are mostly affecting stream flow in this river. We modeled flood extremes using peaks over threshold (POT) method rather than conventional annual maximum flood (AMF) mainly because it is possible to base the model on more information. We used available threshold selection methods to select a suitable threshold for the study area. Accounting for non-stationarity, model parameters vary through time with climate indices. We developed a couple of model scenarios and chose one which could best explain the variation in data based on performance measures. We also estimated return periods under non-stationarity condition. Results show that ignoring stationarity could increase the flood hazard up to four times which could increase the probability of an in-stream structure being overtopped.
Choi, Leena; Caffo, Brian S; Kohli, Utkarsh; Pandharipande, Pratik; Kurnik, Daniel; Ely, E Wesley; Stein, C Michael
2011-10-01
The purpose of this study is to develop a statistical methodology to handle a large proportion of artifactual outliers in a population pharmacokinetic (PK) modeling. The motivating PK data were obtained from a population PK study to examine associations between PK parameters such as clearance of dexmedetomidine (DEX) and cytochrome P450 2A6 phenotypes. The blood samples were sparsely sampled from patients in intensive care units (ICUs) while different doses of DEX were continuously infused. Conventional population PK analysis of these data revealed several challenges and intricacies. Especially, there was strong evidence that some plasma drug concentrations were artifactually high and likely contaminated with the infused drug due to blood sampling processes that are sometimes unavoidable in an ICU setting. If not addressed, or if arbitrarily excluded, these outlying values could lead to biased estimates of PK parameters and miss important relationships between PK parameters and covariates due to increased variability. We propose a novel population PK model, a Bayesian hierarchical nonlinear mixture model, to accommodate the artifactual outliers using a finite mixture as the residual error model. Our results showed that the proposed model handles the outliers well. We also conducted simulation studies with a varying proportion of the outliers. These simulation results showed that the proposed model can accommodate the outliers well so that the estimated PK parameters are less biased.
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.
Buhule, O D; Wahed, A S; Youk, A O
2017-08-22
Modeling of correlated biomarkers jointly has been shown to improve the efficiency of parameter estimates, leading to better clinical decisions. In this paper, we employ a joint modeling approach to a unique diabetes dataset, where blood glucose (continuous) and urine glucose (ordinal) measures of disease severity for diabetes are known to be correlated. The postulated joint model assumes that the outcomes are from distributions that are in the exponential family and hence modeled as multivariate generalized linear mixed effects model associated through correlated and/or shared random effects. The Markov chain Monte Carlo Bayesian approach is used to approximate posterior distribution and draw inference on the parameters. This proposed methodology provides a flexible framework to account for the hierarchical structure of the highly unbalanced data as well as the association between the 2 outcomes. The results indicate improved efficiency of parameter estimates when blood glucose and urine glucose are modeled jointly. Moreover, the simulation studies show that estimates obtained from the joint model are consistently less biased and more efficient than those in the separate models. Copyright © 2017 John Wiley & Sons, Ltd.
Licquia, Timothy C
2014-01-01
We present improved estimates of several global properties of the Milky Way, including its current star formation rate (SFR), the stellar mass contained in its disk and bulge+bar components, as well as its total stellar mass. We do so by combining previous measurements from the literature using a hierarchical Bayesian (HB) statistical method that allows us to account for the possibility that any value may be incorrect or have underestimated errors. We show that this method is robust to a wide variety of assumptions about the nature of problems in individual measurements or error estimates. Ultimately, our analysis yields a SFR for the Galaxy of $\\dot{\\rm M}_\\star=1.65\\pm0.19$ ${\\rm M}_\\odot$ yr$^{-1}$. By combining HB methods with Monte Carlo simulations that incorporate the latest estimates of the Galactocentric radius of the Sun, $R_0$, the exponential scale-length of the disk, $L_d$, and the local surface density of stellar mass, $\\Sigma_\\star(R_0)$, we show that the mass of the Galactic bulge+bar is ${\\rm...
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J.-J. Boreux
2009-03-01
Full Text Available Dendrochronology, the scientific dating method based on the analysis of tree-ring growth patterns, has been frequently applied in climatology. The basic premise of dendroclimatology is that tree rings can be viewed as climate proxies, i.e. rings are assumed to contain some hidden information about past climate. From a statistical perspective, this extraction problem can be understood as the search of a hidden variable which represents the common signal within a collection of tree-ring width series. Classical average-based techniques used in dendrochronology have been, with different degrees of success (depending on tree species, regional factors and statistical methods, applied to estimate the mean behavior of this latent variable. Still, a precise quantification of uncertainties associated to the hidden variable distribution is difficult to assess. To model the error propagation throughout the extraction procedure, we propose and study a Bayesian hierarchical model that focuses on extracting an inter-annual high frequency signal. Our method is applied to black spruce (Picea mariana tree-rings recorded in northern Quebec and compared to a classical average-based techniques used by dendrochronologists.
Manual hierarchical clustering of regional geochemical data using a Bayesian finite mixture model
Ellefsen, Karl J.; Smith, David
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.
Bayesian framework to constrain the photon mass with a catalog of fast radio bursts
Shao, Lijing; Zhang, Bing
2017-06-01
A hypothetical photon mass, mγ, gives an energy-dependent light speed in a Lorentz-invariant theory. Such a modification causes an additional time delay between photons of different energies when they travel through a fixed distance. Fast radio bursts (FRBs), with their short time duration and cosmological propagation distance, are excellent astrophysical objects to constrain mγ. Here for the first time we develop a Bayesian framework to study this problem with a catalog of FRBs. Those FRBs with and without redshift measurement are both useful in this framework, and can be combined in a Bayesian way. A catalog of 21 FRBs (including 20 FRBs without redshift measurement, and one, FRB 121102, with a measured redshift z =0.19273 ±0.00008 ) give a combined limit mγ≤8.7 ×10-51 kg , or equivalently mγ≤4.9 ×10-15 eV /c2 (mγ≤1.5 ×10-50 kg , or equivalently mγ≤8.4 ×10-15 eV /c2 ) at 68% (95%) confidence level, which represents the best limit that comes purely from kinematics. The framework proposed here will be valuable when FRBs are observed daily in the future. Increment in the number of FRBs, and refinement in the knowledge about the electron distributions in the Milky Way, the host galaxies of FRBs, and the intergalactic medium, will further tighten the constraint.
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Han Zhang
2014-01-01
Full Text Available A novel fast SAR image change detection method is presented in this paper. Based on a Bayesian approach, the prior information that speckles follow the Nakagami distribution is incorporated into the difference image (DI generation process. The new DI performs much better than the familiar log ratio (LR DI as well as the cumulant based Kullback-Leibler divergence (CKLD DI. The statistical region merging (SRM approach is first introduced to change detection context. A new clustering procedure with the region variance as the statistical inference variable is exhibited to tailor SAR image change detection purposes, with only two classes in the final map, the unchanged and changed classes. The most prominent advantages of the proposed modified SRM (MSRM method are the ability to cope with noise corruption and the quick implementation. Experimental results show that the proposed method is superior in both the change detection accuracy and the operation efficiency.
A BAYESIAN HIERARCHICAL SPATIAL POINT PROCESS MODEL FOR MULTI-TYPE NEUROIMAGING META-ANALYSIS.
Kang, Jian; Nichols, Thomas E; Wager, Tor D; Johnson, Timothy D
2014-09-01
Neuroimaging meta-analysis is an important tool for finding consistent effects over studies that each usually have 20 or fewer subjects. Interest in meta-analysis in brain mapping is also driven by a recent focus on so-called "reverse inference": where as traditional "forward inference" identifies the regions of the brain involved in a task, a reverse inference identifies the cognitive processes that a task engages. Such reverse inferences, however, requires a set of meta-analysis, one for each possible cognitive domain. However, existing methods for neuroimaging meta-analysis have significant limitations. Commonly used methods for neuroimaging meta-analysis are not model based, do not provide interpretable parameter estimates, and only produce null hypothesis inferences; further, they are generally designed for a single group of studies and cannot produce reverse inferences. In this work we address these limitations by adopting a non-parametric Bayesian approach for meta analysis data from multiple classes or types of studies. In particular, foci from each type of study are modeled as a cluster process driven by a random intensity function that is modeled as a kernel convolution of a gamma random field. The type-specific gamma random fields are linked and modeled as a realization of a common gamma random field, shared by all types, that induces correlation between study types and mimics the behavior of a univariate mixed effects model. We illustrate our model on simulation studies and a meta analysis of five emotions from 219 studies and check model fit by a posterior predictive assessment. In addition, we implement reverse inference by using the model to predict study type from a newly presented study. We evaluate this predictive performance via leave-one-out cross validation that is efficiently implemented using importance sampling techniques.
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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
Yu, Rongjie; Abdel-Aty, Mohamed
2014-01-01
Severe crashes are causing serious social and economic loss, and because of this, reducing crash injury severity has become one of the key objectives of the high speed facilities' (freeway and expressway) management. Traditional crash injury severity analysis utilized data mainly from crash reports concerning the crash occurrence information, drivers' characteristics and roadway geometric related variables. In this study, real-time traffic and weather data were introduced to analyze the crash injury severity. The space mean speeds captured by the Automatic Vehicle Identification (AVI) system on the two roadways were used as explanatory variables in this study; and data from a mountainous freeway (I-70 in Colorado) and an urban expressway (State Road 408 in Orlando) have been used to identify the analysis result's consistence. Binary probit (BP) models were estimated to classify the non-severe (property damage only) crashes and severe (injury and fatality) crashes. Firstly, Bayesian BP models' results were compared to the results from Maximum Likelihood Estimation BP models and it was concluded that Bayesian inference was superior with more significant variables. Then different levels of hierarchical Bayesian BP models were developed with random effects accounting for the unobserved heterogeneity at segment level and crash individual level, respectively. Modeling results from both studied locations demonstrate that large variations of speed prior to the crash occurrence would increase the likelihood of severe crash occurrence. Moreover, with considering unobserved heterogeneity in the Bayesian BP models, the model goodness-of-fit has improved substantially. Finally, possible future applications of the model results and the hierarchical Bayesian probit models were discussed.
Giovanini, Jack; Kroll, Andrew J; Jones, Jay E; Altman, Bob; Arnett, Edward B
2013-01-01
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 respond to severe
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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
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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
Mandel, Kaisey S.; Scolnic, Daniel M.; Shariff, Hikmatali; Foley, Ryan J.; Kirshner, Robert P.
2017-06-01
Conventional Type Ia supernova (SN Ia) cosmology analyses currently use a simplistic linear regression of magnitude versus color and light curve shape, which does not model intrinsic SN Ia variations and host galaxy dust as physically distinct effects, resulting in low color-magnitude slopes. We construct a probabilistic generative model for the dusty distribution of extinguished absolute magnitudes and apparent colors as the convolution of an intrinsic SN Ia color-magnitude distribution and a host galaxy dust reddening-extinction distribution. If the intrinsic color-magnitude (M B versus B - V) slope {β }{int} differs from the host galaxy dust law R B , this convolution results in a specific curve of mean extinguished absolute magnitude versus apparent color. The derivative of this curve smoothly transitions from {β }{int} in the blue tail to R B in the red tail of the apparent color distribution. The conventional linear fit approximates this effective curve near the average apparent color, resulting in an apparent slope {β }{app} between {β }{int} and R B . We incorporate these effects into a hierarchical Bayesian statistical model for SN Ia light curve measurements, and analyze a data set of SALT2 optical light curve fits of 248 nearby SNe Ia at zlinear fit gives {β }{app}≈ 3. Our model finds {β }{int}=2.3+/- 0.3 and a distinct dust law of {R}B=3.8+/- 0.3, consistent with the average for Milky Way dust, while correcting a systematic distance bias of ˜0.10 mag in the tails of the apparent color distribution. Finally, we extend our model to examine the SN Ia luminosity-host mass dependence in terms of intrinsic and dust components.
Pardo, Mario A; Gerrodette, Tim; Beier, Emilio; Gendron, Diane; Forney, Karin A; Chivers, Susan J; Barlow, Jay; Palacios, Daniel M
2015-01-01
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 southern portion of the
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.
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.
Gelman, Andrew; Stern, Hal S; Dunson, David B; Vehtari, Aki; Rubin, Donald B
2013-01-01
FUNDAMENTALS OF BAYESIAN INFERENCEProbability and InferenceSingle-Parameter Models Introduction to Multiparameter Models Asymptotics and Connections to Non-Bayesian ApproachesHierarchical ModelsFUNDAMENTALS OF BAYESIAN DATA ANALYSISModel Checking Evaluating, Comparing, and Expanding ModelsModeling Accounting for Data Collection Decision AnalysisADVANCED COMPUTATION Introduction to Bayesian Computation Basics of Markov Chain Simulation Computationally Efficient Markov Chain Simulation Modal and Distributional ApproximationsREGRESSION MODELS Introduction to Regression Models Hierarchical Linear
Zhang, Feng-Liang; Ni, Yan-Chun; Au, Siu-Kui; Lam, Heung-Fai
2016-03-01
The identification of modal properties from field testing of civil engineering structures is becoming economically viable, thanks to the advent of modern sensor and data acquisition technology. Its demand is driven by innovative structural designs and increased performance requirements of dynamic-prone structures that call for a close cross-checking or monitoring of their dynamic properties and responses. Existing instrumentation capabilities and modal identification techniques allow structures to be tested under free vibration, forced vibration (known input) or ambient vibration (unknown broadband loading). These tests can be considered complementary rather than competing as they are based on different modeling assumptions in the identification model and have different implications on costs and benefits. Uncertainty arises naturally in the dynamic testing of structures due to measurement noise, sensor alignment error, modeling error, etc. This is especially relevant in field vibration tests because the test condition in the field environment can hardly be controlled. In this work, a Bayesian statistical approach is developed for modal identification using the free vibration response of structures. A frequency domain formulation is proposed that makes statistical inference based on the Fast Fourier Transform (FFT) of the data in a selected frequency band. This significantly simplifies the identification model because only the modes dominating the frequency band need to be included. It also legitimately ignores the information in the excluded frequency bands that are either irrelevant or difficult to model, thereby significantly reducing modeling error risk. The posterior probability density function (PDF) of the modal parameters is derived rigorously from modeling assumptions and Bayesian probability logic. Computational difficulties associated with calculating the posterior statistics, including the most probable value (MPV) and the posterior covariance matrix
Directory of Open Access Journals (Sweden)
Ying Cao
Full Text Available Childhood acute lymphoblastic leukemia (ALL is a condition that arises from complex etiologies. The absence of consistent environmental risk factors and the presence of modest familial associations suggest ALL is a complex trait with an underlying genetic component. The identification of genetic factors associated with disease is complicated by complex genetic covariance structures and multiple testing issues. Both issues can be resolved with appropriate Bayesian variable selection methods. The present study was undertaken to extend our hierarchical Bayesian model for case-parent triads to incorporate single nucleotide polymorphisms (SNPs and incorporate the biological grouping of SNPs within genes. Based on previous evidence that genetic variation in the folate metabolic pathway influences ALL risk, we evaluated 128 tagging SNPs in 16 folate metabolic genes among 118 ALL case-parent triads recruited from the Texas Children's Cancer Center (Houston, TX between 2003 and 2010. We used stochastic search gene suggestion (SSGS in hierarchical Bayesian models to evaluate the association between folate metabolic SNPs and ALL. Using Bayes factors among these variants in childhood ALL case-parent triads, two SNPs were identified with a Bayes factor greater than 1. There was evidence that the minor alleles of NOS3 rs3918186 (OR = 2.16; 95% CI: 1.51-3.15 and SLC19A1 rs1051266 (OR = 2.07; 95% CI: 1.25-3.46 were positively associated with childhood ALL. Our findings are suggestive of the role of inherited genetic variation in the folate metabolic pathway on childhood ALL risk, and they also suggest the utility of Bayesian variable selection methods in the context of case-parent triads for evaluating the role of SNPs on disease risk.
Mandel, Kaisey; Scolnic, Daniel; Shariff, Hikmatali; Foley, Ryan; Kirshner, Robert
2017-01-01
Inferring peak optical absolute magnitudes of Type Ia supernovae (SN Ia) from distance-independent measures such as their light curve shapes and colors underpins the evidence for cosmic acceleration. SN Ia with broader, slower declining optical light curves are more luminous (“broader-brighter”) and those with redder colors are dimmer. But the “redder-dimmer” color-luminosity relation widely used in cosmological SN Ia analyses confounds its two separate physical origins. An intrinsic correlation arises from the physics of exploding white dwarfs, while interstellar dust in the host galaxy also makes SN Ia appear dimmer and redder. Conventional SN Ia cosmology analyses currently use a simplistic linear regression of magnitude versus color and light curve shape, which does not model intrinsic SN Ia variations and host galaxy dust as physically distinct effects, resulting in low color-magnitude slopes. We construct a probabilistic generative model for the dusty distribution of extinguished absolute magnitudes and apparent colors as the convolution of an intrinsic SN Ia color-magnitude distribution and a host galaxy dust reddening-extinction distribution. If the intrinsic color-magnitude (MB vs. B-V) slope βint differs from the host galaxy dust law RB, this convolution results in a specific curve of mean extinguished absolute magnitude vs. apparent color. The derivative of this curve smoothly transitions from βint in the blue tail to RB in the red tail of the apparent color distribution. The conventional linear fit approximates this effective curve near the average apparent color, resulting in an apparent slope βapp between βint and RB. We incorporate these effects into a hierarchical Bayesian statistical model for SN Ia light curve measurements, and analyze a dataset of SALT2 optical light curve fits of 277 nearby SN Ia at z < 0.10. The conventional linear fit obtains βapp ≈ 3. Our model finds a βint = 2.2 ± 0.3 and a distinct dust law of RB = 3.7 ± 0
Evaluating the Performance of Fast Handover for Hierarchical MIPv6 in Cellular Networks
Directory of Open Access Journals (Sweden)
Li Jun Zhang
2008-06-01
Full Text Available Next-Generation Wireless Networks (NGWNs present an all-IP-based architecture integrating existing cellular networks with Wireless Local Area Networks (WLANs, Wireless Metropolitan Area Networks (WMANs, ad hoc networks, Bluetooth, etc. This makes mobility management an important issue for users roaming among these networks/systems. On one hand, intelligent schemes need to be devised to empower mobile users to benefit from the IP-based technology. On the other hand, new solutions are required to take into account global roaming among various radio access technologies and support of real-time multimedia services. This paper presents a comprehensive performance analysis of Fast handover for Hierarchical Mobile IPv6 (F-HMIPv6 using the fluid-flow and randomwalk mobility models. Location update cost, packet delivery cost and total cost functions are formulated based on the proposed analytical models. We investigate the impact of several wireless system factors such as user velocity, user density, mobility domain size, session-to-mobility ratio on these costs, and present some numerical results.
Wan, Rongrong; Cai, Shanshan; Li, Hengpeng; Yang, Guishan; Li, Zhaofu; Nie, Xiaofei
2014-01-15
Lake eutrophication has become a very serious environmental problem in China. If water pollution is to be controlled and ultimately eliminated, it is essential to understand how human activities affect surface water quality. A recently developed technique using the Bayesian hierarchical linear regression model revealed the effects of land use and land cover (LULC) on stream water quality at a watershed scale. Six LULC categories combined with watershed characteristics, including size, slope, and permeability were the variables that were studied. The pollutants of concern were nutrient concentrations of total nitrogen (TN) and total phosphorus (TP), common pollutants found in eutrophication. The monthly monitoring data at 41 sites in the Xitiaoxi Watershed, China during 2009-2010 were used for model demonstration. The results showed that the relationships between LULC and stream water quality are so complicated that the effects are varied over large areas. The models suggested that urban and agricultural land are important sources of TN and TP concentrations, while rural residential land is one of the major sources of TN. Certain agricultural practices (excessive fertilizer application) result in greater concentrations of nutrients in paddy fields, artificial grasslands, and artificial woodlands. This study suggests that Bayesian hierarchical modeling is a powerful tool for examining the complicated relationships between land use and water quality on different scales, and for developing land use and water management policies. Copyright © 2013 Elsevier Ltd. All rights reserved.
Anderson, Christian C; Bauer, Adam Q; Holland, Mark R; Pakula, Michal; Laugier, Pascal; Bretthorst, G Larry; Miller, James G
2010-11-01
Quantitative ultrasonic characterization of cancellous bone can be complicated by artifacts introduced by analyzing acquired data consisting of two propagating waves (a fast wave and a slow wave) as if only one wave were present. Recovering the ultrasonic properties of overlapping fast and slow waves could therefore lead to enhancement of bone quality assessment. The current study uses Bayesian probability theory to estimate phase velocity and normalized broadband ultrasonic attenuation (nBUA) parameters in a model of fast and slow wave propagation. Calculations are carried out using Markov chain Monte Carlo with simulated annealing to approximate the marginal posterior probability densities for parameters in the model. The technique is applied to simulated data, to data acquired on two phantoms capable of generating two waves in acquired signals, and to data acquired on a human femur condyle specimen. The models are in good agreement with both the simulated and experimental data, and the values of the estimated ultrasonic parameters fall within expected ranges.
MacNab, Ying C
2007-11-20
This paper presents a Bayesian disability-adjusted life year (DALY) methodology for spatial and spatiotemporal analyses of disease and/or injury burden. A Bayesian disease mapping model framework, which blends together spatial modelling, shared-component modelling (SCM), temporal modelling, ecological modelling, and non-linear modelling, is developed for small-area DALY estimation and inference. In particular, we develop a model framework that enables SCM as well as multivariate CAR modelling of non-fatal and fatal disease or injury rates and facilitates spline smoothing for non-linear modelling of temporal rate and risk trends. Using British Columbia (Canada) hospital admission-separation data and vital statistics mortality data on non-fatal and fatal road traffic injuries to male population age 20-39 for year 1991-2000 and for 84 local health areas and 16 health service delivery areas, spatial and spatiotemporal estimation and inference on years of life lost due to premature death, years lived with disability, and DALYs are presented. Fully Bayesian estimation and inference, with Markov chain Monte Carlo implementation, are illustrated. We present a methodological framework within which the DALY and the Bayesian disease mapping methodologies interface and intersect. Its development brings the relative importance of premature mortality and disability into the assessment of community health and health needs in order to provide reliable information and evidence for community-based public health surveillance and evaluation, disease and injury prevention, and resource provision.
Song, Hae-Ryoung; Lawson, Andrew; D'Agostino, Ralph B; Liese, Angela D
2011-03-01
Sparse count data violate assumptions of traditional Poisson models due to the excessive amount of zeros, and modeling sparse data becomes challenging. However, since aggregation to reduce sparseness may result in biased estimates of risk, solutions need to be found at the level of disaggregated data. We investigated different statistical approaches within a Bayesian hierarchical framework for modeling sparse data without aggregation of data. We compared our proposed models with the traditional Poisson model and the zero-inflated model based on simulated data. We applied statistical models to type 1 and type 2 diabetes in youth 10-19 years known as rare diseases, and compared models using the inference results and various model diagnostic tools. We showed that one of the models we proposed, a sparse Poisson convolution model, performed better than other models in the simulation and application based on the deviance information criterion (DIC) and the mean squared prediction error.
Lucka, Felix; Pursiainen, Sampsa; Burger, Martin; Wolters, Carsten H
2012-07-16
The estimation of the activity-related ion currents by measuring the induced electromagnetic fields at the head surface is a challenging and severely ill-posed inverse problem. This is especially true in the recovery of brain networks involving deep-lying sources by means of EEG/MEG recordings which is still a challenging task for any inverse method. Recently, hierarchical Bayesian modeling (HBM) emerged as a unifying framework for current density reconstruction (CDR) approaches comprising most established methods as well as offering promising new methods. Our work examines the performance of fully-Bayesian inference methods for HBM for source configurations consisting of few, focal sources when used with realistic, high-resolution finite element (FE) head models. The main foci of interest are the correct depth localization, a well-known source of systematic error of many CDR methods, and the separation of single sources in multiple-source scenarios. Both aspects are very important in the analysis of neurophysiological data and in clinical applications. For these tasks, HBM provides a promising framework and is able to improve upon established CDR methods such as minimum norm estimation (MNE) or sLORETA in many aspects. For challenging multiple-source scenarios where the established methods show crucial errors, promising results are attained. Additionally, we introduce Wasserstein distances as performance measures for the validation of inverse methods in complex source scenarios.
Kim, Jang-Gyeong; Kwon, Hyun-Han; Kim, Dongkyun
2017-01-01
Poisson cluster stochastic rainfall generators (e.g., modified Bartlett-Lewis rectangular pulse, MBLRP) have been widely applied to generate synthetic sub-daily rainfall sequences. The MBLRP model reproduces the underlying distribution of the rainfall generating process. The existing optimization techniques are typically based on individual parameter estimates that treat each parameter as independent. However, parameter estimates sometimes compensate for the estimates of other parameters, which can cause high variability in the results if the covariance structure is not formally considered. Moreover, uncertainty associated with model parameters in the MBLRP rainfall generator is not usually addressed properly. Here, we develop a hierarchical Bayesian model (HBM)-based MBLRP model to jointly estimate parameters across weather stations and explicitly consider the covariance and uncertainty through a Bayesian framework. The model is tested using weather stations in South Korea. The HBM-based MBLRP model improves the identification of parameters with better reproduction of rainfall statistics at various temporal scales. Additionally, the spatial variability of the parameters across weather stations is substantially reduced compared to that of other methods.
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.
Babcock, C. R.; Andersen, H. E.; Finley, A. O.; Cook, B.; Morton, D. C.
2015-12-01
Models using repeat LiDAR and field campaigns may be one mechanism to monitor carbon storage and flux in forested regions. Considering the ability of multi-temporal LiDAR to estimate growth, it is not surprising that there is great interest in developing forest carbon monitoring strategies that rely on repeated LiDAR acquisitions. Allowing for sparser field campaigns, LiDAR stands to make monitoring forest carbon cheaper and more efficient than field-only sampling procedures. Here, we look to the spatio-temporally data-rich Kenai Peninsula in Alaska to examine the potential for Bayesian spatio-temporal mapping of forest carbon storage and uncertainty. The framework explored here can predict forest carbon through space and time, while formally propagating uncertainty through to prediction. Bayesian spatio-temporal models are flexible frameworks allowing for forest growth processes to be formally integrated into the model. By incorporating a mechanism for growth---using temporally repeated field and LiDAR data---we can more fully exploit the information-rich inventory network to improve prediction accuracy. LiDAR data for the Kenai Peninsula has been collected on four different occasions---spatially coincident LiDAR strip samples in 2004, 09 and 14, along with a wall-to-wall collection in 2008. There were 436 plots measured twice between 2002 and 2014. LiDAR was acquired at least once over most inventory plots with many having LiDAR collected during 2, 3 or 4 different campaigns. Results from this research will impact how forests are inventoried. It is too expensive to monitor terrestrial carbon using field-only sampling strategies and currently proposed LiDAR model-based techniques lack the ability to properly utilize temporally repeated and misaligned data. Bayesian hierarchical spatio-temporal models offer a solution to these shortcomings and allow for formal predictive error assessment, which is useful for policy development and decision making.
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…
A New Module for Large Scale Bayesian Evaluation in the Fast Neutron Energy Region
Energy Technology Data Exchange (ETDEWEB)
Schnabel, G., E-mail: gschnabel@ati.ac.at; Leeb, H.
2015-01-15
We present an improved update scheme for the Linearized Bayesian Update procedure (LBUP). The revised procedure extends the application of the LBUP to a large number of observables. The consistent update of dozens of millions of observables becomes manageable by circumventing the costly calculation of the prior covariance matrix. Nuclear data evaluations based on the revised scheme may exhaustively enclose all differential and angle-integrated channels, treating all correlations between them exactly in the update procedure.
DEFF Research Database (Denmark)
Lin, Lin; Chan, Cliburn; Hadrup, Sine R
2013-01-01
Novel uses of automated flow cytometry technology for measuring levels of protein markers on thousands to millions of cells are promoting increasing need for relevant, customized Bayesian mixture modelling approaches in many areas of biomedical research and application. In studies of immune...... profiling in many biological areas, traditional flow cytometry measures relative levels of abundance of marker proteins using fluorescently labeled tags that identify specific markers by a single-color. One specific and important recent development in this area is the use of combinatorial marker assays...
Moran, Emily V; Clark, James S
2011-03-01
The scale of seed and pollen movement in plants has a critical influence on population dynamics and interspecific interactions, as well as on their capacity to respond to environmental change through migration or local adaptation. However, dispersal can be challenging to quantify. Here, we present a Bayesian model that integrates genetic and ecological data to simultaneously estimate effective seed and pollen dispersal parameters and the parentage of sampled seedlings. This model is the first developed for monoecious plants that accounts for genotyping error and treats dispersal from within and beyond a plot in a fully consistent manner. The flexible Bayesian framework allows the incorporation of a variety of ecological variables, including individual variation in seed production, as well as multiple sources of uncertainty. We illustrate the method using data from a mixed population of red oak (Quercus rubra, Q. velutina, Q. falcata) in the NC piedmont. For simulated test data sets, the model successfully recovered the simulated dispersal parameters and pedigrees. Pollen dispersal in the example population was extensive, with an average father-mother distance of 178 m. Estimated seed dispersal distances at the piedmont site were substantially longer than previous estimates based on seed-trap data (average 128 m vs. 9.3 m), suggesting that, under some circumstances, oaks may be less dispersal-limited than is commonly thought, with a greater potential for range shifts in response to climate change.
Directory of Open Access Journals (Sweden)
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.
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.
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.
Stewart, David R.; Long, James M.
2015-01-01
Species distribution models are useful tools to evaluate habitat relationships of fishes. We used hierarchical Bayesian multispecies mixture models to evaluate the relationships of both detection and abundance with habitat of reservoir fishes caught using tandem hoop nets. A total of 7,212 fish from 12 species were captured, and the majority of the catch was composed of Channel Catfish Ictalurus punctatus (46%), Bluegill Lepomis macrochirus(25%), and White Crappie Pomoxis annularis (14%). Detection estimates ranged from 8% to 69%, and modeling results suggested that fishes were primarily influenced by reservoir size and context, water clarity and temperature, and land-use types. Species were differentially abundant within and among habitat types, and some fishes were found to be more abundant in turbid, less impacted (e.g., by urbanization and agriculture) reservoirs with longer shoreline lengths; whereas, other species were found more often in clear, nutrient-rich impoundments that had generally shorter shoreline length and were surrounded by a higher percentage of agricultural land. Our results demonstrated that habitat and reservoir characteristics may differentially benefit species and assemblage structure. This study provides a useful framework for evaluating capture efficiency for not only hoop nets but other gear types used to sample fishes in reservoirs.
Ma, Xiaoye; Chen, Yong; Cole, Stephen R; Chu, Haitao
2014-05-26
To account for between-study heterogeneity in meta-analysis of diagnostic accuracy studies, bivariate random effects models have been recommended to jointly model the sensitivities and specificities. As study design and population vary, the definition of disease status or severity could differ across studies. Consequently, sensitivity and specificity may be correlated with disease prevalence. To account for this dependence, a trivariate random effects model had been proposed. However, the proposed approach can only include cohort studies with information estimating study-specific disease prevalence. In addition, some diagnostic accuracy studies only select a subset of samples to be verified by the reference test. It is known that ignoring unverified subjects may lead to partial verification bias in the estimation of prevalence, sensitivities, and specificities in a single study. However, the impact of this bias on a meta-analysis has not been investigated. In this paper, we propose a novel hybrid Bayesian hierarchical model combining cohort and case-control studies and correcting partial verification bias at the same time. We investigate the performance of the proposed methods through a set of simulation studies. Two case studies on assessing the diagnostic accuracy of gadolinium-enhanced magnetic resonance imaging in detecting lymph node metastases and of adrenal fluorine-18 fluorodeoxyglucose positron emission tomography in characterizing adrenal masses are presented.
Vercelloni, Julie; Caley, M Julian; Kayal, Mohsen; Low-Choy, Samantha; Mengersen, Kerrie
2014-01-01
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.
Seichter, Felicia; Vogt, Josef; Radermacher, Peter; Mizaikoff, Boris
2017-01-25
The calibration of analytical systems is time-consuming and the effort for daily calibration routines should therefore be minimized, while maintaining the analytical accuracy and precision. The 'calibration transfer' approach proposes to combine calibration data already recorded with actual calibrations measurements. However, this strategy was developed for the multivariate, linear analysis of spectroscopic data, and thus, cannot be applied to sensors with a single response channel and/or a non-linear relationship between signal and desired analytical concentration. To fill this gap for a non-linear calibration equation, we assume that the coefficients for the equation, collected over several calibration runs, are normally distributed. Considering that coefficients of an actual calibration are a sample of this distribution, only a few standards are needed for a complete calibration data set. The resulting calibration transfer approach is demonstrated for a fluorescence oxygen sensor and implemented as a hierarchical Bayesian model, combined with a Lagrange Multipliers technique and Monte-Carlo Markov-Chain sampling. The latter provides realistic estimates for coefficients and prediction together with accurate error bounds by simulating known measurement errors and system fluctuations. Performance criteria for validation and optimal selection of a reduced set of calibration samples were developed and lead to a setup which maintains the analytical performance of a full calibration. Strategies for a rapid determination of problems occurring in a daily calibration routine, are proposed, thereby opening the possibility of correcting the problem just in time.
Toman, Blaza; Nelson, Michael A; Lippa, Katrice A
2016-01-01
Chemical purity assessment using quantitative (1)H-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.
Pham, Lisa M; Carvalho, Luis; Schaus, Scott; Kolaczyk, Eric D
Cellular response to a perturbation is the result of a dynamic system of biological variables linked in a complex network. A major challenge in drug and disease studies is identifying the key factors of a biological network that are essential in determining the cell's fate. Here our goal is the identification of perturbed pathways from high-throughput gene expression data. We develop a three-level hierarchical model, where (i) the first level captures the relationship between gene expression and biological pathways using confirmatory factor analysis, (ii) the second level models the behavior within an underlying network of pathways induced by an unknown perturbation using a conditional autoregressive model, and (iii) the third level is a spike-and-slab prior on the perturbations. We then identify perturbations through posterior-based variable selection. We illustrate our approach using gene transcription drug perturbation profiles from the DREAM7 drug sensitivity predication challenge data set. Our proposed method identified regulatory pathways that are known to play a causative role and that were not readily resolved using gene set enrichment analysis or exploratory factor models. Simulation results are presented assessing the performance of this model relative to a network-free variant and its robustness to inaccuracies in biological databases.
Lashkari, Danial; Sridharan, Ramesh; Vul, Edward; Hsieh, Po-Jang; Kanwisher, Nancy; Golland, Polina
2012-01-16
Functional MRI studies have uncovered a number of brain areas that demonstrate highly specific functional patterns. In the case of visual object recognition, small, focal regions have been characterized with selectivity for visual categories such as human faces. In this paper, we develop an algorithm that automatically learns patterns of functional specificity from fMRI data in a group of subjects. The method does not require spatial alignment of functional images from different subjects. The algorithm is based on a generative model that comprises two main layers. At the lower level, we express the functional brain response to each stimulus as a binary activation variable. At the next level, we define a prior over sets of activation variables in all subjects. We use a Hierarchical Dirichlet Process as the prior in order to learn the patterns of functional specificity shared across the group, which we call functional systems, and estimate the number of these systems. Inference based on our model enables automatic discovery and characterization of dominant and consistent functional systems. We apply the method to data from a visual fMRI study comprised of 69 distinct stimulus images. The discovered system activation profiles correspond to selectivity for a number of image categories such as faces, bodies, and scenes. Among systems found by our method, we identify new areas that are deactivated by face stimuli. In empirical comparisons with previously proposed exploratory methods, our results appear superior in capturing the structure in the space of visual categories of stimuli.
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
We propose an iterative algorithm for OFDM receivers operating over fast time-varying channels. The design relies on the assumptions that the channel response can be characterized by a few non-negligible separable multipath components, and the temporal variation of each component gain can be well...
Tonini, Chiara; Croton, Darren J; Wyithe, J Stuart B
2016-01-01
We present a theoretical model for the evolution of mass, angular momentum and size of galaxy disks and bulges, and we implement it into the semi-analytic galaxy formation code SAGE. The model follows both secular and violent evolutionary channels, including smooth accretion, disk instabilities, minor and major mergers. We find that the combination of our recipe with hierarchical clustering produces two distinct populations of bulges: merger-driven bulges, akin to classical bulges and ellipticals, and instability-driven bulges, akin to secular (or pseudo-)bulges. The model can successfully reproduce the mass-size relation of gaseous and stellar disks, the evolution of the mass-size relation of ellipticals, the Faber-Jackson relation, and the magnitude-colour diagram of classical and secular bulges. The model predicts only a small overlap of merger-driven and instability-driven components in the same galaxy, and predicts different bulge types as a function of galaxy mass and disk fraction. Bulge type also affe...
O' Lenick, Cassandra R; Chang, Howard H; Kramer, Michael R; Winquist, Andrea; Mulholland, James A; Friberg, Mariel D; Sarnat, Stefanie Ebelt
2017-04-05
Ground-level ozone is a potent airway irritant and a determinant of respiratory morbidity. Susceptibility to the health effects of ambient ozone may be influenced by both intrinsic and extrinsic factors, such as neighborhood socioeconomic status (SES). Questions remain regarding the manner and extent that factors such as SES influence ozone-related health effects, particularly across different study areas. Using a 2-stage modeling approach we evaluated neighborhood SES as a modifier of ozone-related pediatric respiratory morbidity in Atlanta, Dallas, & St. Louis. We acquired multi-year data on emergency department (ED) visits among 5-18 year olds with a primary diagnosis of respiratory disease in each city. Daily concentrations of 8-h maximum ambient ozone were estimated for all ZIP Code Tabulation Areas (ZCTA) in each city by fusing observed concentration data from available network monitors with simulations from an emissions-based chemical transport model. In the first stage, we used conditional logistic regression to estimate ZCTA-specific odds ratios (OR) between ozone and respiratory ED visits, controlling for temporal trends and meteorology. In the second stage, we combined ZCTA-level estimates in a Bayesian hierarchical model to assess overall associations and effect modification by neighborhood SES considering categorical and continuous SES indicators (e.g., ZCTA-specific levels of poverty). We estimated ORs and 95% posterior intervals (PI) for a 25 ppb increase in ozone. The hierarchical model combined effect estimates from 179 ZCTAs in Atlanta, 205 ZCTAs in Dallas, and 151 ZCTAs in St. Louis. The strongest overall association of ozone and pediatric respiratory disease was in Atlanta (OR = 1.08, 95% PI: 1.06, 1.11), followed by Dallas (OR = 1.04, 95% PI: 1.01, 1.07) and St. Louis (OR = 1.03, 95% PI: 0.99, 1.07). Patterns of association across levels of neighborhood SES in each city suggested stronger ORs in low compared to high SES areas, with
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
We propose an iterative algorithm for OFDM receivers operating over fast time-varying channels. The design relies on the assumptions that the channel response can be characterized by a few non-negligible separable multipath components, and the temporal variation of each component gain can be well...... 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....
Directory of Open Access Journals (Sweden)
Yi-Qing Wang
2015-09-01
Full Text Available Recent years have seen a surge of interest in multilayer neural networks fueled by their successful applications in numerous image processing and computer vision tasks. In this article, we describe a C++ implementation of the stochastic gradient descent to train a multilayer neural network, where a fast and accurate acceleration of tanh(· is achieved with linear interpolation. As an example of application, we present a neural network able to deliver state-of-the-art performance in image demosaicing.
基于DNA微阵列数据分析的分级Bayes模型%A Bayesian Hierarchical Model for DNA Microarray Data
Institute of Scientific and Technical Information of China (English)
刘妍岩; 杨丹
2009-01-01
In DNA microarray analysis, there is often interest in isolating a few genes that best discriminate between tissue types. In particular, it is critical to develop suitable models to explain the patterns of DNA expression for these different types of tissues. Toward this goal, we propose a methodology for the analysis of high-density oligonucleotide arrays.The log-transformed data are assumed to follow a mixture normal distribution based on the characteristic of gene itself. The variation in the data can reasonably be thought to arise from the effects of genes, tissue types, and their interactions. We introduce a hierarchical Bayesian priors for the parameters and propose a model selection criterion for identifying subsets of genes that show different expression levels between normal and tumor types. In addition, we develop Markov chain Monte Carlo algorithms for sampling from the posterior distribution of parameters and for computing criterion. The proposed methodology is evaluated via simulations studies.%如何分离出少量区别不同组织类型的特异性基因是DNA微阵列数据分析中的主要问题,特别是构建恰当的统计模型来刻画这些不同组织类型的DNA表达形式尤为重要.为此,基于基因DNA微阵列数据的特点,我们假定对数变换后的微阵列数据服从混合正态分布.我们采用分级Bayesian先验刻画不同基因的相关性,利用分级Bayesian方法构建模型,给出了刻画不同组织基因表达的差异的一个标准,用MCMC迭代计算该标准.模拟计算表明我们的模型具有较好的识别能力.
Institute of Scientific and Technical Information of China (English)
无
2010-01-01
Spherical molecular brushes with amphiphilic heteroarms were facilely synthesized by grafting the arms of hydrophobic 2-azidoethyle palmitate and hydrophilic monoazide-terminated poly(ethylene glycol) onto the core of alkyne-modified hyperbranched polyglycerol (HPG) with high molecular weight (Mn=122 kDa) via one-pot parallel click chemistry.The parallel click grafting strategy was demonstrated to be highly efficient (～100%),very fast (～ 2 h) and well controllable to the amphilicity of molecular brushes.Through adjusting the feeding ratio of hydrophobic and hydrophilic arms,a series of brushes with different arm ratios were readily obtained.The resulting miktoarms hyperbranched polymer brushes (HPG-g-C16/PEG350) were characterized by hydrogen-nuclear magnetic resonance (1H NMR),Fourier transform infrared (FT-IR) spectroscopy,gel permeation chromatography (GPC),and differential scanning calorimetry (DSC) measurements.The spherical molecular brushes showed high molecular weights up to 230 kDa,and thus could be visualized by atomic force microscopy (AFM).AFM and dynamic laser light scattering (DLS) were employed to investigate the self-assembly properties of amphiphilic molecular brushes with closed proportion of hydrophobic and hydrophilic arms.The brushes could self-assemble hierarchically into spherical micelles,and network-like fibre structures,and again spherical micelles by addition of n-hexane into the dichloromethane or chloroform solution of brushes.In addition,this kind of miktoarms polymer brush also showed the ability of dye loading via host-guest encapsulation,which promises the potential application of spherical molecular brushes in supramolecular chemistry.
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.
Tan, L.; Zhang, S.; Deng, C.
2015-02-01
Lithium iron pyrophosphate has drawn great attention because of its interesting physical and electrochemical properties, whereas its high rate capability is far from satisfactory. We synthesize nano-Li2FeP2O7/C with hierarchical pore via a low cost method which uses iron powder instead of Vitamin C as the reducing agent. The hierarchical pore is constructed through a "combustion" mechanism according to the thermogravimetric and morphological characterizations. The phase-pure nanoparticles of Li2FeP2O7 are embedded in the three-dimensional network of amorphous carbon. The hierarchical pore together with the two-dimensional diffusion channel of lithium in Li2FeP2O7 is beneficial to lithium diffusion capability which is evaluated by the lithium diffusion coefficients calculated from the results of GITT measurements. The fast lithium intercalation chemistry facilitates the reversible de/intercalation of lithium, resulting in the high cycling stability and rate-capability. After 100 cycles at the current density of 1C, 93.8% of the initial capacity is retained. The discharge capacity is 62.1 mAh g-1 at the current density of 4C. Therefore, the hierarchically porous nano-Li2FeP2O7/C is a promising cathode material for advanced rechargeable lithium ion battery.
Chen, Zerui; Zhang, Yu; Wang, Xiaoling; Sun, Wenping; Dou, Shixue; Huang, Xin; Shi, Bi
2017-09-01
Electrochemical-grinding induced pulverization is the origin of capacity fading in NiFe2O4. Increasing current density normally accelerates the pulverization that deteriorates lithium storage properties of NiFe2O4. Here we show that the high current induced fast-pulverization can serve as an efficient activation strategy for quick and simultaneous enhancement on cycling stability and rate capability of NiFe2O4 nanoparticles (NPs) that are densely packed on the hierarchically structured carbon nanofiber strand. At a high current density, the pulverization of NiFe2O4 NPs can be accomplished in a few cycles exposing more active surface. During the fast-pulverization, the hierarchically structured carbon nanofiber strand maintains conductive contact for the densely packed NiFe2O4 NPs regardless of charge or discharge, which also effectively suppresses the repetitive breaks and growths of solid-electrolyte-interphase (SEI) via multiple-level structural adaption that favourites the quick formation of a thin and dense SEI, thus providing strong interparticle connectivity with enhancement on cycling stability and rate capability (e.g. doubled capacity). Our findings demonstrate the potential importance of high current induced fast-pulverization as an efficient activation strategy for achieving durable electrode materials suffering from electrochemical-grinding effects.
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.
Bayesian Inference: with ecological applications
Link, William A.; Barker, Richard J.
2010-01-01
This text provides a mathematically rigorous yet accessible and engaging introduction to Bayesian inference with relevant examples that will be of interest to biologists working in the fields of ecology, wildlife management and environmental studies as well as students in advanced undergraduate statistics.. This text opens the door to Bayesian inference, taking advantage of modern computational efficiencies and easily accessible software to evaluate complex hierarchical models.
Bayesian Methods for Statistical Analysis
Puza, Borek
2015-01-01
Bayesian methods for statistical analysis is a book on statistical methods for analysing a wide variety of data. The book consists of 12 chapters, starting with basic concepts and covering numerous topics, including Bayesian estimation, decision theory, prediction, hypothesis testing, hierarchical models, Markov chain Monte Carlo methods, finite population inference, biased sampling and nonignorable nonresponse. The book contains many exercises, all with worked solutions, including complete c...
Detecting Hierarchical Structure in Networks
DEFF Research Database (Denmark)
Herlau, Tue; Mørup, Morten; Schmidt, Mikkel Nørgaard;
2012-01-01
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......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....... 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....
Introduction to Bayesian modelling in dental research.
Gilthorpe, M S; Maddick, I H; Petrie, A
2000-12-01
To explain the concepts and application of Bayesian modelling and how it can be applied to the analysis of dental research data. Methodological in nature, this article introduces Bayesian modelling through hypothetical dental examples. The synthesis of RCT results with previous evidence, including expert opinion, is used to illustrate full Bayesian modelling. Meta-analysis, in the form of empirical Bayesian modelling, is introduced. An example of full Bayesian modelling is described for the synthesis of evidence from several studies that investigate the success of root canal treatment. Hierarchical (Bayesian) modelling is demonstrated for a survey of childhood caries, where surface data is nested within subjects. Bayesian methods enhance interpretation of research evidence through the synthesis of information from multiple sources. Bayesian modelling is now readily accessible to clinical researchers and is able to augment the application of clinical decision making in the development of guidelines and clinical practice.
Bayesian modeling using WinBUGS
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 ...
Schwarz, L.K.; Runge, M.C.
2009-01-01
Age estimation of individuals is often an integral part of species management research, and a number of ageestimation techniques are commonly employed. Often, the error in these techniques is not quantified or accounted for in other analyses, particularly in growth curve models used to describe physiological responses to environment and human impacts. Also, noninvasive, quick, and inexpensive methods to estimate age are needed. This research aims to provide two Bayesian methods to (i) incorporate age uncertainty into an age-length Schnute growth model and (ii) produce a method from the growth model to estimate age from length. The methods are then employed for Florida manatee (Trichechus manatus) carcasses. After quantifying the uncertainty in the aging technique (counts of ear bone growth layers), we fit age-length data to the Schnute growth model separately by sex and season. Independent prior information about population age structure and the results of the Schnute model are then combined to estimate age from length. Results describing the age-length relationship agree with our understanding of manatee biology. The new methods allow us to estimate age, with quantified uncertainty, for 98% of collected carcasses: 36% from ear bones, 62% from length.
Serang, Oliver
2015-08-01
Observations depending on sums of random variables are common throughout many fields; however, no efficient solution is currently known for performing max-product inference on these sums of general discrete distributions (max-product inference can be used to obtain maximum a posteriori estimates). The limiting step to max-product inference is the max-convolution problem (sometimes presented in log-transformed form and denoted as "infimal convolution," "min-convolution," or "convolution on the tropical semiring"), for which no O(k log(k)) method is currently known. Presented here is an O(k log(k)) numerical method for estimating the max-convolution of two nonnegative vectors (e.g., two probability mass functions), where k is the length of the larger vector. This numerical max-convolution method is then demonstrated by performing fast max-product inference on a convolution tree, a data structure for performing fast inference given information on the sum of n discrete random variables in O(nk log(nk)log(n)) steps (where each random variable has an arbitrary prior distribution on k contiguous possible states). The numerical max-convolution method can be applied to specialized classes of hidden Markov models to reduce the runtime of computing the Viterbi path from nk(2) to nk log(k), and has potential application to the all-pairs shortest paths problem.
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.
Blundell, Charles; Heller, Katherine A
2012-01-01
Hierarchical structure is ubiquitous in data across many domains. There are many hier- archical clustering methods, frequently used by domain experts, which strive to discover this structure. However, most of these meth- ods limit discoverable hierarchies to those with binary branching structure. This lim- itation, while computationally convenient, is often undesirable. In this paper we ex- plore a Bayesian hierarchical clustering algo- rithm that can produce trees with arbitrary branching structure at each node, known as rose trees. We interpret these trees as mixtures over partitions of a data set, and use a computationally efficient, greedy ag- glomerative algorithm to find the rose trees which have high marginal likelihood given the data. Lastly, we perform experiments which demonstrate that rose trees are better models of data than the typical binary trees returned by other hierarchical clustering algorithms.
DEFF Research Database (Denmark)
Zuidmeer-Jongejan, Laurian; Fernandez-Rivas, Montserrat; Poulsen, Lars K.
2012-01-01
ABSTRACT: The FAST project (Food Allergy Specific Immunotherapy) aims at the development of safe and effective treatment of food allergies, targeting prevalent, persistent and severe allergy to fish and peach. Classical allergen-specific immunotherapy (SIT), using subcutaneous injections with aqu......ABSTRACT: The FAST project (Food Allergy Specific Immunotherapy) aims at the development of safe and effective treatment of food allergies, targeting prevalent, persistent and severe allergy to fish and peach. Classical allergen-specific immunotherapy (SIT), using subcutaneous injections...... with aqueous food extracts may be effective but has proven to be accompanied by too many anaphylactic side-effects. FAST aims to develop a safe alternative by replacing food extracts with hypoallergenic recombinant major allergens as the active ingredients of SIT. Both severe fish and peach allergy are caused...... in depth serological and cellular immune analyses will be performed, allowing identification of novel biomarkers for monitoring treatment efficacy. FAST aims at improving the quality of life of food allergic patients by providing a safe and effective treatment that will significantly lower their threshold...
spTimer: Spatio-Temporal Bayesian Modeling Using R
Directory of Open Access Journals (Sweden)
Khandoker Shuvo Bakar
2015-02-01
Full Text Available Hierarchical Bayesian modeling of large point-referenced space-time data is increasingly becoming feasible in many environmental applications due to the recent advances in both statistical methodology and computation power. Implementation of these methods using the Markov chain Monte Carlo (MCMC computational techniques, however, requires development of problem-specific and user-written computer code, possibly in a low-level language. This programming requirement is hindering the widespread use of the Bayesian model-based methods among practitioners and, hence there is an urgent need to develop high-level software that can analyze large data sets rich in both space and time. This paper develops the package spTimer for hierarchical Bayesian modeling of stylized environmental space-time monitoring data as a contributed software package in the R language that is fast becoming a very popular statistical computing platform. The package is able to fit, spatially and temporally predict large amounts of space-time data using three recently developed Bayesian models. The user is given control over many options regarding covariance function selection, distance calculation, prior selection and tuning of the implemented MCMC algorithms, although suitable defaults are provided. The package has many other attractive features such as on the fly transformations and an ability to spatially predict temporally aggregated summaries on the original scale, which saves the problem of storage when using MCMC methods for large datasets. A simulation example, with more than a million observations, and a real life data example are used to validate the underlying code and to illustrate the software capabilities.
Dissecting magnetar variability with Bayesian hierarchical models
Huppenkothen, D; Hogg, D W; Murray, I; Frean, M; Elenbaas, C; Watts, A L; Levin, Y; van der Horst, A J; Kouveliotou, C
2015-01-01
Neutron stars are a prime laboratory for testing physical processes under conditions of strong gravity, high density, and extreme magnetic fields. Among the zoo of neutron star phenomena, magnetars stand out for their bursting behaviour, ranging from extremely bright, rare giant flares to numerous, less energetic recurrent bursts. The exact trigger and emission mechanisms for these bursts are not known; favoured models involve either a crust fracture and subsequent energy release into the magnetosphere, or explosive reconnection of magnetic field lines. In the absence of a predictive model, understanding the physical processes responsible for magnetar burst variability is difficult. Here, we develop an empirical model that decomposes magnetar bursts into a superposition of small spike-like features with a simple functional form, where the number of model components is itself part of the inference problem. The cascades of spikes that we model might be formed by avalanches of reconnection, or crust rupture afte...
Studies on Routing Optimization of Fast and Hierarchical Mobile Multicast%快速分层移动组播的路径优化研究
Institute of Scientific and Technical Information of China (English)
李彬; 冯祖洪
2015-01-01
随着科学技术的飞速发展，多媒体通信的需求导致了组播技术的快速进步。如何节约网络资源，为移动设备提供更好的支持也引起了人们的普遍关注。由于组播具有可扩展性强、高效的特点，因此移动组播的应用已经得到了越来越多的关注。本文根据快速分层移动组播现有算法中的传输路径问题，介绍一种新的路由路径选择方法。该算法依据移动节点在新接入点停留的时间长短，选择不同的数据传输路径加入组播。可以优化组播分组的传输路径，有效减少网络资源的浪费。%With the rapid progress of science and technology, the requirement of multimedia communication let to the rapid advancement of the multicast technology. How to save network resources and determine the best way to provide services to mobile devices is the most important issue need to solve. As multicast naturally has the merit of high scalability and efficiency, more and more people pay attention to mobile multicast. Based on the transmission path problem of the fast and hierarchical mobile multicast, this paper introduces a new method. which is an improved algorithm based on the staying time of mobile devices under new access router, through prediction staying time mobile devices, it chooses a better path to join multicast. This new method can optimization routing path and save network resources.
Dichroic polarization at mid-infrared wavelengths: a Bayesian approach
Lopez-Rodriguez, E
2015-01-01
A fast and general Bayesian inference framework to infer the physical properties of dichroic polarization using mid-infrared imaging- and spectro-polarimetric observations is presented. The Bayesian approach is based on a hierarchical regression and No-U-Turn Sampler method. This approach simultaneously infers the normalized Stokes parameters to find the full family of solutions that best describe the observations. In comparison with previous methods, the developed Bayesian approach allows the user to introduce a customized absorptive polarization component based on the dust composition, and the appropriate extinction curve of the object. This approach allows the user to obtain more precise estimations of the magnetic field strength and geometry for tomographic studies, and information about the dominant polarization components of the object. Based on this model, imaging-polarimetric observations using two or three filters located in the central 9.5-10.5 $\\mu$m, and the edges 8-9 $\\mu$m and/or 11-13 $\\mu$m, o...
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
When mechanism matters: Bayesian forecasting using models of ecological diffusion
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.
新家, 健精
2013-01-01
© 2012 Springer Science+Business Media, LLC. All rights reserved. Article Outline: Glossary Definition of the Subject and Introduction The Bayesian Statistical Paradigm Three Examples Comparison with the Frequentist Statistical Paradigm Future Directions Bibliography
Bayesian theory and applications
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...
Multiview Bayesian Correlated Component Analysis
DEFF Research Database (Denmark)
Kamronn, Simon Due; Poulsen, Andreas Trier; Hansen, Lars Kai
2015-01-01
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....... 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...
Morton, Kenneth D., Jr.; Torrione, Peter A.; Collins, Leslie
2010-04-01
Time domain ground penetrating radar (GPR) has been shown to be a powerful sensing phenomenology for detecting buried objects such as landmines. Landmine detection with GPR data typically utilizes a feature-based pattern classification algorithm to discriminate buried landmines from other sub-surface objects. In high-fidelity GPR, the time-frequency characteristics of a landmine response should be indicative of the physical construction and material composition of the landmine and could therefore be useful for discrimination from other non-threatening sub-surface objects. In this research we propose modeling landmine time-domain responses with a nonparametric Bayesian time-series model and we perform clustering of these time-series models with a hierarchical nonparametric Bayesian model. Each time-series is modeled as a hidden Markov model (HMM) with autoregressive (AR) state densities. The proposed nonparametric Bayesian prior allows for automated learning of the number of states in the HMM as well as the AR order within each state density. This creates a flexible time-series model with complexity determined by the data. Furthermore, a hierarchical non-parametric Bayesian prior is used to group landmine responses with similar HMM model parameters, thus learning the number of distinct landmine response models within a data set. Model inference is accomplished using a fast variational mean field approximation that can be implemented for on-line learning.
Weber, Stephanie A; Insaf, Tabassum Z; Hall, Eric S; Talbot, Thomas O; Huff, Amy K
2016-11-01
An enhanced research paradigm is presented to address the spatial and temporal gaps in fine particulate matter (PM2.5) measurements and generate realistic and representative concentration fields for use in epidemiological studies of human exposure to ambient air particulate concentrations. The general approach for research designed to analyze health impacts of exposure to PM2.5 is to use concentration data from the nearest ground-based air quality monitor(s), which typically have missing data on the temporal and spatial scales due to filter sampling schedules and monitor placement, respectively. To circumvent these data gaps, this research project uses a Hierarchical Bayesian Model (HBM) to generate estimates of PM2.5 in areas with and without air quality monitors by combining PM2.5 concentrations measured by monitors, PM2.5 concentration estimates derived from satellite aerosol optical depth (AOD) data, and Community-Multiscale Air Quality (CMAQ) model predictions of PM2.5 concentrations. This methodology represents a substantial step forward in the approach for developing representative PM2.5 concentration datasets to correlate with inpatient hospitalizations and emergency room visits data for asthma and inpatient hospitalizations for myocardial infarction (MI) and heart failure (HF) using case-crossover analysis. There were two key objective of this current study. First was to show that the inputs to the HBM could be expanded to include AOD data in addition to data from PM2.5 monitors and predictions from CMAQ. The second objective was to determine if inclusion of AOD surfaces in HBM model algorithms results in PM2.5 air pollutant concentration surfaces which more accurately predict hospital admittance and emergency room visits for MI, asthma, and HF. This study focuses on the New York City, NY metropolitan and surrounding areas during the 2004-2006 time period, in order to compare the health outcome impacts with those from previous studies and focus on any
ANALYSIS OF BAYESIAN CLASSIFIER ACCURACY
Directory of Open Access Journals (Sweden)
Felipe Schneider Costa
2013-01-01
Full Text Available The naÃ¯ve Bayes classifier is considered one of the most effective classification algorithms today, competing with more modern and sophisticated classifiers. Despite being based on unrealistic (naÃ¯ve assumption that all variables are independent, given the output class, the classifier provides proper results. However, depending on the scenario utilized (network structure, number of samples or training cases, number of variables, the network may not provide appropriate results. This study uses a process variable selection, using the chi-squared test to verify the existence of dependence between variables in the data model in order to identify the reasons which prevent a Bayesian network to provide good performance. A detailed analysis of the data is also proposed, unlike other existing work, as well as adjustments in case of limit values between two adjacent classes. Furthermore, variable weights are used in the calculation of a posteriori probabilities, calculated with mutual information function. Tests were applied in both a naÃ¯ve Bayesian network and a hierarchical Bayesian network. After testing, a significant reduction in error rate has been observed. The naÃ¯ve Bayesian network presented a drop in error rates from twenty five percent to five percent, considering the initial results of the classification process. In the hierarchical network, there was not only a drop in fifteen percent error rate, but also the final result came to zero.
Hierarchical topic modeling with nested hierarchical Dirichlet process
Institute of Scientific and Technical Information of China (English)
Yi-qun DING; Shan-ping LI; Zhen ZHANG; Bin SHEN
2009-01-01
This paper deals with the statistical modeling of latent topic hierarchies in text corpora. The height of the topic tree is assumed as fixed, while the number of topics on each level as unknown a priori and to be inferred from data. Taking a nonparametric Bayesian approach to this problem, we propose a new probabilistic generative model based on the nested hierarchical Dirichlet process (nHDP) and present a Markov chain Monte Carlo sampling algorithm for the inference of the topic tree structure as welt as the word distribution of each topic and topic distribution of each document. Our theoretical analysis and experiment results show that this model can produce a more compact hierarchical topic structure and captures more free-grained topic relationships compared to the hierarchical latent Dirichlet allocation model.
A variational Bayesian method to inverse problems with impulsive noise
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.
Visual tracker using sequential bayesian learning: discriminative, generative, and hybrid.
Lei, Yun; Ding, Xiaoqing; Wang, Shengjin
2008-12-01
This paper presents a novel solution to track a visual object under changes in illumination, viewpoint, pose, scale, and occlusion. Under the framework of sequential Bayesian learning, we first develop a discriminative model-based tracker with a fast relevance vector machine algorithm, and then, a generative model-based tracker with a novel sequential Gaussian mixture model algorithm. Finally, we present a three-level hierarchy to investigate different schemes to combine the discriminative and generative models for tracking. The presented hierarchical model combination contains the learner combination (at level one), classifier combination (at level two), and decision combination (at level three). The experimental results with quantitative comparisons performed on many realistic video sequences show that the proposed adaptive combination of discriminative and generative models achieves the best overall performance. Qualitative comparison with some state-of-the-art methods demonstrates the effectiveness and efficiency of our method in handling various challenges during tracking.
Bernardo, Jose M
2000-01-01
This highly acclaimed text, now available in paperback, provides a thorough account of key concepts and theoretical results, with particular emphasis on viewing statistical inference as a special case of decision theory. Information-theoretic concepts play a central role in the development of the theory, which provides, in particular, a detailed discussion of the problem of specification of so-called prior ignorance . The work is written from the authors s committed Bayesian perspective, but an overview of non-Bayesian theories is also provided, and each chapter contains a wide-ranging critica
Villalba, Jesús
2015-01-01
In this document we are going to derive the equations needed to implement a Variational Bayes estimation of the parameters of the simplified probabilistic linear discriminant analysis (SPLDA) model. This can be used to adapt SPLDA from one database to another with few development data or to implement the fully Bayesian recipe. Our approach is similar to Bishop's VB PPCA.
Li, Xin; Yu, Jiaguo; Jaroniec, Mietek
2016-05-01
As a green and sustainable technology, semiconductor-based heterogeneous photocatalysis has received much attention in the last few decades because it has potential to solve both energy and environmental problems. To achieve efficient photocatalysts, various hierarchical semiconductors have been designed and fabricated at the micro/nanometer scale in recent years. This review presents a critical appraisal of fabrication methods, growth mechanisms and applications of advanced hierarchical photocatalysts. Especially, the different synthesis strategies such as two-step templating, in situ template-sacrificial dissolution, self-templating method, in situ template-free assembly, chemically induced self-transformation and post-synthesis treatment are highlighted. Finally, some important applications including photocatalytic degradation of pollutants, photocatalytic H2 production and photocatalytic CO2 reduction are reviewed. A thorough assessment of the progress made in photocatalysis may open new opportunities in designing highly effective hierarchical photocatalysts for advanced applications ranging from thermal catalysis, separation and purification processes to solar cells.
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.
Energy Technology Data Exchange (ETDEWEB)
Tian, Yaxi; Cui, Guijia; Liu, Yan; Li, Haizhen; Sun, Zebin; Yan, Shiqiang, E-mail: yansq@lzu.edu.cn
2016-11-30
Highlights: • Hollow double silica @ mesoporous magnesium silicate magnetic hierarchical nanotubes were synthesized for the first time. • MgSNTs showed excellent prformance for the removal of low concentration methylene blue and high concentration rodamine B. • It could be easily discovered from solution. - Abstract: In this work, novel hollow double silica @ mesoporous magnesium silicate magnetic hierarchical nanotubes (MgSNTs) were successfully synthesized by using magnetic mesoporous silica nanocapsules (MSNCs) as morphology templates via a hydrothermal method for the first time. MgSNTs were characterized by transmission electron microscopy, Mapping, X-ray diffraction, Fourier transform infraed spetroscopy, N{sub 2} adorption-desorption, X-ray photoelectron spectroscopy and vibrating sample magnetometry. The synthesized MgSNTs with high specific surface area (588 m{sup 2}/g), average pore width (7.13 nm) and pore volume (1.05 cm{sup 3}/g) had high removal efficiency for low concentration methylene blue (70 mg/L, 299 mg/g) and high adsorption capacities for high concentration rodamine B (300 mg/L, 752 mg/g). Besides, it could be easily recovered due with the help of γ-Fe{sub 2}O{sub 3} in the inner chamber. Moreover, the adsorption capacity, the influence of pH, adsorption kinetics and adsorption mechanism were also carefully and comprehensively investigated. The results indicated that magnetic magnesium silicate nanotubes (MgSNTs) using mesoporous silica nanocapsules as the assisted templates were promsing adsorbents for water purification.
The DWG Data Fast Hierarchical Method Based on Attributes of the CASS%基于CASS属性的DWG数据快速分层方法
Institute of Scientific and Technical Information of China (English)
刘虎
2016-01-01
按照分层需求编制数据分层规则，并存储于数据库中。采用VBA语言编写分层程序，遍历DWG数据对象，读取其CASS码，检索分层规则确定所属图层，并将对象移动到目标图层中，实现对DWG数据的快速分层。此方法避免人工直接操作实体对象，效率和准确性较高。尤其在对大面积地形图进行分层时，相对人工分层，优势明显。%Data compiled in accordance with the rules of hierarchical stratification requirements and stored in the da-tabase. Layered program using VBA language,traversing DWG data object,read its CASS code,retrieve hierarchical rules to determine belongs layer,and the object is moved to the target layer,to achieve rapid stratification of DWG data. This method avoids artificial entity objects directly operated,high efficiency and accuracy. Especially when a large area topo-graphic map stratified,relatively artificial stratification,have obvious advantages.
Doing bayesian data analysis a tutorial with R and BUGS
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
Institute of Scientific and Technical Information of China (English)
王小龙; 宋裕农; 丁文强
2014-01-01
应用贝叶斯网络模型进行威胁估计是当前研究的热点和难点。提出了应用分层贝叶斯网络模型构建威胁估计网络，用于估计反潜编队对潜威胁等级。首先，对分层贝叶斯网络模型进行了简要的阐述，并对利用该模型进行威胁估计的可行性进行了分析。其次，分析了反潜编队对潜威胁产生的原因和机理，在此基础上，构建了威胁估计网络。最后，通过算例仿真验证了威胁估计网络的有效性。%Usage of bayesian network for threat evaluation is a hot and difficult problem. The threat evaluation network is constructed by the method of the bayesian network,which uses for evaluating the threat level of the anti-submarine war fleet. First,the principle of the bayesian network is constructed,and the feasibility of using bayesian network is analyzed for threat evaluation. Second, the causes and mechanism of the anti-submarine fleet submarine threat is analyzed,on this basis,the threat evaluation network is constructed. Finally,simulation experiment is used to verify the validity of the threat evaluation network constructed.
Hedlund, Jonas
2014-01-01
This paper introduces private sender information into a sender-receiver game of Bayesian persuasion with monotonic sender preferences. I derive properties of increasing differences related to the precision of signals and use these to fully characterize the set of equilibria robust to the intuitive criterion. In particular, all such equilibria are either separating, i.e., the sender's choice of signal reveals his private information to the receiver, or fully disclosing, i.e., the outcome of th...
Kirstein, Roland
2005-01-01
This paper presents a modification of the inspection game: The ?Bayesian Monitoring? model rests on the assumption that judges are interested in enforcing compliant behavior and making correct decisions. They may base their judgements on an informative but imperfect signal which can be generated costlessly. In the original inspection game, monitoring is costly and generates a perfectly informative signal. While the inspection game has only one mixed strategy equilibrium, three Perfect Bayesia...
Probability biases as Bayesian inference
Directory of Open Access Journals (Sweden)
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.
Bessiere, Pierre; Ahuactzin, Juan Manuel; Mekhnacha, Kamel
2013-01-01
Probability as an Alternative to Boolean LogicWhile logic is the mathematical foundation of rational reasoning and the fundamental principle of computing, it is restricted to problems where information is both complete and certain. However, many real-world problems, from financial investments to email filtering, are incomplete or uncertain in nature. Probability theory and Bayesian computing together provide an alternative framework to deal with incomplete and uncertain data. Decision-Making Tools and Methods for Incomplete and Uncertain DataEmphasizing probability as an alternative to Boolean
Bayesian astrostatistics: a backward look to the future
Loredo, Thomas J
2012-01-01
This perspective chapter briefly surveys: (1) past growth in the use of Bayesian methods in astrophysics; (2) current misconceptions about both frequentist and Bayesian statistical inference that hinder wider adoption of Bayesian methods by astronomers; and (3) multilevel (hierarchical) Bayesian modeling as a major future direction for research in Bayesian astrostatistics, exemplified in part by presentations at the first ISI invited session on astrostatistics, commemorated in this volume. It closes with an intentionally provocative recommendation for astronomical survey data reporting, motivated by the multilevel Bayesian perspective on modeling cosmic populations: that astronomers cease producing catalogs of estimated fluxes and other source properties from surveys. Instead, summaries of likelihood functions (or marginal likelihood functions) for source properties should be reported (not posterior probability density functions), including nontrivial summaries (not simply upper limits) for candidate objects ...
ProFit: Bayesian galaxy fitting tool
Robotham, A. S. G.; Taranu, D.; Tobar, R.
2016-12-01
ProFit is a Bayesian galaxy fitting tool that uses the fast C++ image generation library libprofit (ascl:1612.003) and a flexible R interface to a large number of likelihood samplers. It offers a fully featured Bayesian interface to galaxy model fitting (also called profiling), using mostly the same standard inputs as other popular codes (e.g. GALFIT ascl:1104.010), but it is also able to use complex priors and a number of likelihoods.
Petra, N.; Alexanderian, A.; Stadler, G.; Ghattas, O.
2015-12-01
We address the problem of optimal experimental design (OED) for Bayesian nonlinear inverse problems governed by partial differential equations (PDEs). The inverse problem seeks to infer a parameter field (e.g., the log permeability field in a porous medium flow model problem) from synthetic observations at a set of sensor locations and from the governing PDEs. The goal of the OED problem is to find an optimal placement of sensors so as to minimize the uncertainty in the inferred parameter field. We formulate the OED objective function by generalizing the classical A-optimal experimental design criterion using the expected value of the trace of the posterior covariance. This expected value is computed through sample averaging over the set of likely experimental data. Due to the infinite-dimensional character of the parameter field, we seek an optimization method that solves the OED problem at a cost (measured in the number of forward PDE solves) that is independent of both the parameter and the sensor dimension. To facilitate this goal, we construct a Gaussian approximation to the posterior at the maximum a posteriori probability (MAP) point, and use the resulting covariance operator to define the OED objective function. We use randomized trace estimation to compute the trace of this covariance operator. The resulting OED problem includes as constraints the system of PDEs characterizing the MAP point, and the PDEs describing the action of the covariance (of the Gaussian approximation to the posterior) to vectors. We control the sparsity of the sensor configurations using sparsifying penalty functions, and solve the resulting penalized bilevel optimization problem via an interior-point quasi-Newton method, where gradient information is computed via adjoints. We elaborate our OED method for the problem of determining the optimal sensor configuration to best infer the log permeability field in a porous medium flow problem. Numerical results show that the number of PDE
The Infinite Hierarchical Factor Regression Model
Rai, Piyush
2009-01-01
We propose a nonparametric Bayesian factor regression model that accounts for uncertainty in the number of factors, and the relationship between factors. To accomplish this, we propose a sparse variant of the Indian Buffet Process and couple this with a hierarchical model over factors, based on Kingman's coalescent. We apply this model to two problems (factor analysis and factor regression) in gene-expression data analysis.
Hierarchical Reverberation Mapping
Brewer, Brendon J
2013-01-01
Reverberation mapping (RM) is an important technique in studies of active galactic nuclei (AGN). The key idea of RM is to measure the time lag $\\tau$ between variations in the continuum emission from the accretion disc and subsequent response of the broad line region (BLR). The measurement of $\\tau$ is typically used to estimate the physical size of the BLR and is combined with other measurements to estimate the black hole mass $M_{\\rm BH}$. A major difficulty with RM campaigns is the large amount of data needed to measure $\\tau$. Recently, Fine et al (2012) introduced a new approach to RM where the BLR light curve is sparsely sampled, but this is counteracted by observing a large sample of AGN, rather than a single system. The results are combined to infer properties of the sample of AGN. In this letter we implement this method using a hierarchical Bayesian model and contrast this with the results from the previous stacked cross-correlation technique. We find that our inferences are more precise and allow fo...
Evaluation of hierarchical temporal memory for a real world application
Melis, Wim J.C.; Chizuwa, Shuhei; Kameyama, Michitaka
2010-01-01
A large number of real world applications, such as user support systems, can still not be performed easily by conventional algorithms in comparison with the human brain. Such intelligence is often implemented, by using probability based systems. This paper focuses on comparing the implementation of a cellular phone intention estimation example on a Bayesian Network and Hierarchical Temporal Memory. It is found that Hierarchical Temporal Memory is a system that requires little effort for desig...
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...
Introduction to Bayesian statistics
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...
Bayesian data analysis in population ecology: motivations, methods, and benefits
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.
Bayesian artificial intelligence
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 artificial intelligence
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.
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...... is largely due to the availability of efficient inference algorithms for answering probabilistic queries about the states of the variables in the network. Furthermore, to support the construction of Bayesian network models, learning algorithms are also available. We give an overview of the Bayesian network...
Institute of Scientific and Technical Information of China (English)
曹怀术; 廖华
2013-01-01
In this paper, the public's willingness to pay for the long-run air quality improvement is examined based on the internet survey data and the employed multinomial Probit model is estimated in a hierarchical Bayes framework. Our results show that the public's willingness to pay for the long-run increase in air quality to the best level in our survey in 20 years is about 47 RMB per person per month for the next 5 years, and the discount rate of that payment is about 3.8%.%公众改善环境之意愿的最直接体现是支付意愿.在介绍了多项式概率模型及其层次贝叶斯估计方法后,利用问卷数据研究了北京市公众(大学生群体)对于改善长期空气质量的支付意愿.结果显示,为了在20年内北京市空气质量良级天数(API＜100)达到90％以上,公众的支付意愿为未来5年47元/人/月,支付意愿随时间的贴现率大约为3.8％.
Institute of Scientific and Technical Information of China (English)
何永强; 宫玉荣; 朱予聪
2015-01-01
提出了运用贝叶斯理论和层次模型对传感器网络节点故障进行预测的方法，结合传感器网络各节点处理信息的时序关系，用定性分析将时间信息融合到节点中分析故障传播机制和故障预测。根据节点的历史信息和当前运行情况，预测和确定节点的故障概率；利用参数学习和概率推理，预测上层节点的故障概率。通过仿真实验并与其他预测方法进行比较分析，验证了该方法的可靠性和精确性，为传感器网络节点的故障预测提供了新的思路和方法。%This paper presents the method for sensor network node failure prediction with the relationship between timing and level using Bayesian model methods. The method combines processing information in each node sensor network and uses qualitative analysis to integrate time information into the node to analyze the fault propagation mechanism and failure prediction. According to the probabili-ty of failure history information of node and the current operating conditions,nodes failure probabilities are forecasted and determined. Using the parameters of learning and probabilistic reasoning,the probability of failure of the upper node is predicted. Through simula-tion analysis and comparative analysis with other forecasting methods,the accuracy and precision of the method for sensor network node failure prediction is verified,providing new ideas and methods for nodes failure detection.
An introduction to Bayesian statistics in health psychology.
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.
Flexible Bayesian Human Fecundity Models.
Kim, Sungduk; Sundaram, Rajeshwari; Buck Louis, Germaine M; Pyper, Cecilia
2012-12-01
Human fecundity is an issue of considerable interest for both epidemiological and clinical audiences, and is dependent upon a couple's biologic capacity for reproduction coupled with behaviors that place a couple at risk for pregnancy. Bayesian hierarchical models have been proposed to better model the conception probabilities by accounting for the acts of intercourse around the day of ovulation, i.e., during the fertile window. These models can be viewed in the framework of a generalized nonlinear model with an exponential link. However, a fixed choice of link function may not always provide the best fit, leading to potentially biased estimates for probability of conception. Motivated by this, we propose a general class of models for fecundity by relaxing the choice of the link function under the generalized nonlinear model framework. We use a sample from the Oxford Conception Study (OCS) to illustrate the utility and fit of this general class of models for estimating human conception. Our findings reinforce the need for attention to be paid to the choice of link function in modeling conception, as it may bias the estimation of conception probabilities. Various properties of the proposed models are examined and a Markov chain Monte Carlo sampling algorithm was developed for implementing the Bayesian computations. The deviance information criterion measure and logarithm of pseudo marginal likelihood are used for guiding the choice of links. The supplemental material section contains technical details of the proof of the theorem stated in the paper, and contains further simulation results and analysis.
Bayesian modeling in conjoint analysis
Directory of Open Access Journals (Sweden)
Janković-Milić Vesna
2010-01-01
Full Text Available Statistical analysis in marketing is largely influenced by the availability of various types of data. There is sudden increase in the number and types of information available to market researchers in the last decade. In such conditions, traditional statistical methods have limited ability to solve problems related to the expression of market uncertainty. The aim of this paper is to highlight the advantages of bayesian inference, as an alternative approach to classical inference. Multivariate statistic methods offer extremely powerful tools to achieve many goals of marketing research. One of these methods is the conjoint analysis, which provides a quantitative measure of the relative importance of product or service attributes in relation to the other attribute. The application of this method involves interviewing consumers, where they express their preferences, and statistical analysis provides numerical indicators of each attribute utility. One of the main objections to the method of discrete choice in the conjoint analysis is to use this method to estimate the utility only at the aggregate level and by expressing the average utility for all respondents in the survey. Application of hierarchical Bayesian models enables capturing of individual utility ratings for each attribute level.
DEFF Research Database (Denmark)
Thomadsen, Tommy
2005-01-01
of different types of hierarchical networks. This is supplemented by a review of ring network design problems and a presentation of a model allowing for modeling most hierarchical networks. We use methods based on linear programming to design the hierarchical networks. Thus, a brief introduction to the various....... The thesis investigates models for hierarchical network design and methods used to design such networks. In addition, ring network design is considered, since ring networks commonly appear in the design of hierarchical networks. The thesis introduces hierarchical networks, including a classification scheme...... linear programming based methods is included. The thesis is thus suitable as a foundation for study of design of hierarchical networks. The major contribution of the thesis consists of seven papers which are included in the appendix. The papers address hierarchical network design and/or ring network...
A Bayesian formulation of seismic fragility analysis of safety related equipment
Energy Technology Data Exchange (ETDEWEB)
Wang, Z-L.; Pandey, M.; Xie, W-C., E-mail: z268wang@uwaterloo.ca, E-mail: mdpandey@uwaterloo.ca, E-mail: xie@uwaterloo.ca [Univ. of Waterloo, Ontario (Canada)
2013-07-01
A Bayesian approach to seismic fragility analysis of safety-related equipment is formulated. Unlike treating two sources of uncertainty of in the parameter estimation in two steps separately using the classical statistics, a Bayesian hierarchical model is advocated for interpreting and combining the various uncertainties more clearly in this article. In addition, with the availability of additional earthquake experience data and shaking table test results, a Bayesian approach to updating the fragility model of safety-related equipment is formulated by incorporating acquired failure and survivor evidence. Numerical results show the significance in fragility analysis using the Bayesian approach. (author)
Hierarchical Multiagent Reinforcement Learning
2004-01-25
In this paper, we investigate the use of hierarchical reinforcement learning (HRL) to speed up the acquisition of cooperative multiagent tasks. We...introduce a hierarchical multiagent reinforcement learning (RL) framework and propose a hierarchical multiagent RL algorithm called Cooperative HRL. In
Hierarchical modularity in human brain functional networks
Meunier, D; Fornito, A; Ersche, K D; Bullmore, E T; 10.3389/neuro.11.037.2009
2010-01-01
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 ...
Robust Bayesian Regularized Estimation Based on t Regression Model
Directory of Open Access Journals (Sweden)
Zean Li
2015-01-01
Full Text Available The t distribution is a useful extension of the normal distribution, which can be used for statistical modeling of data sets with heavy tails, and provides robust estimation. In this paper, in view of the advantages of Bayesian analysis, we propose a new robust coefficient estimation and variable selection method based on Bayesian adaptive Lasso t regression. A Gibbs sampler is developed based on the Bayesian hierarchical model framework, where we treat the t distribution as a mixture of normal and gamma distributions and put different penalization parameters for different regression coefficients. We also consider the Bayesian t regression with adaptive group Lasso and obtain the Gibbs sampler from the posterior distributions. Both simulation studies and real data example show that our method performs well compared with other existing methods when the error distribution has heavy tails and/or outliers.
Bayesian Games with Intentions
Directory of Open Access Journals (Sweden)
Adam Bjorndahl
2016-06-01
Full Text Available We show that standard Bayesian games cannot represent the full spectrum of belief-dependent preferences. However, by introducing a fundamental distinction between intended and actual strategies, we remove this limitation. We define Bayesian games with intentions, generalizing both Bayesian games and psychological games, and prove that Nash equilibria in psychological games correspond to a special class of equilibria as defined in our setting.
Bayesian Population Projections for the United Nations.
Raftery, Adrian E; Alkema, Leontine; Gerland, Patrick
2014-02-01
The United Nations regularly publishes projections of the populations of all the world's countries broken down by age and sex. These projections are the de facto standard and are widely used by international organizations, governments and researchers. Like almost all other population projections, they are produced using the standard deterministic cohort-component projection method and do not yield statements of uncertainty. We describe a Bayesian method for producing probabilistic population projections for most countries that the United Nations could use. It has at its core Bayesian hierarchical models for the total fertility rate and life expectancy at birth. We illustrate the method and show how it can be extended to address concerns about the UN's current assumptions about the long-term distribution of fertility. The method is implemented in the R packages bayesTFR, bayesLife, bayesPop and bayesDem.
Understanding Computational Bayesian Statistics
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
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
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...... 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....... The thesis investigates models for hierarchical network design and methods used to design such networks. In addition, ring network design is considered, since ring networks commonly appear in the design of hierarchical networks. The thesis introduces hierarchical networks, including a classification scheme...
What are hierarchical models and how do we analyze them?
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)
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…
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.
Introduction to applied Bayesian statistics and estimation for social scientists
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 Hierarchical Models to Augment the Mediterranean Forecast System
2016-06-07
terms of the standard deviations (computed over 10 ensemble members) of sea surface height ( SSH ; top panel) and sea surface temperature (SST; bottom...mean SSH forecast (top panel) and SSH standard deviation of the ensemble forecast (bottom panel) on day 10 of the forecast. The concentration of...spread for SSH (top panel; cm) and SST (bottom panel; ° C). The standard deviation of the SSH and SST are computed at day 14 of the data assimilation
Bayesian Hierarchical Models to Augment the Mediterranean Forecast System
2012-02-17
Climate, 21, 1891-1910. Berliner, L.M. and C.K. Wikle, 2007: Approximate importance sampling Monte Carlo for data assimilation, Physica D, 230, 37-49...representations for spatial processes, In: Handbook of Spatial Statis- tics, A.Gelfand, P. Diggle, M. Fuentes , P. Guttorp (eds), Chapman and Hall. 107-118. Wikle
Bayesian Hierarchical Modeling of Cardiac Response to Particulate Matter Exposure
Studies have linked increased levels of particulate air pollution to decreased autonomic control, as measured by heart rate variability (HRV), particularly in populations such as the elderly. In this study, we use data obtained from the 1998 USEPA epidemiology-exposure longitudin...
Hierarchical Bayesian parameter estimation for cumulative prospect theory
Nilsson, H.; Rieskamp, J.; Wagenmakers, E.-J.
2011-01-01
Cumulative prospect theory (CPT Tversky & Kahneman, 1992) has provided one of the most influential accounts of how people make decisions under risk. CPT is a formal model with parameters that quantify psychological processes such as loss aversion, subjective values of gains and losses, and
Bayesian hierarchical error model for analysis of gene expression data
National Research Council Canada - National Science Library
Cho, HyungJun; Lee, Jae K
2004-01-01
.... Moreover, the same gene often shows quite heterogeneous error variability under different biological and experimental conditions, which must be estimated separately for evaluating the statistical...
Hierarchical Bayesian inference of galaxy redshift distributions from photometric surveys
Leistedt, Boris; Peiris, Hiranya V
2016-01-01
Accurately characterizing the redshift distributions of galaxies is essential for analysing deep photometric surveys and testing cosmological models. We present a technique to simultaneously infer redshift distributions and individual redshifts from photometric galaxy catalogues. Our model constructs a piecewise constant representation (effectively a histogram) of the distribution of galaxy types and redshifts, the parameters of which are efficiently inferred from noisy photometric flux measurements. This approach can be seen as a generalization of template-fitting photometric redshift methods and relies on a library of spectral templates to relate the photometric fluxes of individual galaxies to their redshifts. We illustrate this technique on simulated galaxy survey data, and demonstrate that it delivers correct posterior distributions on the underlying type and redshift distributions, as well as on the individual types and redshifts of galaxies. We show that even with uninformative priors, large photometri...
Konstruksi Bayesian Network Dengan Algoritma Bayesian Association Rule Mining Network
Octavian
2015-01-01
Beberapa tahun terakhir, Bayesian Network telah menjadi konsep yang populer digunakan dalam berbagai bidang kehidupan seperti dalam pengambilan sebuah keputusan dan menentukan peluang suatu kejadian dapat terjadi. Sayangnya, pengkonstruksian struktur dari Bayesian Network itu sendiri bukanlah hal yang sederhana. Oleh sebab itu, penelitian ini mencoba memperkenalkan algoritma Bayesian Association Rule Mining Network untuk memudahkan kita dalam mengkonstruksi Bayesian Network berdasarkan data ...
Learning Bayesian Networks from Data by Particle Swarm Optimization
Institute of Scientific and Technical Information of China (English)
无
2006-01-01
Learning Bayesian network is an NP-hard problem. When the number of variables is large, the process of searching optimal network structure could be very time consuming and tends to return a structure which is local optimal. The particle swarm optimization (PSO) was introduced to the problem of learning Bayesian networks and a novel structure learning algorithm using PSO was proposed. To search in directed acyclic graphs spaces efficiently, a discrete PSO algorithm especially for structure learning was proposed based on the characteristics of Bayesian networks. The results of experiments show that our PSO based algorithm is fast for convergence and can obtain better structures compared with genetic algorithm based algorithms.
Bayesian distributed articulated object tracking using multiple collaborative trackers
Qu, Wei; Schonfeld, Dan
2007-01-01
In this paper, we propose two novel articulated object tracking approaches. The Decentralized Articulated Object Tracking approach avoids the common practice of using a high-dimensional joint state representation for articulated object tracking. Instead, it introduces a decentralized scheme and models the inter-part interaction within an innovative Bayesian framework. To handle severe self-occlusions, we further extend the first approach by modeling high-level inter-unit interactions and develop the Hierarchical Articulated Object Tracking algorithm within a consistent hierarchical framework. Preliminary experimental results have demonstrated the superior performance of the proposed approaches for real-world videos sequences.
Model Diagnostics for Bayesian Networks
Sinharay, Sandip
2006-01-01
Bayesian networks are frequently used in educational assessments primarily for learning about students' knowledge and skills. There is a lack of works on assessing fit of Bayesian networks. This article employs the posterior predictive model checking method, a popular Bayesian model checking tool, to assess fit of simple Bayesian networks. A…
Bayesian data analysis for newcomers.
Kruschke, John K; Liddell, Torrin M
2017-04-12
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.
Bayesian model reduction and empirical Bayes for group (DCM) studies.
Friston, Karl J; Litvak, Vladimir; Oswal, Ashwini; Razi, Adeel; Stephan, Klaas E; van Wijk, Bernadette C M; Ziegler, Gabriel; Zeidman, Peter
2016-03-01
This technical note describes some Bayesian procedures for the analysis of group studies that use nonlinear models at the first (within-subject) level - e.g., dynamic causal models - and linear models at subsequent (between-subject) levels. Its focus is on using Bayesian model reduction to finesse the inversion of multiple models of a single dataset or a single (hierarchical or empirical Bayes) model of multiple datasets. These applications of Bayesian model reduction allow one to consider parametric random effects and make inferences about group effects very efficiently (in a few seconds). We provide the relatively straightforward theoretical background to these procedures and illustrate their application using a worked example. This example uses a simulated mismatch negativity study of schizophrenia. We illustrate the robustness of Bayesian model reduction to violations of the (commonly used) Laplace assumption in dynamic causal modelling and show how its recursive application can facilitate both classical and Bayesian inference about group differences. Finally, we consider the application of these empirical Bayesian procedures to classification and prediction.
Bayesian Compressed Sensing with Unknown Measurement Noise Level
DEFF Research Database (Denmark)
Hansen, Thomas Lundgaard; Jørgensen, Peter Bjørn; Pedersen, Niels Lovmand
2013-01-01
algorithms based on the fast inference scheme noise precision estimation results in increased computational complexity and reconstruction error. We propose a three-layer hierarchical prior model which allows for the derivation of a fast inference algorithm that estimates the noise precision...
Fox, G.J.A.; Berg, van den S.M.; Veldkamp, B.P.; Irwing, P.; Booth, T.; Hughes, D.
2015-01-01
In educational and psychological studies, psychometric methods are involved in the measurement of constructs, and in constructing and validating measurement instruments. Assessment results are typically used to measure student proficiency levels and test characteristics. Recently, Bayesian item resp
Fox, Gerardus J.A.; van den Berg, Stéphanie Martine; Veldkamp, Bernard P.; Irwing, P.; Booth, T.; Hughes, D.
2015-01-01
In educational and psychological studies, psychometric methods are involved in the measurement of constructs, and in constructing and validating measurement instruments. Assessment results are typically used to measure student proficiency levels and test characteristics. Recently, Bayesian item
Granade, Christopher; Cory, D G
2015-01-01
In recent years, Bayesian methods have been proposed as a solution to a wide range of issues in quantum state and process tomography. State-of- the-art Bayesian tomography solutions suffer from three problems: numerical intractability, a lack of informative prior distributions, and an inability to track time-dependent processes. Here, we solve all three problems. First, we use modern statistical methods, as pioneered by Husz\\'ar and Houlsby and by Ferrie, to make Bayesian tomography numerically tractable. Our approach allows for practical computation of Bayesian point and region estimators for quantum states and channels. Second, we propose the first informative priors on quantum states and channels. Finally, we develop a method that allows online tracking of time-dependent states and estimates the drift and diffusion processes affecting a state. We provide source code and animated visual examples for our methods.
Discriminative Bayesian Dictionary Learning for Classification.
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.
A Bayesian Predictive Discriminant Analysis with Screened Data
Hea-Jung Kim
2015-01-01
In the application of discriminant analysis, a situation sometimes arises where individual measurements are screened by a multidimensional screening scheme. For this situation, a discriminant analysis with screened populations is considered from a Bayesian viewpoint, and an optimal predictive rule for the analysis is proposed. In order to establish a flexible method to incorporate the prior information of the screening mechanism, we propose a hierarchical screened scale mixture of normal (HSS...
Bayesian seismic AVO inversion
Energy Technology Data Exchange (ETDEWEB)
Buland, Arild
2002-07-01
A new linearized AVO inversion technique is developed in a Bayesian framework. The objective is to obtain posterior distributions for P-wave velocity, S-wave velocity and density. Distributions for other elastic parameters can also be assessed, for example acoustic impedance, shear impedance and P-wave to S-wave velocity ratio. The inversion algorithm is based on the convolutional model and a linearized weak contrast approximation of the Zoeppritz equation. The solution is represented by a Gaussian posterior distribution with explicit expressions for the posterior expectation and covariance, hence exact prediction intervals for the inverted parameters can be computed under the specified model. The explicit analytical form of the posterior distribution provides a computationally fast inversion method. Tests on synthetic data show that all inverted parameters were almost perfectly retrieved when the noise approached zero. With realistic noise levels, acoustic impedance was the best determined parameter, while the inversion provided practically no information about the density. The inversion algorithm has also been tested on a real 3-D dataset from the Sleipner Field. The results show good agreement with well logs but the uncertainty is high. The stochastic model includes uncertainties of both the elastic parameters, the wavelet and the seismic and well log data. The posterior distribution is explored by Markov chain Monte Carlo simulation using the Gibbs sampler algorithm. The inversion algorithm has been tested on a seismic line from the Heidrun Field with two wells located on the line. The uncertainty of the estimated wavelet is low. In the Heidrun examples the effect of including uncertainty of the wavelet and the noise level was marginal with respect to the AVO inversion results. We have developed a 3-D linearized AVO inversion method with spatially coupled model parameters where the objective is to obtain posterior distributions for P-wave velocity, S
A Goal-Directed Bayesian Framework for Categorization
Rigoli, Francesco; Pezzulo, Giovanni; Dolan, Raymond; Friston, Karl
2017-01-01
Categorization is a fundamental ability for efficient behavioral control. It allows organisms to remember the correct responses to categorical cues and not for every stimulus encountered (hence eluding computational cost or complexity), and to generalize appropriate responses to novel stimuli dependant on category assignment. Assuming the brain performs Bayesian inference, based on a generative model of the external world and future goals, we propose a computational model of categorization in which important properties emerge. These properties comprise the ability to infer latent causes of sensory experience, a hierarchical organization of latent causes, and an explicit inclusion of context and action representations. Crucially, these aspects derive from considering the environmental statistics that are relevant to achieve goals, and from the fundamental Bayesian principle that any generative model should be preferred over alternative models based on an accuracy-complexity trade-off. Our account is a step toward elucidating computational principles of categorization and its role within the Bayesian brain hypothesis.
Robust full Bayesian learning for radial basis networks.
Andrieu, C; de Freitas, N; Doucet, A
2001-10-01
We propose a hierarchical full Bayesian model for radial basis networks. This model treats the model dimension (number of neurons), model parameters, regularization parameters, and noise parameters as unknown random variables. We develop a reversible-jump Markov chain Monte Carlo (MCMC) method to perform the Bayesian computation. We find that the results obtained using this method are not only better than the ones reported previously, but also appear to be robust with respect to the prior specification. In addition, we propose a novel and computationally efficient reversible-jump MCMC simulated annealing algorithm to optimize neural networks. This algorithm enables us to maximize the joint posterior distribution of the network parameters and the number of basis function. It performs a global search in the joint space of the parameters and number of parameters, thereby surmounting the problem of local minima to a large extent. We show that by calibrating the full hierarchical Bayesian prior, we can obtain the classical Akaike information criterion, Bayesian information criterion, and minimum description length model selection criteria within a penalized likelihood framework. Finally, we present a geometric convergence theorem for the algorithm with homogeneous transition kernel and a convergence theorem for the reversible-jump MCMC simulated annealing method.
Bayesian methods for the design and analysis of noninferiority trials.
Gamalo-Siebers, Margaret; Gao, Aijun; Lakshminarayanan, Mani; Liu, Guanghan; Natanegara, Fanni; Railkar, Radha; Schmidli, Heinz; Song, Guochen
2016-01-01
The gold standard for evaluating treatment efficacy of a medical product is a placebo-controlled trial. However, when the use of placebo is considered to be unethical or impractical, a viable alternative for evaluating treatment efficacy is through a noninferiority (NI) study where a test treatment is compared to an active control treatment. The minimal objective of such a study is to determine whether the test treatment is superior to placebo. An assumption is made that if the active control treatment remains efficacious, as was observed when it was compared against placebo, then a test treatment that has comparable efficacy with the active control, within a certain range, must also be superior to placebo. Because of this assumption, the design, implementation, and analysis of NI trials present challenges for sponsors and regulators. In designing and analyzing NI trials, substantial historical data are often required on the active control treatment and placebo. Bayesian approaches provide a natural framework for synthesizing the historical data in the form of prior distributions that can effectively be used in design and analysis of a NI clinical trial. Despite a flurry of recent research activities in the area of Bayesian approaches in medical product development, there are still substantial gaps in recognition and acceptance of Bayesian approaches in NI trial design and analysis. The Bayesian Scientific Working Group of the Drug Information Association provides a coordinated effort to target the education and implementation issues on Bayesian approaches for NI trials. In this article, we provide a review of both frequentist and Bayesian approaches in NI trials, and elaborate on the implementation for two common Bayesian methods including hierarchical prior method and meta-analytic-predictive approach. Simulations are conducted to investigate the properties of the Bayesian methods, and some real clinical trial examples are presented for illustration.
Application of hierarchical matrices for partial inverse
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.
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...
Hierarchical auxetic mechanical metamaterials.
Gatt, Ruben; Mizzi, Luke; Azzopardi, Joseph I; Azzopardi, Keith M; Attard, Daphne; Casha, Aaron; Briffa, Joseph; Grima, Joseph N
2015-02-11
Auxetic mechanical metamaterials are engineered systems that exhibit the unusual macroscopic property of a negative Poisson's ratio due to sub-unit structure rather than chemical composition. Although their unique behaviour makes them superior to conventional materials in many practical applications, they are limited in availability. Here, we propose a new class of hierarchical auxetics based on the rotating rigid units mechanism. These systems retain the enhanced properties from having a negative Poisson's ratio with the added benefits of being a hierarchical system. Using simulations on typical hierarchical multi-level rotating squares, we show that, through design, one can control the extent of auxeticity, degree of aperture and size of the different pores in the system. This makes the system more versatile than similar non-hierarchical ones, making them promising candidates for industrial and biomedical applications, such as stents and skin grafts.
Introduction into Hierarchical Matrices
Litvinenko, Alexander
2013-12-05
Hierarchical matrices allow us to reduce computational storage and cost from cubic to almost linear. This technique can be applied for solving PDEs, integral equations, matrix equations and approximation of large covariance and precision matrices.
Hierarchical Auxetic Mechanical Metamaterials
Gatt, Ruben; Mizzi, Luke; Azzopardi, Joseph I.; Azzopardi, Keith M.; Attard, Daphne; Casha, Aaron; Briffa, Joseph; Grima, Joseph N.
2015-02-01
Auxetic mechanical metamaterials are engineered systems that exhibit the unusual macroscopic property of a negative Poisson's ratio due to sub-unit structure rather than chemical composition. Although their unique behaviour makes them superior to conventional materials in many practical applications, they are limited in availability. Here, we propose a new class of hierarchical auxetics based on the rotating rigid units mechanism. These systems retain the enhanced properties from having a negative Poisson's ratio with the added benefits of being a hierarchical system. Using simulations on typical hierarchical multi-level rotating squares, we show that, through design, one can control the extent of auxeticity, degree of aperture and size of the different pores in the system. This makes the system more versatile than similar non-hierarchical ones, making them promising candidates for industrial and biomedical applications, such as stents and skin grafts.
Programming with Hierarchical Maps
DEFF Research Database (Denmark)
Ørbæk, Peter
This report desribes the hierarchical maps used as a central data structure in the Corundum framework. We describe its most prominent features, ague for its usefulness and briefly describe some of the software prototypes implemented using the technology....
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...
Bayesian Face Sketch Synthesis.
Wang, Nannan; Gao, Xinbo; Sun, Leiyu; Li, Jie
2017-03-01
Exemplar-based face sketch synthesis has been widely applied to both digital entertainment and law enforcement. In this paper, we propose a Bayesian framework for face sketch synthesis, which provides a systematic interpretation for understanding the common properties and intrinsic difference in different methods from the perspective of probabilistic graphical models. The proposed Bayesian framework consists of two parts: the neighbor selection model and the weight computation model. Within the proposed framework, we further propose a Bayesian face sketch synthesis method. The essential rationale behind the proposed Bayesian method is that we take the spatial neighboring constraint between adjacent image patches into consideration for both aforementioned models, while the state-of-the-art methods neglect the constraint either in the neighbor selection model or in the weight computation model. Extensive experiments on the Chinese University of Hong Kong face sketch database demonstrate that the proposed Bayesian method could achieve superior performance compared with the state-of-the-art methods in terms of both subjective perceptions and objective evaluations.
APPLICATION OF HIERARCHICAL REINFORCEMENT LEARNING IN ENGINEERING DOMAIN
Institute of Scientific and Technical Information of China (English)
WEI LI; Qingtai YE; Changming ZHU
2005-01-01
The slow convergence rate of reinforcement learning algorithms limits their wider application.In engineering domains, hierarchical reinforcement learning is developed to perform actions temporally according to prior knowledge. This system can converge fast due to reduced state space.There is a test of elevator group control to show the power of the new system. Two conventional group control algorithms are adopted as prior knowledge. Performance indicates that hierarchical reinforcement learning can reduce the learning time dramatically.
Center, Julian L.; Knuth, Kevin H.
2011-03-01
Visual odometry refers to tracking the motion of a body using an onboard vision system. Practical visual odometry systems combine the complementary accuracy characteristics of vision and inertial measurement units. The Mars Exploration Rovers, Spirit and Opportunity, used this type of visual odometry. The visual odometry algorithms in Spirit and Opportunity were based on Bayesian methods, but a number of simplifying approximations were needed to deal with onboard computer limitations. Furthermore, the allowable motion of the rover had to be severely limited so that computations could keep up. Recent advances in computer technology make it feasible to implement a fully Bayesian approach to visual odometry. This approach combines dense stereo vision, dense optical flow, and inertial measurements. As with all true Bayesian methods, it also determines error bars for all estimates. This approach also offers the possibility of using Micro-Electro Mechanical Systems (MEMS) inertial components, which are more economical, weigh less, and consume less power than conventional inertial components.
Hybrid Batch Bayesian Optimization
Azimi, Javad; Fern, Xiaoli
2012-01-01
Bayesian Optimization aims at optimizing an unknown non-convex/concave function that is costly to evaluate. We are interested in application scenarios where concurrent function evaluations are possible. Under such a setting, BO could choose to either sequentially evaluate the function, one input at a time and wait for the output of the function before making the next selection, or evaluate the function at a batch of multiple inputs at once. These two different settings are commonly referred to as the sequential and batch settings of Bayesian Optimization. In general, the sequential setting leads to better optimization performance as each function evaluation is selected with more information, whereas the batch setting has an advantage in terms of the total experimental time (the number of iterations). In this work, our goal is to combine the strength of both settings. Specifically, we systematically analyze Bayesian optimization using Gaussian process as the posterior estimator and provide a hybrid algorithm t...
Bayesian least squares deconvolution
Asensio Ramos, A.; Petit, P.
2015-11-01
Aims: We develop a fully Bayesian least squares deconvolution (LSD) that can be applied to the reliable detection of magnetic signals in noise-limited stellar spectropolarimetric observations using multiline techniques. Methods: We consider LSD under the Bayesian framework and we introduce a flexible Gaussian process (GP) prior for the LSD profile. This prior allows the result to automatically adapt to the presence of signal. We exploit several linear algebra identities to accelerate the calculations. The final algorithm can deal with thousands of spectral lines in a few seconds. Results: We demonstrate the reliability of the method with synthetic experiments and we apply it to real spectropolarimetric observations of magnetic stars. We are able to recover the magnetic signals using a small number of spectral lines, together with the uncertainty at each velocity bin. This allows the user to consider if the detected signal is reliable. The code to compute the Bayesian LSD profile is freely available.
Bayesian Exploratory Factor Analysis
DEFF Research Database (Denmark)
Conti, Gabriella; Frühwirth-Schnatter, Sylvia; Heckman, James J.;
2014-01-01
This paper develops and applies a Bayesian approach to Exploratory Factor Analysis that improves on ad hoc classical approaches. Our framework relies on dedicated factor models and simultaneously determines the number of factors, the allocation of each measurement to a unique factor, and the corr......This paper develops and applies a Bayesian approach to Exploratory Factor Analysis that improves on ad hoc classical approaches. Our framework relies on dedicated factor models and simultaneously determines the number of factors, the allocation of each measurement to a unique factor......, and the corresponding factor loadings. Classical identification criteria are applied and integrated into our Bayesian procedure to generate models that are stable and clearly interpretable. A Monte Carlo study confirms the validity of the approach. The method is used to produce interpretable low dimensional aggregates...
Bayesian least squares deconvolution
Ramos, A Asensio
2015-01-01
Aims. To develop a fully Bayesian least squares deconvolution (LSD) that can be applied to the reliable detection of magnetic signals in noise-limited stellar spectropolarimetric observations using multiline techniques. Methods. We consider LSD under the Bayesian framework and we introduce a flexible Gaussian Process (GP) prior for the LSD profile. This prior allows the result to automatically adapt to the presence of signal. We exploit several linear algebra identities to accelerate the calculations. The final algorithm can deal with thousands of spectral lines in a few seconds. Results. We demonstrate the reliability of the method with synthetic experiments and we apply it to real spectropolarimetric observations of magnetic stars. We are able to recover the magnetic signals using a small number of spectral lines, together with the uncertainty at each velocity bin. This allows the user to consider if the detected signal is reliable. The code to compute the Bayesian LSD profile is freely available.
Probabilistic Inferences in Bayesian Networks
Ding, Jianguo
2010-01-01
This chapter summarizes the popular inferences methods in Bayesian networks. The results demonstrates that the evidence can propagated across the Bayesian networks by any links, whatever it is forward or backward or intercausal style. The belief updating of Bayesian networks can be obtained by various available inference techniques. Theoretically, exact inferences in Bayesian networks is feasible and manageable. However, the computing and inference is NP-hard. That means, in applications, in ...
Bayesian Exploratory Factor Analysis
DEFF Research Database (Denmark)
Conti, Gabriella; Frühwirth-Schnatter, Sylvia; Heckman, James J.
2014-01-01
This paper develops and applies a Bayesian approach to Exploratory Factor Analysis that improves on ad hoc classical approaches. Our framework relies on dedicated factor models and simultaneously determines the number of factors, the allocation of each measurement to a unique factor......, and the corresponding factor loadings. Classical identification criteria are applied and integrated into our Bayesian procedure to generate models that are stable and clearly interpretable. A Monte Carlo study confirms the validity of the approach. The method is used to produce interpretable low dimensional aggregates...
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...
Explaining Inference on a Population of Independent Agents Using Bayesian Networks
Sutovsky, Peter
2013-01-01
The main goal of this research is to design, implement, and evaluate a novel explanation method, the hierarchical explanation method (HEM), for explaining Bayesian network (BN) inference when the network is modeling a population of conditionally independent agents, each of which is modeled as a subnetwork. For example, consider disease-outbreak…
Parallel hierarchical radiosity rendering
Energy Technology Data Exchange (ETDEWEB)
Carter, M.
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.
Bayesian methods for hackers probabilistic programming and Bayesian inference
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...
The Bayesian Inventory Problem
1984-05-01
Bayesian Approach to Demand Estimation and Inventory Provisioning," Naval Research Logistics Quarterly. Vol 20, 1973, (p607-624). 4 DeGroot , Morris H...page is blank APPENDIX A SUFFICIENT STATISTICS A convenient reference for moat of this material is DeGroot (41. Su-pose that we are sampling from a
Neutrosophic Hierarchical Clustering Algoritms
Directory of Open Access Journals (Sweden)
Rıdvan Şahin
2014-03-01
Full Text Available Interval neutrosophic set (INS is a generalization of interval valued intuitionistic fuzzy set (IVIFS, whose the membership and non-membership values of elements consist of fuzzy range, while single valued neutrosophic set (SVNS is regarded as extension of intuitionistic fuzzy set (IFS. In this paper, we extend the hierarchical clustering techniques proposed for IFSs and IVIFSs to SVNSs and INSs respectively. Based on the traditional hierarchical clustering procedure, the single valued neutrosophic aggregation operator, and the basic distance measures between SVNSs, we define a single valued neutrosophic hierarchical clustering algorithm for clustering SVNSs. Then we extend the algorithm to classify an interval neutrosophic data. Finally, we present some numerical examples in order to show the effectiveness and availability of the developed clustering algorithms.
Bayesian modeling of ChIP-chip data using latent variables.
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
Hierarchical hybrid testability modeling and evaluation method based on information fusion
Institute of Scientific and Technical Information of China (English)
Xishan Zhang; Kaoli Huang; Pengcheng Yan; Guangyao Lian
2015-01-01
In order to meet the demand of testability analysis and evaluation for complex equipment under a smal sample test in the equipment life cycle, the hierarchical hybrid testability model-ing and evaluation method (HHTME), which combines the testabi-lity structure model (TSM) with the testability Bayesian networks model (TBNM), is presented. Firstly, the testability network topo-logy of complex equipment is built by using the hierarchical hybrid testability modeling method. Secondly, the prior conditional prob-ability distribution between network nodes is determined through expert experience. Then the Bayesian method is used to update the conditional probability distribution, according to history test information, virtual simulation information and similar product in-formation. Final y, the learned hierarchical hybrid testability model (HHTM) is used to estimate the testability of equipment. Compared with the results of other modeling methods, the relative deviation of the HHTM is only 0.52%, and the evaluation result is the most accurate.
Structure-based bayesian sparse reconstruction
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.
Bayesian of inductive cognition algorithm for adaptive classification
Jin, Longcun; Wan, Wanggen; Cui, Bin; Wu, Yongliang
2009-07-01
In this paper, we proposed a Bayesian of inductive cognition algorithm using in virtual reality multimedia classification. We present a Bayesian of inductive cognition algorithm framework model for adaptively classifying scenes in virtual reality multimedia data. The Multimedia can switch between different shots, the unknown objects can leave or enter the scene at multiple times, and the scenes can be adaptively classified. The proposed algorithm consists of Bayesian inductive cognition part and Dirichlet process part. This algorithm has several advantages over traditional distance-based agglomerative adaptively classifying algorithms. Bayesian of inductive cognition algorithm based on Dirichlet process hypothesis testing is used to decide which merges are advantageous and to output the recommended depth of the scenes. The algorithm can be interpreted as a novel fast bottom-up approximate inference method for a Dirichlet process mixture model. We describe procedures for learning the model hyperparameters, computing the predictive distribution, and extensions to the Bayesian of inductive cognition algorithm. Experimental results on virtual reality multimedia data sets demonstrate useful properties of the Bayesian of inductive cognition algorithm.
A Bayesian framework for active artificial perception.
Ferreira, João Filipe; Lobo, Jorge; Bessière, Pierre; Castelo-Branco, Miguel; Dias, Jorge
2013-04-01
In this paper, we present a Bayesian framework for the active multimodal perception of 3-D structure and motion. The design of this framework finds its inspiration in the role of the dorsal perceptual pathway of the human brain. Its composing models build upon a common egocentric spatial configuration that is naturally fitting for the integration of readings from multiple sensors using a Bayesian approach. In the process, we will contribute with efficient and robust probabilistic solutions for cyclopean geometry-based stereovision and auditory perception based only on binaural cues, modeled using a consistent formalization that allows their hierarchical use as building blocks for the multimodal sensor fusion framework. We will explicitly or implicitly address the most important challenges of sensor fusion using this framework, for vision, audition, and vestibular sensing. Moreover, interaction and navigation require maximal awareness of spatial surroundings, which, in turn, is obtained through active attentional and behavioral exploration of the environment. The computational models described in this paper will support the construction of a simultaneously flexible and powerful robotic implementation of multimodal active perception to be used in real-world applications, such as human-machine interaction or mobile robot navigation.
Bayesian Analysis of High Dimensional Classification
Mukhopadhyay, Subhadeep; Liang, Faming
2009-12-01
Modern data mining and bioinformatics have presented an important playground for statistical learning techniques, where the number of input variables is possibly much larger than the sample size of the training data. In supervised learning, logistic regression or probit regression can be used to model a binary output and form perceptron classification rules based on Bayesian inference. In these cases , there is a lot of interest in searching for sparse model in High Dimensional regression(/classification) setup. we first discuss two common challenges for analyzing high dimensional data. The first one is the curse of dimensionality. The complexity of many existing algorithms scale exponentially with the dimensionality of the space and by virtue of that algorithms soon become computationally intractable and therefore inapplicable in many real applications. secondly, multicollinearities among the predictors which severely slowdown the algorithm. In order to make Bayesian analysis operational in high dimension we propose a novel 'Hierarchical stochastic approximation monte carlo algorithm' (HSAMC), which overcomes the curse of dimensionality, multicollinearity of predictors in high dimension and also it possesses the self-adjusting mechanism to avoid the local minima separated by high energy barriers. Models and methods are illustrated by simulation inspired from from the feild of genomics. Numerical results indicate that HSAMC can work as a general model selection sampler in high dimensional complex model space.
Hierarchical Porous Structures
Energy Technology Data Exchange (ETDEWEB)
Grote, Christopher John [Los Alamos National Lab. (LANL), Los Alamos, NM (United States)
2016-06-07
Materials Design is often at the forefront of technological innovation. While there has always been a push to generate increasingly low density materials, such as aero or hydrogels, more recently the idea of bicontinuous structures has gone more into play. This review will cover some of the methods and applications for generating both porous, and hierarchically porous structures.
A hierarchical model for spatial capture-recapture data
Royle, J. Andrew; Young, K.V.
2008-01-01
Estimating density is a fundamental objective of many animal population studies. Application of methods for estimating population size from ostensibly closed populations is widespread, but ineffective for estimating absolute density because most populations are subject to short-term movements or so-called temporary emigration. This phenomenon invalidates the resulting estimates because the effective sample area is unknown. A number of methods involving the adjustment of estimates based on heuristic considerations are in widespread use. In this paper, a hierarchical model of spatially indexed capture recapture data is proposed for sampling based on area searches of spatial sample units subject to uniform sampling intensity. The hierarchical model contains explicit models for the distribution of individuals and their movements, in addition to an observation model that is conditional on the location of individuals during sampling. Bayesian analysis of the hierarchical model is achieved by the use of data augmentation, which allows for a straightforward implementation in the freely available software WinBUGS. We present results of a simulation study that was carried out to evaluate the operating characteristics of the Bayesian estimator under variable densities and movement patterns of individuals. An application of the model is presented for survey data on the flat-tailed horned lizard (Phrynosoma mcallii) in Arizona, USA.
BNFinder2: Faster Bayesian network learning and Bayesian classification.
Dojer, Norbert; Bednarz, Pawel; Podsiadlo, Agnieszka; Wilczynski, Bartek
2013-08-15
Bayesian Networks (BNs) are versatile probabilistic models applicable to many different biological phenomena. In biological applications the structure of the network is usually unknown and needs to be inferred from experimental data. BNFinder is a fast software implementation of an exact algorithm for finding the optimal structure of the network given a number of experimental observations. Its second version, presented in this article, represents a major improvement over the previous version. The improvements include (i) a parallelized learning algorithm leading to an order of magnitude speed-ups in BN structure learning time; (ii) inclusion of an additional scoring function based on mutual information criteria; (iii) possibility of choosing the resulting network specificity based on statistical criteria and (iv) a new module for classification by BNs, including cross-validation scheme and classifier quality measurements with receiver operator characteristic scores. BNFinder2 is implemented in python and freely available under the GNU general public license at the project Web site https://launchpad.net/bnfinder, together with a user's manual, introductory tutorial and supplementary methods.
Xu, Hongwei; Short, Susan E; Liu, Tao
2013-01-01
Background 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. Methods 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. Results 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. Conclusions 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. PMID:22923769
Probability and Bayesian statistics
1987-01-01
This book contains selected and refereed contributions to the "Inter national Symposium on Probability and Bayesian Statistics" which was orga nized to celebrate the 80th birthday of Professor Bruno de Finetti at his birthplace Innsbruck in Austria. Since Professor de Finetti died in 1985 the symposium was dedicated to the memory of Bruno de Finetti and took place at Igls near Innsbruck from 23 to 26 September 1986. Some of the pa pers are published especially by the relationship to Bruno de Finetti's scientific work. The evolution of stochastics shows growing importance of probability as coherent assessment of numerical values as degrees of believe in certain events. This is the basis for Bayesian inference in the sense of modern statistics. The contributions in this volume cover a broad spectrum ranging from foundations of probability across psychological aspects of formulating sub jective probability statements, abstract measure theoretical considerations, contributions to theoretical statistics an...
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....
Bayesian modeling of differential gene expression.
Lewin, Alex; Richardson, Sylvia; Marshall, Clare; Glazier, Anne; Aitman, Tim
2006-03-01
We present a Bayesian hierarchical model for detecting differentially expressing genes that includes simultaneous estimation of array effects, and show how to use the output for choosing lists of genes for further investigation. We give empirical evidence that expression-level dependent array effects are needed, and explore different nonlinear functions as part of our model-based approach to normalization. The model includes gene-specific variances but imposes some necessary shrinkage through a hierarchical structure. Model criticism via posterior predictive checks is discussed. Modeling the array effects (normalization) simultaneously with differential expression gives fewer false positive results. To choose a list of genes, we propose to combine various criteria (for instance, fold change and overall expression) into a single indicator variable for each gene. The posterior distribution of these variables is used to pick the list of genes, thereby taking into account uncertainty in parameter estimates. In an application to mouse knockout data, Gene Ontology annotations over- and underrepresented among the genes on the chosen list are consistent with biological expectations.
Introduction to Bayesian statistics
Koch, Karl-Rudolf
2007-01-01
This book presents Bayes' theorem, the estimation of unknown parameters, the determination of confidence regions and the derivation of tests of hypotheses for the unknown parameters. It does so in a simple manner that is easy to comprehend. The book compares traditional and Bayesian methods with the rules of probability presented in a logical way allowing an intuitive understanding of random variables and their probability distributions to be formed.
Shterev, Ivo; Dunson, David
2012-01-01
This paper presents an application of statistical machine learning to the field of watermarking. We propose a new attack model on additive spread-spectrum watermarking systems. The proposed attack is based on Bayesian statistics. We consider the scenario in which a watermark signal is repeatedly embedded in specific, possibly chosen based on a secret message bitstream, segments (signals) of the host data. The host signal can represent a patch of pixels from an image or a video frame. We propo...
DEFF Research Database (Denmark)
Antoniou, Constantinos; Harrison, Glenn W.; Lau, Morten I.
2015-01-01
A large literature suggests that many individuals do not apply Bayes’ Rule when making decisions that depend on them correctly pooling prior information and sample data. We replicate and extend a classic experimental study of Bayesian updating from psychology, employing the methods of experimental...... economics, with careful controls for the confounding effects of risk aversion. Our results show that risk aversion significantly alters inferences on deviations from Bayes’ Rule....
Himpe, Christian; Ohlberger, Mario
2014-01-01
Bayesian inversion of models with large state and parameter spaces proves to be computationally complex. A combined state and parameter reduction can significantly decrease the computational time and cost required for the parameter estimation. The presented technique is based on the well-known balanced truncation approach. Classically, the balancing of the controllability and observability gramians allows a truncation of discardable states. Here the underlying model, being a linear or nonline...
Bayesian Independent Component Analysis
DEFF Research Database (Denmark)
Winther, Ole; Petersen, Kaare Brandt
2007-01-01
In this paper we present an empirical Bayesian framework for independent component analysis. The framework provides estimates of the sources, the mixing matrix and the noise parameters, and is flexible with respect to choice of source prior and the number of sources and sensors. Inside the engine...... in a Matlab toolbox, is demonstrated for non-negative decompositions and compared with non-negative matrix factorization....
Fast Hierarchical Registration Method for Remote Sensing Image based on SIFT%一种基于SIFT特征的快速逐层遥感图像配准方法
Institute of Scientific and Technical Information of China (English)
侯鹏洋; 季艳; 高峰; 胡蕾
2014-01-01
当前SIFT特征分层配准方法中存在特征点匹配复杂度高以及不同时相地物变化导致特征点误匹配等问题,提出一种基于SIFT特征的“低分辨率配准、高分辨率验证”快速逐层遥感图像配准方法.该方法针对同源同分辨率不同时相的遥感图像,通过在金字塔的低分辨率图层匹配特征点对并建立仿射变换模型,在金字塔的高分辨率图层评估并修正模型.实验表明:提出的方法在保证配准精度的前提下,有效提高了配准算法的效率.%For the current automatic image registration based on SIFT,feature point matching algorithm is time-consuming,in addition,the changes of multi-temporal images affect the accuracy of registration,this paper proposes a SIFT-based feature of the "low-resolution matching,high resolution authentication" hierarchical image registration algorithm to improve the above issues.In the proposed algorithm,affine transformation model is established in low-resolution pyramid images and sequentially evaluated and revised by match points in high resolution pyramid images.Experimental results show that the improved SIFT algorithm can reduce the time complexity with rather considerable accuracy.
Bayesian Models for Astrophysical Data Using R, JAGS, Python, and Stan
Hilbe, Joseph M.; de Souza, Rafael S.; Ishida, Emille E. O.
2017-05-01
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.
Institute of Scientific and Technical Information of China (English)
王琪; 李玮
2011-01-01
The Bayesian and hierarchical Bayesian estimators of reliability of negative binomial distribution are obtained, and the E Bayesian estimator is also discussed by E Bayesian approach. Finally, a numberical example is given to compare the former three estmators, and the contusion shows that the E Bayesian estimator is better than the hierarchical Bayesian estimator.%在一类新的加权平方损失函数下,给出了负二项分布可靠度的Bayes和多层Bayes估计,并利用EBayes方法给出了负二项分布可靠度的E Bayes估计.针对得到的3种估计,给出了数值模拟,结果表明:EBayes估计比多层Bayes估计优良.
Nonparametric Bayesian inference of the microcanonical stochastic block model
Peixoto, Tiago P
2016-01-01
A principled approach to characterize the hidden modular structure of networks is to formulate generative models, and then infer their parameters from data. When the desired structure is composed of modules or "communities", a suitable choice for this task is the stochastic block model (SBM), where nodes are divided into groups, and the placement of edges is conditioned on the group memberships. Here, we present a nonparametric Bayesian method to infer the modular structure of empirical networks, including the number of modules and their hierarchical organization. We focus on a microcanonical variant of the SBM, where the structure is imposed via hard constraints. We show how this simple model variation allows simultaneously for two important improvements over more traditional inference approaches: 1. Deeper Bayesian hierarchies, with noninformative priors replaced by sequences of priors and hyperpriors, that not only remove limitations that seriously degrade the inference on large networks, but also reveal s...
A Bayesian Predictive Discriminant Analysis with Screened Data
Directory of Open Access Journals (Sweden)
Hea-Jung Kim
2015-09-01
Full Text Available In the application of discriminant analysis, a situation sometimes arises where individual measurements are screened by a multidimensional screening scheme. For this situation, a discriminant analysis with screened populations is considered from a Bayesian viewpoint, and an optimal predictive rule for the analysis is proposed. In order to establish a flexible method to incorporate the prior information of the screening mechanism, we propose a hierarchical screened scale mixture of normal (HSSMN model, which makes provision for flexible modeling of the screened observations. An Markov chain Monte Carlo (MCMC method using the Gibbs sampler and the Metropolis–Hastings algorithm within the Gibbs sampler is used to perform a Bayesian inference on the HSSMN models and to approximate the optimal predictive rule. A simulation study is given to demonstrate the performance of the proposed predictive discrimination procedure.
Sparse Bayesian learning for DOA estimation with mutual coupling.
Dai, Jisheng; Hu, Nan; Xu, Weichao; Chang, Chunqi
2015-10-16
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.
Commentary on Bayesian coincidence assessment (cross-matching)
Loredo, Thomas J
2012-01-01
This paper is an invited commentary on Tamas Budavari's presentation, "On statistical cross-identification in astronomy," for the Statistical Challenges in Modern Astronomy V conference held at Pennsylvania State University in June 2011. I begin with a brief review of previous work on probabilistic (Bayesian) assessment of directional and spatio-temporal coincidences in astronomy (e.g., cross-matching or cross-identification of objects across multiple catalogs). Then I discuss an open issue in the recent innovative work of Budavari and his colleagues on large-scale probabilistic cross-identification: how to assign prior probabilities that play an important role in the analysis. With a simple toy problem, I show how Bayesian multilevel modeling (hierarchical Bayes) provides a principled framework that justifies and generalizes pragmatic rules of thumb that have been successfully used by Budavari's team to assign priors.
Sparse Bayesian Learning for DOA Estimation with Mutual Coupling
Directory of Open Access Journals (Sweden)
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.
Collaborative Hierarchical Sparse Modeling
Sprechmann, Pablo; Sapiro, Guillermo; Eldar, Yonina C
2010-01-01
Sparse modeling is a powerful framework for data analysis and processing. Traditionally, encoding in this framework is done by solving an l_1-regularized linear regression problem, usually called Lasso. In this work we first combine the sparsity-inducing property of the Lasso model, at the individual feature level, with the block-sparsity property of the group Lasso model, where sparse groups of features are jointly encoded, obtaining a sparsity pattern hierarchically structured. This results in the hierarchical Lasso, which shows important practical modeling advantages. We then extend this approach to the collaborative case, where a set of simultaneously coded signals share the same sparsity pattern at the higher (group) level but not necessarily at the lower one. Signals then share the same active groups, or classes, but not necessarily the same active set. This is very well suited for applications such as source separation. An efficient optimization procedure, which guarantees convergence to the global opt...
Hierarchical manifold learning.
Bhatia, Kanwal K; Rao, Anil; Price, Anthony N; Wolz, Robin; Hajnal, Jo; Rueckert, Daniel
2012-01-01
We present a novel method of hierarchical manifold learning which aims to automatically discover regional variations within images. This involves constructing manifolds in a hierarchy of image patches of increasing granularity, while ensuring consistency between hierarchy levels. We demonstrate its utility in two very different settings: (1) to learn the regional correlations in motion within a sequence of time-resolved images of the thoracic cavity; (2) to find discriminative regions of 3D brain images in the classification of neurodegenerative disease,
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...
Hierarchically Structured Electrospun Fibers
Directory of Open Access Journals (Sweden)
Nicole E. Zander
2013-01-01
Full Text Available Traditional electrospun nanofibers have a myriad of applications ranging from scaffolds for tissue engineering to components of biosensors and energy harvesting devices. The generally smooth one-dimensional structure of the fibers has stood as a limitation to several interesting novel applications. Control of fiber diameter, porosity and collector geometry will be briefly discussed, as will more traditional methods for controlling fiber morphology and fiber mat architecture. The remainder of the review will focus on new techniques to prepare hierarchically structured fibers. Fibers with hierarchical primary structures—including helical, buckled, and beads-on-a-string fibers, as well as fibers with secondary structures, such as nanopores, nanopillars, nanorods, and internally structured fibers and their applications—will be discussed. These new materials with helical/buckled morphology are expected to possess unique optical and mechanical properties with possible applications for negative refractive index materials, highly stretchable/high-tensile-strength materials, and components in microelectromechanical devices. Core-shell type fibers enable a much wider variety of materials to be electrospun and are expected to be widely applied in the sensing, drug delivery/controlled release fields, and in the encapsulation of live cells for biological applications. Materials with a hierarchical secondary structure are expected to provide new superhydrophobic and self-cleaning materials.
Pearce, Dave; Walter, Anton; Lupton, W. F.; Warren-Smith, Rodney F.; Lawden, Mike; McIlwrath, Brian; Peden, J. C. M.; Jenness, Tim; Draper, Peter W.
2015-02-01
The Hierarchical Data System (HDS) is a file-based hierarchical data system designed for the storage of a wide variety of information. It is particularly suited to the storage of large multi-dimensional arrays (with their ancillary data) where efficient access is needed. It is a key component of the Starlink software collection (ascl:1110.012) and is used by the Starlink N-Dimensional Data Format (NDF) library (ascl:1411.023). HDS organizes data into hierarchies, broadly similar to the directory structure of a hierarchical filing system, but contained within a single HDS container file. The structures stored in these files are self-describing and flexible; HDS supports modification and extension of structures previously created, as well as functions such as deletion, copying, and renaming. All information stored in HDS files is portable between the machines on which HDS is implemented. Thus, there are no format conversion problems when moving between machines. HDS can write files in a private binary format (version 4), or be layered on top of HDF5 (version 5).
Hierarchical video summarization
Ratakonda, Krishna; Sezan, M. Ibrahim; Crinon, Regis J.
1998-12-01
We address the problem of key-frame summarization of vide in the absence of any a priori information about its content. This is a common problem that is encountered in home videos. We propose a hierarchical key-frame summarization algorithm where a coarse-to-fine key-frame summary is generated. A hierarchical key-frame summary facilitates multi-level browsing where the user can quickly discover the content of the video by accessing its coarsest but most compact summary and then view a desired segment of the video with increasingly more detail. At the finest level, the summary is generated on the basis of color features of video frames, using an extension of a recently proposed key-frame extraction algorithm. The finest level key-frames are recursively clustered using a novel pairwise K-means clustering approach with temporal consecutiveness constraint. We also address summarization of MPEG-2 compressed video without fully decoding the bitstream. We also propose efficient mechanisms that facilitate decoding the video when the hierarchical summary is utilized in browsing and playback of video segments starting at selected key-frames.
Macnab, Ying C
2009-04-30
This paper presents Bayesian multivariate disease mapping and ecological regression models that take into account errors in covariates. Bayesian hierarchical formulations of multivariate disease models and covariate measurement models, with related methods of estimation and inference, are developed as an integral part of a Bayesian disability adjusted life years (DALYs) methodology for the analysis of multivariate disease or injury data and associated ecological risk factors and for small area DALYs estimation, inference, and mapping. The methodology facilitates the estimation of multivariate small area disease and injury rates and associated risk effects, evaluation of DALYs and 'preventable' DALYs, and identification of regions to which disease or injury prevention resources may be directed to reduce DALYs. The methodology interfaces and intersects the Bayesian disease mapping methodology and the global burden of disease framework such that the impact of disease, injury, and risk factors on population health may be evaluated to inform community health, health needs, and priority considerations for disease and injury prevention. A burden of injury study on road traffic accidents in local health areas in British Columbia, Canada, is presented as an illustrative example.
Bayesian Inference in Monte-Carlo Tree Search
Tesauro, Gerald; Segal, Richard
2012-01-01
Monte-Carlo Tree Search (MCTS) methods are drawing great interest after yielding breakthrough results in computer Go. This paper proposes a Bayesian approach to MCTS that is inspired by distributionfree approaches such as UCT [13], yet significantly differs in important respects. The Bayesian framework allows potentially much more accurate (Bayes-optimal) estimation of node values and node uncertainties from a limited number of simulation trials. We further propose propagating inference in the tree via fast analytic Gaussian approximation methods: this can make the overhead of Bayesian inference manageable in domains such as Go, while preserving high accuracy of expected-value estimates. We find substantial empirical outperformance of UCT in an idealized bandit-tree test environment, where we can obtain valuable insights by comparing with known ground truth. Additionally we rigorously prove on-policy and off-policy convergence of the proposed methods.
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.
Image meshing via hierarchical optimization
Institute of Scientific and Technical Information of China (English)
Hao XIE; Ruo-feng TONG‡
2016-01-01
Vector graphic, as a kind of geometric representation of raster images, has many advantages, e.g., defi nition independence and editing facility. A popular way to convert raster images into vector graphics is image meshing, the aim of which is to fi nd a mesh to represent an image as faithfully as possible. For traditional meshing algorithms, the crux of the problem resides mainly in the high non-linearity and non-smoothness of the objective, which makes it diﬃcult to fi nd a desirable optimal solution. To ameliorate this situation, we present a hierarchical optimization algorithm solving the problem from coarser levels to fi ner ones, providing initialization for each level with its coarser ascent. To further simplify the problem, the original non-convex problem is converted to a linear least squares one, and thus becomes convex, which makes the problem much easier to solve. A dictionary learning framework is used to combine geometry and topology elegantly. Then an alternating scheme is employed to solve both parts. Experiments show that our algorithm runs fast and achieves better results than existing ones for most images.
Image meshing via hierarchical optimization＊
Institute of Scientific and Technical Information of China (English)
Hao XIE; Ruo-feng TONGS
2016-01-01
Vector graphic, as a kind of geometric representation of raster images, has many advantages, e.g., definition independence and editing facility. A popular way to convert raster images into vector graphics is image meshing, the aim of which is to find a mesh to represent an image as faithfully as possible. For traditional meshing algorithms, the crux of the problem resides mainly in the high non-linearity and non-smoothness of the objective, which makes it difficult to find a desirable optimal solution. To ameliorate this situation, we present a hierarchical optimization algorithm solving the problem from coarser levels to finer ones, providing initialization for each level with its coarser ascent. To further simplify the problem, the original non-convex problem is converted to a linear least squares one, and thus becomes convex, which makes the problem much easier to solve. A dictionary learning framework is used to combine geometry and topology elegantly. Then an alternating scheme is employed to solve both parts. Experiments show that our algorithm runs fast and achieves better results than existing ones for most images.
Bayesian state space models for dynamic genetic network construction across multiple tissues.
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.
A Bayesian model of context-sensitive value attribution.
Rigoli, Francesco; Friston, Karl J; Martinelli, Cristina; Selaković, Mirjana; Shergill, Sukhwinder S; Dolan, Raymond J
2016-06-22
Substantial evidence indicates that incentive value depends on an anticipation of rewards within a given context. However, the computations underlying this context sensitivity remain unknown. To address this question, we introduce a normative (Bayesian) account of how rewards map to incentive values. This assumes that the brain inverts a model of how rewards are generated. Key features of our account include (i) an influence of prior beliefs about the context in which rewards are delivered (weighted by their reliability in a Bayes-optimal fashion), (ii) the notion that incentive values correspond to precision-weighted prediction errors, (iii) and contextual information unfolding at different hierarchical levels. This formulation implies that incentive value is intrinsically context-dependent. We provide empirical support for this model by showing that incentive value is influenced by context variability and by hierarchically nested contexts. The perspective we introduce generates new empirical predictions that might help explaining psychopathologies, such as addiction.
Bayesian nonparametric data analysis
Müller, Peter; Jara, Alejandro; Hanson, Tim
2015-01-01
This book reviews nonparametric Bayesian methods and models that have proven useful in the context of data analysis. Rather than providing an encyclopedic review of probability models, the book’s structure follows a data analysis perspective. As such, the chapters are organized by traditional data analysis problems. In selecting specific nonparametric models, simpler and more traditional models are favored over specialized ones. The discussed methods are illustrated with a wealth of examples, including applications ranging from stylized examples to case studies from recent literature. The book also includes an extensive discussion of computational methods and details on their implementation. R code for many examples is included in on-line software pages.
Congdon, Peter
2014-01-01
This book provides an accessible approach to Bayesian computing and data analysis, with an emphasis on the interpretation of real data sets. Following in the tradition of the successful first edition, this book aims to make a wide range of statistical modeling applications accessible using tested code that can be readily adapted to the reader's own applications. The second edition has been thoroughly reworked and updated to take account of advances in the field. A new set of worked examples is included. The novel aspect of the first edition was the coverage of statistical modeling using WinBU
DEFF Research Database (Denmark)
Hartelius, Karsten; Carstensen, Jens Michael
2003-01-01
A method for locating distorted grid structures in images is presented. The method is based on the theories of template matching and Bayesian image restoration. The grid is modeled as a deformable template. Prior knowledge of the grid is described through a Markov random field (MRF) model which...... nodes and the arc prior models variations in row and column spacing across the grid. Grid matching is done by placing an initial rough grid over the image and applying an ensemble annealing scheme to maximize the posterior distribution of the grid. The method can be applied to noisy images with missing...
Institute of Scientific and Technical Information of China (English)
韩明
2013-01-01
作者以前提出了一种新的参数估计方法——E-Bayes估计法,对二项分布的可靠度,给出了E-Bayes估计的定义、E-Bayes估计和多层Bayes估计公式,但没有给出E-Bayes估计的性质.该文给出了二项分布可靠度F-Bayes估计的性质.%Previously, the author introduces a new parameter estimation method-E-Bayesian estimation method, to estimate the reliability derived form Binomial distribution, the definition of E-Bayesian estimation of the reliability is provided; moreover, formulas of E-Bayesian estimation and hierarchical Bayesian estimation for the reliability are also provided, but the author did not provide propertiy of E-Bayesian estimation. This paper, properties of E-Bayesian estimation are provided.
Bayesian Approach for Inconsistent Information.
Stein, M; Beer, M; Kreinovich, V
2013-10-01
In engineering situations, we usually have a large amount of prior knowledge that needs to be taken into account when processing data. Traditionally, the Bayesian approach is used to process data in the presence of prior knowledge. Sometimes, when we apply the traditional Bayesian techniques to engineering data, we get inconsistencies between the data and prior knowledge. These inconsistencies are usually caused by the fact that in the traditional approach, we assume that we know the exact sample values, that the prior distribution is exactly known, etc. In reality, the data is imprecise due to measurement errors, the prior knowledge is only approximately known, etc. So, a natural way to deal with the seemingly inconsistent information is to take this imprecision into account in the Bayesian approach - e.g., by using fuzzy techniques. In this paper, we describe several possible scenarios for fuzzifying the Bayesian approach. Particular attention is paid to the interaction between the estimated imprecise parameters. In this paper, to implement the corresponding fuzzy versions of the Bayesian formulas, we use straightforward computations of the related expression - which makes our computations reasonably time-consuming. Computations in the traditional (non-fuzzy) Bayesian approach are much faster - because they use algorithmically efficient reformulations of the Bayesian formulas. We expect that similar reformulations of the fuzzy Bayesian formulas will also drastically decrease the computation time and thus, enhance the practical use of the proposed methods.
Classification using Bayesian neural nets
J.C. Bioch (Cor); O. van der Meer; R. Potharst (Rob)
1995-01-01
textabstractRecently, Bayesian methods have been proposed for neural networks to solve regression and classification problems. These methods claim to overcome some difficulties encountered in the standard approach such as overfitting. However, an implementation of the full Bayesian approach to neura
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....
Interactive Instruction in Bayesian Inference
DEFF Research Database (Denmark)
Khan, Azam; Breslav, Simon; Hornbæk, Kasper
2017-01-01
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...... that an instructional approach to improving human performance in Bayesian inference is a promising direction....
Bayesian Intersubjectivity and Quantum Theory
Pérez-Suárez, Marcos; Santos, David J.
2005-02-01
Two of the major approaches to probability, namely, frequentism and (subjectivistic) Bayesian theory, are discussed, together with the replacement of frequentist objectivity for Bayesian intersubjectivity. This discussion is then expanded to Quantum Theory, as quantum states and operations can be seen as structural elements of a subjective nature.
Bayesian Inference on Gravitational Waves
Directory of Open Access Journals (Sweden)
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.
Approximate Bayesian computation.
Directory of Open Access Journals (Sweden)
Mikael Sunnåker
Full Text Available Approximate Bayesian computation (ABC constitutes a class of computational methods rooted in Bayesian statistics. In all model-based statistical inference, the likelihood function is of central importance, since it expresses the probability of the observed data under a particular statistical model, and thus quantifies the support data lend to particular values of parameters and to choices among different models. For simple models, an analytical formula for the likelihood function can typically be derived. However, for more complex models, an analytical formula might be elusive or the likelihood function might be computationally very costly to evaluate. ABC methods bypass the evaluation of the likelihood function. In this way, ABC methods widen the realm of models for which statistical inference can be considered. ABC methods are mathematically well-founded, but they inevitably make assumptions and approximations whose impact needs to be carefully assessed. Furthermore, the wider application domain of ABC exacerbates the challenges of parameter estimation and model selection. ABC has rapidly gained popularity over the last years and in particular for the analysis of complex problems arising in biological sciences (e.g., in population genetics, ecology, epidemiology, and systems biology.
Bayesian and variational Bayesian approaches for flows in heterogeneous random media
Yang, Keren; Guha, Nilabja; Efendiev, Yalchin; Mallick, Bani K.
2017-09-01
In this paper, we study porous media flows in heterogeneous stochastic media. We propose an efficient forward simulation technique that is tailored for variational Bayesian inversion. As a starting point, the proposed forward simulation technique decomposes the solution into the sum of separable functions (with respect to randomness and the space), where each term is calculated based on a variational approach. This is similar to Proper Generalized Decomposition (PGD). Next, we apply a multiscale technique to solve for each term (as in [1]) and, further, decompose the random function into 1D fields. As a result, our proposed method provides an approximation hierarchy for the solution as we increase the number of terms in the expansion and, also, increase the spatial resolution of each term. We use the hierarchical solution distributions in a variational Bayesian approximation to perform uncertainty quantification in the inverse problem. We conduct a detailed numerical study to explore the performance of the proposed uncertainty quantification technique and show the theoretical posterior concentration.
Context updates are hierarchical
Directory of Open Access Journals (Sweden)
Anton Karl Ingason
2016-10-01
Full Text Available This squib studies the order in which elements are added to the shared context of interlocutors in a conversation. It focuses on context updates within one hierarchical structure and argues that structurally higher elements are entered into the context before lower elements, even if the structurally higher elements are pronounced after the lower elements. The crucial data are drawn from a comparison of relative clauses in two head-initial languages, English and Icelandic, and two head-final languages, Korean and Japanese. The findings have consequences for any theory of a dynamic semantics.
Zhang, Zhidong
2016-01-01
This study explored an alternative assessment procedure to examine learning trajectories of matrix multiplication. It took rule-based analytical and cognitive task analysis methods specifically to break down operation rules for a given matrix multiplication. Based on the analysis results, a hierarchical Bayesian network, an assessment model,…
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 5123 to 81923 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 Ht (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.
A Bayesian Model of Biases in Artificial Language Learning: The Case of a Word-Order Universal
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…
Link, William; Sauer, John R.
2016-01-01
The analysis of ecological data has changed in two important ways over the last 15 years. The development and easy availability of Bayesian computational methods has allowed and encouraged the fitting of complex hierarchical models. At the same time, there has been increasing emphasis on acknowledging and accounting for model uncertainty. Unfortunately, the ability to fit complex models has outstripped the development of tools for model selection and model evaluation: familiar model selection tools such as Akaike's information criterion and the deviance information criterion are widely known to be inadequate for hierarchical models. In addition, little attention has been paid to the evaluation of model adequacy in context of hierarchical modeling, i.e., to the evaluation of fit for a single model. In this paper, we describe Bayesian cross-validation, which provides tools for model selection and evaluation. We describe the Bayesian predictive information criterion and a Bayesian approximation to the BPIC known as the Watanabe-Akaike information criterion. We illustrate the use of these tools for model selection, and the use of Bayesian cross-validation as a tool for model evaluation, using three large data sets from the North American Breeding Bird Survey.
Link, William A; Sauer, John R
2016-07-01
The analysis of ecological data has changed in two important ways over the last 15 years. The development and easy availability of Bayesian computational methods has allowed and encouraged the fitting of complex hierarchical models. At the same time, there has been increasing emphasis on acknowledging and accounting for model uncertainty. Unfortunately, the ability to fit complex models has outstripped the development of tools for model selection and model evaluation: familiar model selection tools such as Akaike's information criterion and the deviance information criterion are widely known to be inadequate for hierarchical models. In addition, little attention has been paid to the evaluation of model adequacy in context of hierarchical modeling, i.e., to the evaluation of fit for a single model. In this paper, we describe Bayesian cross-validation, which provides tools for model selection and evaluation. We describe the Bayesian predictive information criterion and a Bayesian approximation to the BPIC known as the Watanabe-Akaike information criterion. We illustrate the use of these tools for model selection, and the use of Bayesian cross-validation as a tool for model evaluation, using three large data sets from the North American Breeding Bird Survey.
Scalable Bayesian modeling, monitoring and analysis of dynamic network flow data
2016-01-01
Traffic flow count data in networks arise in many applications, such as automobile or aviation transportation, certain directed social network contexts, and Internet studies. Using an example of Internet browser traffic flow through site-segments of an international news website, we present Bayesian analyses of two linked classes of models which, in tandem, allow fast, scalable and interpretable Bayesian inference. We first develop flexible state-space models for streaming count data, able to...
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 primar
Implementing Bayesian Vector Autoregressions Implementing Bayesian Vector Autoregressions
Directory of Open Access Journals (Sweden)
Richard M. Todd
1988-03-01
Full Text Available Implementing Bayesian Vector Autoregressions This paper discusses how the Bayesian approach can be used to construct a type of multivariate forecasting model known as a Bayesian vector autoregression (BVAR. In doing so, we mainly explain Doan, Littermann, and Sims (1984 propositions on how to estimate a BVAR based on a certain family of prior probability distributions. indexed by a fairly small set of hyperparameters. There is also a discussion on how to specify a BVAR and set up a BVAR database. A 4-variable model is used to iliustrate the BVAR approach.
Using PSO-Based Hierarchical Feature Selection Algorithm
Directory of Open Access Journals (Sweden)
Zhiwei Ji
2014-01-01
Full Text Available Hepatocellular carcinoma (HCC is one of the most common malignant tumors. Clinical symptoms attributable to HCC are usually absent, thus often miss the best therapeutic opportunities. Traditional Chinese Medicine (TCM plays an active role in diagnosis and treatment of HCC. In this paper, we proposed a particle swarm optimization-based hierarchical feature selection (PSOHFS model to infer potential syndromes for diagnosis of HCC. Firstly, the hierarchical feature representation is developed by a three-layer tree. The clinical symptoms and positive score of patient are leaf nodes and root in the tree, respectively, while each syndrome feature on the middle layer is extracted from a group of symptoms. Secondly, an improved PSO-based algorithm is applied in a new reduced feature space to search an optimal syndrome subset. Based on the result of feature selection, the causal relationships of symptoms and syndromes are inferred via Bayesian networks. In our experiment, 147 symptoms were aggregated into 27 groups and 27 syndrome features were extracted. The proposed approach discovered 24 syndromes which obviously improved the diagnosis accuracy. Finally, the Bayesian approach was applied to represent the causal relationships both at symptom and syndrome levels. The results show that our computational model can facilitate the clinical diagnosis of HCC.
Bayesian inference in geomagnetism
Backus, George E.
1988-01-01
The inverse problem in empirical geomagnetic modeling is investigated, with critical examination of recently published studies. Particular attention is given to the use of Bayesian inference (BI) to select the damping parameter lambda in the uniqueness portion of the inverse problem. The mathematical bases of BI and stochastic inversion are explored, with consideration of bound-softening problems and resolution in linear Gaussian BI. The problem of estimating the radial magnetic field B(r) at the earth core-mantle boundary from surface and satellite measurements is then analyzed in detail, with specific attention to the selection of lambda in the studies of Gubbins (1983) and Gubbins and Bloxham (1985). It is argued that the selection method is inappropriate and leads to lambda values much larger than those that would result if a reasonable bound on the heat flow at the CMB were assumed.
Bayesian Geostatistical Design
DEFF Research Database (Denmark)
Diggle, Peter; Lophaven, Søren Nymand
2006-01-01
This paper describes the use of model-based geostatistics for choosing the set of sampling locations, collectively called the design, to be used in a geostatistical analysis. Two types of design situation are considered. These are retrospective design, which concerns the addition of sampling...... locations to, or deletion of locations from, an existing design, and prospective design, which consists of choosing positions for a new set of sampling locations. We propose a Bayesian design criterion which focuses on the goal of efficient spatial prediction whilst allowing for the fact that model...... parameter values are unknown. The results show that in this situation a wide range of interpoint distances should be included in the design, and the widely used regular design is often not the best choice....
Ortega, Pedro A
2011-01-01
Discovering causal relationships is a hard task, often hindered by the need for intervention, and often requiring large amounts of data to resolve statistical uncertainty. However, humans quickly arrive at useful causal relationships. One possible reason is that humans use strong prior knowledge; and rather than encoding hard causal relationships, they encode beliefs over causal structures, allowing for sound generalization from the observations they obtain from directly acting in the world. In this work we propose a Bayesian approach to causal induction which allows modeling beliefs over multiple causal hypotheses and predicting the behavior of the world under causal interventions. We then illustrate how this method extracts causal information from data containing interventions and observations.
Book review: Bayesian analysis for population ecology
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)
Bayesian adaptive methods for clinical trials
Berry, Scott M; Muller, Peter
2010-01-01
Already popular in the analysis of medical device trials, adaptive Bayesian designs are increasingly being used in drug development for a wide variety of diseases and conditions, from Alzheimer's disease and multiple sclerosis to obesity, diabetes, hepatitis C, and HIV. Written by leading pioneers of Bayesian clinical trial designs, Bayesian Adaptive Methods for Clinical Trials explores the growing role of Bayesian thinking in the rapidly changing world of clinical trial analysis. The book first summarizes the current state of clinical trial design and analysis and introduces the main ideas and potential benefits of a Bayesian alternative. It then gives an overview of basic Bayesian methodological and computational tools needed for Bayesian clinical trials. With a focus on Bayesian designs that achieve good power and Type I error, the next chapters present Bayesian tools useful in early (Phase I) and middle (Phase II) clinical trials as well as two recent Bayesian adaptive Phase II studies: the BATTLE and ISP...
parallelMCMCcombine: an R package for bayesian methods for big data and analytics.
Directory of Open Access Journals (Sweden)
Alexey Miroshnikov
Full Text Available Recent advances in big data and analytics research have provided a wealth of large data sets that are too big to be analyzed in their entirety, due to restrictions on computer memory or storage size. New Bayesian methods have been developed for data sets that are large only due to large sample sizes. These methods partition big data sets into subsets and perform independent Bayesian Markov chain Monte Carlo analyses on the subsets. The methods then combine the independent subset posterior samples to estimate a posterior density given the full data set. These approaches were shown to be effective for Bayesian models including logistic regression models, Gaussian mixture models and hierarchical models. Here, we introduce the R package parallelMCMCcombine which carries out four of these techniques for combining independent subset posterior samples. We illustrate each of the methods using a Bayesian logistic regression model for simulation data and a Bayesian Gamma model for real data; we also demonstrate features and capabilities of the R package. The package assumes the user has carried out the Bayesian analysis and has produced the independent subposterior samples outside of the package. The methods are primarily suited to models with unknown parameters of fixed dimension that exist in continuous parameter spaces. We envision this tool will allow researchers to explore the various methods for their specific applications and will assist future progress in this rapidly developing field.
parallelMCMCcombine: an R package for bayesian methods for big data and analytics.
Miroshnikov, Alexey; Conlon, Erin M
2014-01-01
Recent advances in big data and analytics research have provided a wealth of large data sets that are too big to be analyzed in their entirety, due to restrictions on computer memory or storage size. New Bayesian methods have been developed for data sets that are large only due to large sample sizes. These methods partition big data sets into subsets and perform independent Bayesian Markov chain Monte Carlo analyses on the subsets. The methods then combine the independent subset posterior samples to estimate a posterior density given the full data set. These approaches were shown to be effective for Bayesian models including logistic regression models, Gaussian mixture models and hierarchical models. Here, we introduce the R package parallelMCMCcombine which carries out four of these techniques for combining independent subset posterior samples. We illustrate each of the methods using a Bayesian logistic regression model for simulation data and a Bayesian Gamma model for real data; we also demonstrate features and capabilities of the R package. The package assumes the user has carried out the Bayesian analysis and has produced the independent subposterior samples outside of the package. The methods are primarily suited to models with unknown parameters of fixed dimension that exist in continuous parameter spaces. We envision this tool will allow researchers to explore the various methods for their specific applications and will assist future progress in this rapidly developing field.
Analysis of COSIMA spectra: Bayesian approach
Directory of Open Access Journals (Sweden)
H. J. Lehto
2014-11-01
Full Text Available We describe the use of Bayesian analysis methods applied to TOF-SIMS spectra. The method finds the probability density functions of measured line parameters (number of lines, and their widths, peak amplitudes, integrated amplitudes, positions in mass intervals over the whole spectrum. We discuss the results we can expect from this analysis. We discuss the effects the instrument dead time causes in the COSIMA TOF SIMS. We address this issue in a new way. The derived line parameters can be used to further calibrate the mass scaling of TOF-SIMS and to feed the results into other analysis methods such as multivariate analyses of spectra. We intend to use the method in two ways, first as a comprehensive tool to perform quantitative analysis of spectra, and second as a fast tool for studying interesting targets for obtaining additional TOF-SIMS measurements of the sample, a property unique for COSIMA. Finally, we point out that the Bayesian method can be thought as a means to solve inverse problems but with forward calculations only.
Current trends in Bayesian methodology with applications
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
Hierarchical partial order ranking.
Carlsen, Lars
2008-09-01
Assessing the potential impact on environmental and human health from the production and use of chemicals or from polluted sites involves a multi-criteria evaluation scheme. A priori several parameters are to address, e.g., production tonnage, specific release scenarios, geographical and site-specific factors in addition to various substance dependent parameters. Further socio-economic factors may be taken into consideration. The number of parameters to be included may well appear to be prohibitive for developing a sensible model. The study introduces hierarchical partial order ranking (HPOR) that remedies this problem. By HPOR the original parameters are initially grouped based on their mutual connection and a set of meta-descriptors is derived representing the ranking corresponding to the single groups of descriptors, respectively. A second partial order ranking is carried out based on the meta-descriptors, the final ranking being disclosed though average ranks. An illustrative example on the prioritization of polluted sites is given.
Trees and Hierarchical Structures
Haeseler, Arndt
1990-01-01
The "raison d'etre" of hierarchical dustering theory stems from one basic phe nomenon: This is the notorious non-transitivity of similarity relations. In spite of the fact that very often two objects may be quite similar to a third without being that similar to each other, one still wants to dassify objects according to their similarity. This should be achieved by grouping them into a hierarchy of non-overlapping dusters such that any two objects in ~ne duster appear to be more related to each other than they are to objects outside this duster. In everyday life, as well as in essentially every field of scientific investigation, there is an urge to reduce complexity by recognizing and establishing reasonable das sification schemes. Unfortunately, this is counterbalanced by the experience of seemingly unavoidable deadlocks caused by the existence of sequences of objects, each comparatively similar to the next, but the last rather different from the first.
Hierarchical Affinity Propagation
Givoni, Inmar; Frey, Brendan J
2012-01-01
Affinity propagation is an exemplar-based clustering algorithm that finds a set of data-points that best exemplify the data, and associates each datapoint with one exemplar. We extend affinity propagation in a principled way to solve the hierarchical clustering problem, which arises in a variety of domains including biology, sensor networks and decision making in operational research. We derive an inference algorithm that operates by propagating information up and down the hierarchy, and is efficient despite the high-order potentials required for the graphical model formulation. We demonstrate that our method outperforms greedy techniques that cluster one layer at a time. We show that on an artificial dataset designed to mimic the HIV-strain mutation dynamics, our method outperforms related methods. For real HIV sequences, where the ground truth is not available, we show our method achieves better results, in terms of the underlying objective function, and show the results correspond meaningfully to geographi...
Optimisation by hierarchical search
Zintchenko, Ilia; Hastings, Matthew; Troyer, Matthias
2015-03-01
Finding optimal values for a set of variables relative to a cost function gives rise to some of the hardest problems in physics, computer science and applied mathematics. Although often very simple in their formulation, these problems have a complex cost function landscape which prevents currently known algorithms from efficiently finding the global optimum. Countless techniques have been proposed to partially circumvent this problem, but an efficient method is yet to be found. We present a heuristic, general purpose approach to potentially improve the performance of conventional algorithms or special purpose hardware devices by optimising groups of variables in a hierarchical way. We apply this approach to problems in combinatorial optimisation, machine learning and other fields.
How hierarchical is language use?
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
How hierarchical is language use?
Frank, Stefan L; Bod, Rens; Christiansen, Morten H
2012-11-22
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.
Associative Hierarchical Random Fields.
Ladický, L'ubor; Russell, Chris; Kohli, Pushmeet; Torr, Philip H S
2014-06-01
This paper makes two contributions: the first is the proposal of a new model-The associative hierarchical random field (AHRF), and a novel algorithm for its optimization; the second is the application of this model to the problem of semantic segmentation. Most methods for semantic segmentation are formulated as a labeling problem for variables that might correspond to either pixels or segments such as super-pixels. It is well known that the generation of super pixel segmentations is not unique. This has motivated many researchers to use multiple super pixel segmentations for problems such as semantic segmentation or single view reconstruction. These super-pixels have not yet been combined in a principled manner, this is a difficult problem, as they may overlap, or be nested in such a way that the segmentations form a segmentation tree. Our new hierarchical random field model allows information from all of the multiple segmentations to contribute to a global energy. MAP inference in this model can be performed efficiently using powerful graph cut based move making algorithms. Our framework generalizes much of the previous work based on pixels or segments, and the resulting labelings can be viewed both as a detailed segmentation at the pixel level, or at the other extreme, as a segment selector that pieces together a solution like a jigsaw, selecting the best segments from different segmentations as pieces. We evaluate its performance on some of the most challenging data sets for object class segmentation, and show that this ability to perform inference using multiple overlapping segmentations leads to state-of-the-art results.
Joint hierarchical models for sparsely sampled high-dimensional LiDAR and forest variables
Finley, Andrew O.; Banerjee, Sudipto; Zhou, Yuzhen; Cook, Bruce D; Babcock, Chad
2016-01-01
Recent advancements in remote sensing technology, specifically Light Detection and Ranging (LiDAR) sensors, provide the data needed to quantify forest characteristics at a fine spatial resolution over large geographic domains. From an inferential standpoint, there is interest in prediction and interpolation of the often sparsely sampled and spatially misaligned LiDAR signals and forest variables. We propose a fully process-based Bayesian hierarchical model for above ground biomass (AGB) and L...
Evaluation of the hierarchical temporal memory soft computing platform and its VLSI architecture
Melis, W.J.C.; Chizuwa, S.; Kameyama, M.
2009-01-01
A large number of real world applications, like user support systems, can still not be performed easily by conventional algorithms in comparison with the human brain. Recently, such intelligence has often been reached by using probability based systems. This paper presents results on the implementation of one such user support system, namely an intention estimation information appliance system, on a Bayesian network as well as hierarchical temporal memory. The latter is a new and quite promis...
Irregular-Time Bayesian Networks
Ramati, Michael
2012-01-01
In many fields observations are performed irregularly along time, due to either measurement limitations or lack of a constant immanent rate. While discrete-time Markov models (as Dynamic Bayesian Networks) introduce either inefficient computation or an information loss to reasoning about such processes, continuous-time Markov models assume either a discrete state space (as Continuous-Time Bayesian Networks), or a flat continuous state space (as stochastic dif- ferential equations). To address these problems, we present a new modeling class called Irregular-Time Bayesian Networks (ITBNs), generalizing Dynamic Bayesian Networks, allowing substantially more compact representations, and increasing the expressivity of the temporal dynamics. In addition, a globally optimal solution is guaranteed when learning temporal systems, provided that they are fully observed at the same irregularly spaced time-points, and a semiparametric subclass of ITBNs is introduced to allow further adaptation to the irregular nature of t...
Bayesian analysis in moment inequality models
Liao, Yuan; 10.1214/09-AOS714
2010-01-01
This paper presents a study of the large-sample behavior of the posterior distribution of a structural parameter which is partially identified by moment inequalities. The posterior density is derived based on the limited information likelihood. The posterior distribution converges to zero exponentially fast on any $\\delta$-contraction outside the identified region. Inside, it is bounded below by a positive constant if the identified region is assumed to have a nonempty interior. Our simulation evidence indicates that the Bayesian approach has advantages over frequentist methods, in the sense that, with a proper choice of the prior, the posterior provides more information about the true parameter inside the identified region. We also address the problem of moment and model selection. Our optimality criterion is the maximum posterior procedure and we show that, asymptotically, it selects the true moment/model combination with the most moment inequalities and the simplest model.
Bayesian Tracking of Visual Objects
Zheng, Nanning; Xue, Jianru
Tracking objects in image sequences involves performing motion analysis at the object level, which is becoming an increasingly important technology in a wide range of computer video applications, including video teleconferencing, security and surveillance, video segmentation, and editing. In this chapter, we focus on sequential Bayesian estimation techniques for visual tracking. We first introduce the sequential Bayesian estimation framework, which acts as the theoretic basis for visual tracking. Then, we present approaches to constructing representation models for specific objects.
Bayesian Networks and Influence Diagrams
DEFF Research Database (Denmark)
Kjærulff, Uffe Bro; Madsen, Anders Læsø
Probabilistic networks, also known as Bayesian networks and influence diagrams, have become one of the most promising technologies in the area of applied artificial intelligence, offering intuitive, efficient, and reliable methods for diagnosis, prediction, decision making, classification......, troubleshooting, and data mining under uncertainty. Bayesian Networks and Influence Diagrams: A Guide to Construction and Analysis provides a comprehensive guide for practitioners who wish to understand, construct, and analyze intelligent systems for decision support based on probabilistic networks. Intended...
A Focused Bayesian Information Criterion
Georges Nguefack-Tsague; Ingo Bulla
2014-01-01
Myriads of model selection criteria (Bayesian and frequentist) have been proposed in the literature aiming at selecting a single model regardless of its intended use. An honorable exception in the frequentist perspective is the “focused information criterion” (FIC) aiming at selecting a model based on the parameter of interest (focus). This paper takes the same view in the Bayesian context; that is, a model may be good for one estimand but bad for another. The proposed method exploits the Bay...
Bayesian analysis of CCDM Models
Jesus, J. F.; Valentim, R.; Andrade-Oliveira, F.
2016-01-01
Creation of Cold Dark Matter (CCDM), in the context of Einstein Field Equations, leads to negative creation pressure, which can be used to explain the accelerated expansion of the Universe. In this work we tested six different spatially flat models for matter creation using statistical tools, at light of SN Ia data: Akaike Information Criterion (AIC), Bayesian Information Criterion (BIC) and Bayesian Evidence (BE). These approaches allow to compare models considering goodness of fit and numbe...
Modeling hierarchical structures - Hierarchical Linear Modeling using MPlus
Jelonek, M
2006-01-01
The aim of this paper is to present the technique (and its linkage with physics) of overcoming problems connected to modeling social structures, which are typically hierarchical. Hierarchical Linear Models provide a conceptual and statistical mechanism for drawing conclusions regarding the influence of phenomena at different levels of analysis. In the social sciences it is used to analyze many problems such as educational, organizational or market dilemma. This paper introduces the logic of modeling hierarchical linear equations and estimation based on MPlus software. I present my own model to illustrate the impact of different factors on school acceptation level.
Hierarchical spatiotemporal matrix models for characterizing invasions.
Hooten, Mevin B; Wikle, Christopher K; Dorazio, Robert M; Royle, J Andrew
2007-06-01
The growth and dispersal of biotic organisms is an important subject in ecology. Ecologists are able to accurately describe survival and fecundity in plant and animal populations and have developed quantitative approaches to study the dynamics of dispersal and population size. Of particular interest are the dynamics of invasive species. Such nonindigenous animals and plants can levy significant impacts on native biotic communities. Effective models for relative abundance have been developed; however, a better understanding of the dynamics of actual population size (as opposed to relative abundance) in an invasion would be beneficial to all branches of ecology. In this article, we adopt a hierarchical Bayesian framework for modeling the invasion of such species while addressing the discrete nature of the data and uncertainty associated with the probability of detection. The nonlinear dynamics between discrete time points are intuitively modeled through an embedded deterministic population model with density-dependent growth and dispersal components. Additionally, we illustrate the importance of accommodating spatially varying dispersal rates. The method is applied to the specific case of the Eurasian Collared-Dove, an invasive species at mid-invasion in the United States at the time of this writing.
Bayesian Modeling of ChIP-chip Data Through a High-Order Ising Model
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.
Bayesian Inference of Giant Exoplanet Physics
Thorngren, Daniel; Fortney, Jonathan J.
2017-01-01
The physical processes within a giant planet directly set its observed radius for a given mass, age, and insolation. The important aspects are the planet’s bulk composition and its interior thermal evolution. By studying many giant planets as an ensemble, we can gain insight into this physics. We demonstrate two novel examples here. We examine 50 cooler transiting giant planets, whose insolation is sufficiently low (T_eff < 1000 K) that they are not affected by the hot Jupiter radius inflation effect. For these planets, the thermal evolution is relatively well understood, and we show that the bulk planet metallicity increases with the total planet mass, which directly impacts plans for future atmospheric studies. We also examine the relation with stellar metallicity and discuss how these relations place new constraints on the core accretion model of planet formation. Our newest work seeks to quantify the flow of energy into hot Jupiters needed to explain their enlarged radii, in addition to their bulk composition. Because the former is related to stellar insolation and the latter is related to mass, we are able to create a hierarchical Bayesian model to disentangle the two effects in our sample of ~300 transiting giant planets. Our results show conclusively that the inflation power is not a simple fraction of stellar insolation: instead, the power increases with incident flux at a much higher rate. We use these results to test published models of giant planet inflation and to provide accurate empirical mass-radius relations for giant planets.
Dynamic Batch Bayesian Optimization
Azimi, Javad; Fern, Xiaoli
2011-01-01
Bayesian optimization (BO) algorithms try to optimize an unknown function that is expensive to evaluate using minimum number of evaluations/experiments. Most of the proposed algorithms in BO are sequential, where only one experiment is selected at each iteration. This method can be time inefficient when each experiment takes a long time and more than one experiment can be ran concurrently. On the other hand, requesting a fix-sized batch of experiments at each iteration causes performance inefficiency in BO compared to the sequential policies. In this paper, we present an algorithm that asks a batch of experiments at each time step t where the batch size p_t is dynamically determined in each step. Our algorithm is based on the observation that the sequence of experiments selected by the sequential policy can sometimes be almost independent from each other. Our algorithm identifies such scenarios and request those experiments at the same time without degrading the performance. We evaluate our proposed method us...
Mobile Multicast in Hierarchical Proxy Mobile IPV6
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.
Modeling hierarchical structures - Hierarchical Linear Modeling using MPlus
Jelonek, Magdalena
2006-01-01
The aim of this paper is to present the technique (and its linkage with physics) of overcoming problems connected to modeling social structures, which are typically hierarchical. Hierarchical Linear Models provide a conceptual and statistical mechanism for drawing conclusions regarding the influence of phenomena at different levels of analysis. In the social sciences it is used to analyze many problems such as educational, organizational or market dilemma. This paper introduces the logic of m...
Petrov, Romain G; Boskri, Abdelkarim; Folcher, Jean-Pierre; Lagarde, Stephane; Bresson, Yves; Benkhaldoum, Zouhair; Lazrek, Mohamed; Rakshit, Suvendu
2014-01-01
The limiting magnitude is a key issue for optical interferometry. Pairwise fringe trackers based on the integrated optics concepts used for example in GRAVITY seem limited to about K=10.5 with the 8m Unit Telescopes of the VLTI, and there is a general "common sense" statement that the efficiency of fringe tracking, and hence the sensitivity of optical interferometry, must decrease as the number of apertures increases, at least in the near infrared where we are still limited by detector readout noise. Here we present a Hierarchical Fringe Tracking (HFT) concept with sensitivity at least equal to this of a two apertures fringe trackers. HFT is based of the combination of the apertures in pairs, then in pairs of pairs then in pairs of groups. The key HFT module is a device that behaves like a spatial filter for two telescopes (2TSF) and transmits all or most of the flux of a cophased pair in a single mode beam. We give an example of such an achromatic 2TSF, based on very broadband dispersed fringes analyzed by g...
Tunesi, Luca; Armbruster, Philippe
2004-02-01
The objective of this paper is to demonstrate a suitable hierarchical networking solution to improve capabilities and performances of space systems, with significant recurrent costs saving and more efficient design & manufacturing flows. Classically, a satellite can be split in two functional sub-systems: the platform and the payload complement. The platform is in charge of providing power, attitude & orbit control and up/down-link services, whereas the payload represents the scientific and/or operational instruments/transponders and embodies the objectives of the mission. One major possibility to improve the performance of payloads, by limiting the data return to pertinent information, is to process data on board thanks to a proper implementation of the payload data system. In this way, it is possible to share non-recurring development costs by exploiting a system that can be adopted by the majority of space missions. It is believed that the Modular and Scalable Payload Data System, under development by ESA, provides a suitable solution to fulfil a large range of future mission requirements. The backbone of the system is the standardised high data rate SpaceWire network http://www.ecss.nl/. As complement, a lower speed command and control bus connecting peripherals is required. For instance, at instrument level, there is a need for a "local" low complexity bus, which gives the possibility to command and control sensors and actuators. Moreover, most of the connections at sub-system level are related to discrete signals management or simple telemetry acquisitions, which can easily and efficiently be handled by a local bus. An on-board hierarchical network can therefore be defined by interconnecting high-speed links and local buses. Additionally, it is worth stressing another important aspect of the design process: Agencies and ESA in particular are frequently confronted with a big consortium of geographically spread companies located in different countries, each one
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.
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.
Bayesian Model Selection and Statistical Modeling
Ando, Tomohiro
2010-01-01
Bayesian model selection is a fundamental part of the Bayesian statistical modeling process. The quality of these solutions usually depends on the goodness of the constructed Bayesian model. Realizing how crucial this issue is, many researchers and practitioners have been extensively investigating the Bayesian model selection problem. This book provides comprehensive explanations of the concepts and derivations of the Bayesian approach for model selection and related criteria, including the Bayes factor, the Bayesian information criterion (BIC), the generalized BIC, and the pseudo marginal lik
An accessible method for implementing hierarchical models with spatio-temporal abundance data
Ross, Beth E.; Hooten, Melvin B.; Koons, David N.
2012-01-01
A common goal in ecology and wildlife management is to determine the causes of variation in population dynamics over long periods of time and across large spatial scales. Many assumptions must nevertheless be overcome to make appropriate inference about spatio-temporal variation in population dynamics, such as autocorrelation among data points, excess zeros, and observation error in count data. To address these issues, many scientists and statisticians have recommended the use of Bayesian hierarchical models. Unfortunately, hierarchical statistical models remain somewhat difficult to use because of the necessary quantitative background needed to implement them, or because of the computational demands of using Markov Chain Monte Carlo algorithms to estimate parameters. Fortunately, new tools have recently been developed that make it more feasible for wildlife biologists to fit sophisticated hierarchical Bayesian models (i.e., Integrated Nested Laplace Approximation, ‘INLA’). We present a case study using two important game species in North America, the lesser and greater scaup, to demonstrate how INLA can be used to estimate the parameters in a hierarchical model that decouples observation error from process variation, and accounts for unknown sources of excess zeros as well as spatial and temporal dependence in the data. Ultimately, our goal was to make unbiased inference about spatial variation in population trends over time.
Hierarchical materials: Background and perspectives
DEFF Research Database (Denmark)
2016-01-01
Hierarchical design draws inspiration from analysis of biological materials and has opened new possibilities for enhancing performance and enabling new functionalities and extraordinary properties. With the development of nanotechnology, the necessary technological requirements for the manufactur...
Hierarchical clustering for graph visualization
Clémençon, Stéphan; Rossi, Fabrice; Tran, Viet Chi
2012-01-01
This paper describes a graph visualization methodology based on hierarchical maximal modularity clustering, with interactive and significant coarsening and refining possibilities. An application of this method to HIV epidemic analysis in Cuba is outlined.
Direct hierarchical assembly of nanoparticles
Xu, Ting; Zhao, Yue; Thorkelsson, Kari
2014-07-22
The present invention provides hierarchical assemblies of a block copolymer, a bifunctional linking compound and a nanoparticle. The block copolymers form one micro-domain and the nanoparticles another micro-domain.
A Bayesian Approach for Summarizing and Modeling Time-Series Exposure Data with Left Censoring.
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
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
Bayesian microsaccade detection
Mihali, Andra; van Opheusden, Bas; Ma, Wei Ji
2017-01-01
Microsaccades are high-velocity fixational eye movements, with special roles in perception and cognition. The default microsaccade detection method is to determine when the smoothed eye velocity exceeds a threshold. We have developed a new method, Bayesian microsaccade detection (BMD), which performs inference based on a simple statistical model of eye positions. In this model, a hidden state variable changes between drift and microsaccade states at random times. The eye position is a biased random walk with different velocity distributions for each state. BMD generates samples from the posterior probability distribution over the eye state time series given the eye position time series. Applied to simulated data, BMD recovers the “true” microsaccades with fewer errors than alternative algorithms, especially at high noise. Applied to EyeLink eye tracker data, BMD detects almost all the microsaccades detected by the default method, but also apparent microsaccades embedded in high noise—although these can also be interpreted as false positives. Next we apply the algorithms to data collected with a Dual Purkinje Image eye tracker, whose higher precision justifies defining the inferred microsaccades as ground truth. When we add artificial measurement noise, the inferences of all algorithms degrade; however, at noise levels comparable to EyeLink data, BMD recovers the “true” microsaccades with 54% fewer errors than the default algorithm. Though unsuitable for online detection, BMD has other advantages: It returns probabilities rather than binary judgments, and it can be straightforwardly adapted as the generative model is refined. We make our algorithm available as a software package. PMID:28114483
Maximum margin Bayesian network classifiers.
Pernkopf, Franz; Wohlmayr, Michael; Tschiatschek, Sebastian
2012-03-01
We present a maximum margin parameter learning algorithm for Bayesian network classifiers using a conjugate gradient (CG) method for optimization. In contrast to previous approaches, we maintain the normalization constraints on the parameters of the Bayesian network during optimization, i.e., the probabilistic interpretation of the model is not lost. This enables us to handle missing features in discriminatively optimized Bayesian networks. In experiments, we compare the classification performance of maximum margin parameter learning to conditional likelihood and maximum likelihood learning approaches. Discriminative parameter learning significantly outperforms generative maximum likelihood estimation for naive Bayes and tree augmented naive Bayes structures on all considered data sets. Furthermore, maximizing the margin dominates the conditional likelihood approach in terms of classification performance in most cases. We provide results for a recently proposed maximum margin optimization approach based on convex relaxation. While the classification results are highly similar, our CG-based optimization is computationally up to orders of magnitude faster. Margin-optimized Bayesian network classifiers achieve classification performance comparable to support vector machines (SVMs) using fewer parameters. Moreover, we show that unanticipated missing feature values during classification can be easily processed by discriminatively optimized Bayesian network classifiers, a case where discriminative classifiers usually require mechanisms to complete unknown feature values in the data first.
A Focused Bayesian Information Criterion
Directory of Open Access Journals (Sweden)
Georges Nguefack-Tsague
2014-01-01
Full Text Available Myriads of model selection criteria (Bayesian and frequentist have been proposed in the literature aiming at selecting a single model regardless of its intended use. An honorable exception in the frequentist perspective is the “focused information criterion” (FIC aiming at selecting a model based on the parameter of interest (focus. This paper takes the same view in the Bayesian context; that is, a model may be good for one estimand but bad for another. The proposed method exploits the Bayesian model averaging (BMA machinery to obtain a new criterion, the focused Bayesian model averaging (FoBMA, for which the best model is the one whose estimate is closest to the BMA estimate. In particular, for two models, this criterion reduces to the classical Bayesian model selection scheme of choosing the model with the highest posterior probability. The new method is applied in linear regression, logistic regression, and survival analysis. This criterion is specially important in epidemiological studies in which the objective is often to determine a risk factor (focus for a disease, adjusting for potential confounding factors.
Hierarchical architecture of active knits
Abel, Julianna; Luntz, Jonathan; Brei, Diann
2013-12-01
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.
Advanced hierarchical distance sampling
Royle, Andy
2016-01-01
In this chapter, we cover a number of important extensions of the basic hierarchical distance-sampling (HDS) framework from Chapter 8. First, we discuss the inclusion of “individual covariates,” such as group size, in the HDS model. This is important in many surveys where animals form natural groups that are the primary observation unit, with the size of the group expected to have some influence on detectability. We also discuss HDS integrated with time-removal and double-observer or capture-recapture sampling. These “combined protocols” can be formulated as HDS models with individual covariates, and thus they have a commonality with HDS models involving group structure (group size being just another individual covariate). We cover several varieties of open-population HDS models that accommodate population dynamics. On one end of the spectrum, we cover models that allow replicate distance sampling surveys within a year, which estimate abundance relative to availability and temporary emigration through time. We consider a robust design version of that model. We then consider models with explicit dynamics based on the Dail and Madsen (2011) model and the work of Sollmann et al. (2015). The final major theme of this chapter is relatively newly developed spatial distance sampling models that accommodate explicit models describing the spatial distribution of individuals known as Point Process models. We provide novel formulations of spatial DS and HDS models in this chapter, including implementations of those models in the unmarked package using a hack of the pcount function for N-mixture models.
Bayesian Methods and Universal Darwinism
Campbell, John
2010-01-01
Bayesian methods since the time of Laplace have been understood by their practitioners as closely aligned to the scientific method. Indeed a recent champion of Bayesian methods, E. T. Jaynes, titled his textbook on the subject Probability Theory: the Logic of Science. Many philosophers of science including Karl Popper and Donald Campbell have interpreted the evolution of Science as a Darwinian process consisting of a 'copy with selective retention' algorithm abstracted from Darwin's theory of Natural Selection. Arguments are presented for an isomorphism between Bayesian Methods and Darwinian processes. Universal Darwinism, as the term has been developed by Richard Dawkins, Daniel Dennett and Susan Blackmore, is the collection of scientific theories which explain the creation and evolution of their subject matter as due to the operation of Darwinian processes. These subject matters span the fields of atomic physics, chemistry, biology and the social sciences. The principle of Maximum Entropy states that system...
Near-Optimal Bayesian Active Learning with Noisy Observations
Golovin, Daniel; Ray, Debajyoti
2010-01-01
We tackle the fundamental problem of Bayesian active learning with noise, where we need to adaptively select from a number of expensive tests in order to identify an unknown hypothesis sampled from a known prior distribution. In the case of noise-free observations, a greedy algorithm called generalized binary search (GBS) is known to perform near-optimally. We show that if the observations are noisy, perhaps surprisingly, GBS can perform very poorly. We develop EC2, a novel, greedy active learning algorithm and prove that it is competitive with the optimal policy, thus obtaining the first competitiveness guarantees for Bayesian active learning with noisy observations. Our bounds rely on a recently discovered diminishing returns property called adaptive submodularity, generalizing the classical notion of submodular set functions to adaptive policies. Our results hold even if the tests have non-uniform cost and their noise is correlated. We also propose EffECXtive, a particularly fast approximation of EC2, and ...
Support agnostic Bayesian matching pursuit for block sparse signals
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.
Sparse reconstruction using distribution agnostic bayesian matching pursuit
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.
Approximate Bayesian computation for machine learning, inverse problems and big data
Mohammad-Djafari, Ali
2017-06-01
This paper summarizes my tutorial talk in MaxEnt 2016 workshop. Starting from the basics of the Bayesian approach and simple example of low dimensional parameter estimation where almost all the computations can be done easily, we go very fast to high dimensional case. In those real world cases, even for the sample case of linear model with Gaussian prior, where the posterior law is also Gaussian, the cost of the computation of the posterior covariance becomes important and needs approximate and fast algorithms. Different approximation methods for model comparison and model selection in machine learning problems are presented in summary. Among the existing methods, we mention Laplace approximation, Akaike Information Criterion (AIC), Bayesian Information Criterion (BIC) and Variational Bayesian Approximation (VBA) Methods. Finally, through two examples of inverse problems in imaging systems: X ray and Diffraction wave Computed Tomography (CT), we show how to handle the real great dimensional problems.
Bayesian Missile System Reliability from Point Estimates
2014-10-28
OCT 2014 2. REPORT TYPE N/A 3. DATES COVERED - 4. TITLE AND SUBTITLE Bayesian Missile System Reliability from Point Estimates 5a. CONTRACT...Principle (MEP) to convert point estimates to probability distributions to be used as priors for Bayesian reliability analysis of missile data, and...illustrate this approach by applying the priors to a Bayesian reliability model of a missile system. 15. SUBJECT TERMS priors, Bayesian , missile
3D Bayesian contextual classifiers
DEFF Research Database (Denmark)
Larsen, Rasmus
2000-01-01
We extend a series of multivariate Bayesian 2-D contextual classifiers to 3-D by specifying a simultaneous Gaussian distribution for the feature vectors as well as a prior distribution of the class variables of a pixel and its 6 nearest 3-D neighbours.......We extend a series of multivariate Bayesian 2-D contextual classifiers to 3-D by specifying a simultaneous Gaussian distribution for the feature vectors as well as a prior distribution of the class variables of a pixel and its 6 nearest 3-D neighbours....
Attention in a bayesian framework
DEFF Research Database (Denmark)
Whiteley, Louise Emma; Sahani, Maneesh
2012-01-01
, and include both selective phenomena, where attention is invoked by cues that point to particular stimuli, and integrative phenomena, where attention is invoked dynamically by endogenous processing. However, most previous Bayesian accounts of attention have focused on describing relatively simple experimental......The behavioral phenomena of sensory attention are thought to reflect the allocation of a limited processing resource, but there is little consensus on the nature of the resource or why it should be limited. Here we argue that a fundamental bottleneck emerges naturally within Bayesian models...
Bayesian test and Kuhn's paradigm
Institute of Scientific and Technical Information of China (English)
Chen Xiaoping
2006-01-01
Kuhn's theory of paradigm reveals a pattern of scientific progress,in which normal science alternates with scientific revolution.But Kuhn underrated too much the function of scientific test in his pattern,because he focuses all his attention on the hypothetico-deductive schema instead of Bayesian schema.This paper employs Bayesian schema to re-examine Kuhn's theory of paradigm,to uncover its logical and rational components,and to illustrate the tensional structure of logic and belief,rationality and irrationality,in the process of scientific revolution.
Perception, illusions and Bayesian inference.
Nour, Matthew M; Nour, Joseph M
2015-01-01
Descriptive psychopathology makes a distinction between veridical perception and illusory perception. In both cases a perception is tied to a sensory stimulus, but in illusions the perception is of a false object. This article re-examines this distinction in light of new work in theoretical and computational neurobiology, which views all perception as a form of Bayesian statistical inference that combines sensory signals with prior expectations. Bayesian perceptual inference can solve the 'inverse optics' problem of veridical perception and provides a biologically plausible account of a number of illusory phenomena, suggesting that veridical and illusory perceptions are generated by precisely the same inferential mechanisms.
Plug & Play object oriented Bayesian networks
DEFF Research Database (Denmark)
Bangsø, Olav; Flores, J.; Jensen, Finn Verner
2003-01-01
Object oriented Bayesian networks have proven themselves useful in recent years. The idea of applying an object oriented approach to Bayesian networks has extended their scope to larger domains that can be divided into autonomous but interrelated entities. Object oriented Bayesian networks have b...
A Bayesian Nonparametric Approach to Test Equating
Karabatsos, George; Walker, Stephen G.
2009-01-01
A Bayesian nonparametric model is introduced for score equating. It is applicable to all major equating designs, and has advantages over previous equating models. Unlike the previous models, the Bayesian model accounts for positive dependence between distributions of scores from two tests. The Bayesian model and the previous equating models are…
Bayesian Model Averaging for Propensity Score Analysis
Kaplan, David; Chen, Jianshen
2013-01-01
The purpose of this study is to explore Bayesian model averaging in the propensity score context. Previous research on Bayesian propensity score analysis does not take into account model uncertainty. In this regard, an internally consistent Bayesian framework for model building and estimation must also account for model uncertainty. The…
Bayesian networks and food security - An introduction
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 sup
Choi, Kilchan; Seltzer, Michael
2010-01-01
In studies of change in education and numerous other fields, interest often centers on how differences in the status of individuals at the start of a period of substantive interest relate to differences in subsequent change. In this article, the authors present a fully Bayesian approach to estimating three-level Hierarchical Models in which latent…
The Hierarchical Dirichlet Process Hidden Semi-Markov Model
Johnson, Matthew J
2012-01-01
There is much interest in the Hierarchical Dirichlet Process Hidden Markov Model (HDP-HMM) as a natural Bayesian nonparametric extension of the traditional HMM. However, in many settings the HDP-HMM's strict Markovian constraints are undesirable, particularly if we wish to learn or encode non-geometric state durations. We can extend the HDP-HMM to capture such structure by drawing upon explicit-duration semi- Markovianity, which has been developed in the parametric setting to allow construction of highly interpretable models that admit natural prior information on state durations. In this paper we introduce the explicitduration HDP-HSMM and develop posterior sampling algorithms for efficient inference in both the direct-assignment and weak-limit approximation settings. We demonstrate the utility of the model and our inference methods on synthetic data as well as experiments on a speaker diarization problem and an example of learning the patterns in Morse code.
Bayesian Classification of Image Structures
DEFF Research Database (Denmark)
Goswami, Dibyendu; Kalkan, Sinan; Krüger, Norbert
2009-01-01
In this paper, we describe work on Bayesian classi ers for distinguishing between homogeneous structures, textures, edges and junctions. We build semi-local classiers from hand-labeled images to distinguish between these four different kinds of structures based on the concept of intrinsic dimensi...
Bayesian Analysis of Experimental Data
Directory of Open Access Journals (Sweden)
Lalmohan Bhar
2013-10-01
Full Text Available Analysis of experimental data from Bayesian point of view has been considered. Appropriate methodology has been developed for application into designed experiments. Normal-Gamma distribution has been considered for prior distribution. Developed methodology has been applied to real experimental data taken from long term fertilizer experiments.
Bayesian Networks and Influence Diagrams
DEFF Research Database (Denmark)
Kjærulff, Uffe Bro; Madsen, Anders Læsø
Bayesian Networks and Influence Diagrams: A Guide to Construction and Analysis, Second Edition, provides a comprehensive guide for practitioners who wish to understand, construct, and analyze intelligent systems for decision support based on probabilistic networks. This new edition contains six new...
Bayesian image restoration, using configurations
DEFF Research Database (Denmark)
Thorarinsdottir, Thordis
configurations are expressed in terms of the mean normal measure of the random set. These probabilities are used as prior probabilities in a Bayesian image restoration approach. Estimation of the remaining parameters in the model is outlined for salt and pepper noise. The inference in the model is discussed...
Bayesian image restoration, using configurations
DEFF Research Database (Denmark)
Thorarinsdottir, Thordis Linda
2006-01-01
configurations are expressed in terms of the mean normal measure of the random set. These probabilities are used as prior probabilities in a Bayesian image restoration approach. Estimation of the remaining parameters in the model is outlined for the salt and pepper noise. The inference in the model is discussed...
Differentiated Bayesian Conjoint Choice Designs
Z. Sándor (Zsolt); M. Wedel (Michel)
2003-01-01
textabstractPrevious conjoint choice design construction procedures have produced a single design that is administered to all subjects. This paper proposes to construct a limited set of different designs. The designs are constructed in a Bayesian fashion, taking into account prior uncertainty about
3-D contextual Bayesian classifiers
DEFF Research Database (Denmark)
Larsen, Rasmus
In this paper we will consider extensions of a series of Bayesian 2-D contextual classification pocedures proposed by Owen (1984) Hjort & Mohn (1984) and Welch & Salter (1971) and Haslett (1985) to 3 spatial dimensions. It is evident that compared to classical pixelwise classification further...
Bayesian inference for Hawkes processes
DEFF Research Database (Denmark)
Rasmussen, Jakob Gulddahl
The Hawkes process is a practically and theoretically important class of point processes, but parameter-estimation for such a process can pose various problems. In this paper we explore and compare two approaches to Bayesian inference. The first approach is based on the so-called conditional...
Bayesian inference for Hawkes processes
DEFF Research Database (Denmark)
Rasmussen, Jakob Gulddahl
2013-01-01
The Hawkes process is a practically and theoretically important class of point processes, but parameter-estimation for such a process can pose various problems. In this paper we explore and compare two approaches to Bayesian inference. The first approach is based on the so-called conditional...
Bayesian Evidence and Model Selection
Knuth, Kevin H; Malakar, Nabin K; Mubeen, Asim M; Placek, Ben
2014-01-01
In this paper we review the concept of the Bayesian evidence and its application to model selection. The theory is presented along with a discussion of analytic, approximate and numerical techniques. Application to several practical examples within the context of signal processing are discussed.
Bayesian inference for Hawkes processes
DEFF Research Database (Denmark)
Rasmussen, Jakob Gulddahl
The Hawkes process is a practically and theoretically important class of point processes, but parameter-estimation for such a process can pose various problems. In this paper we explore and compare two approaches to Bayesian inference. The first approach is based on the so-called conditional...
Bayesian stable isotope mixing models
In this paper we review recent advances in Stable Isotope Mixing Models (SIMMs) and place them into an over-arching Bayesian statistical framework which allows for several useful extensions. SIMMs are used to quantify the proportional contributions of various sources to a mixtur...
Naive Bayesian for Email Filtering
Institute of Scientific and Technical Information of China (English)
无
2002-01-01
The paper presents a method of email filter based on Naive Bayesian theory that can effectively filter junk mail and illegal mail. Furthermore, the keys of implementation are discussed in detail. The filtering model is obtained from training set of email. The filtering can be done without the users specification of filtering rules.
Bayesian tests of measurement invariance
Verhagen, A.J.; Fox, J.P.
2013-01-01
Random item effects models provide a natural framework for the exploration of violations of measurement invariance without the need for anchor items. Within the random item effects modelling framework, Bayesian tests (Bayes factor, deviance information criterion) are proposed which enable multiple m
Bayesian NL interpretation and learning
Zeevat, H.
2011-01-01
Everyday natural language communication is normally successful, even though contemporary computational linguistics has shown that NL is characterised by very high degree of ambiguity and the results of stochastic methods are not good enough to explain the high success rate. Bayesian natural language
Bayesian analysis of binary sequences
Torney, David C.
2005-03-01
This manuscript details Bayesian methodology for "learning by example", with binary n-sequences encoding the objects under consideration. Priors prove influential; conformable priors are described. Laplace approximation of Bayes integrals yields posterior likelihoods for all n-sequences. This involves the optimization of a definite function over a convex domain--efficiently effectuated by the sequential application of the quadratic program.
Bayesian Networks and Influence Diagrams
DEFF Research Database (Denmark)
Kjærulff, Uffe Bro; Madsen, Anders Læsø
Bayesian Networks and Influence Diagrams: A Guide to Construction and Analysis, Second Edition, provides a comprehensive guide for practitioners who wish to understand, construct, and analyze intelligent systems for decision support based on probabilistic networks. This new edition contains six new...
Hierarchical Matrices Method and Its Application in Electromagnetic Integral Equations
Directory of Open Access Journals (Sweden)
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.
Bayesian Alternation During Tactile Augmentation
Directory of Open Access Journals (Sweden)
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
A Bayesian approach to linear regression in astronomy
Sereno, Mauro
2015-01-01
Linear regression is common in astronomical analyses. I discuss a Bayesian hierarchical modeling of data with heteroscedastic and possibly correlated measurement errors and intrinsic scatter. The method fully accounts for time evolution. The slope, the normalization, and the intrinsic scatter of the relation can evolve with the redshift. The intrinsic distribution of the independent variable is approximated using a mixture of Gaussian distributions whose means and standard deviations depend on time. The method can address scatter in the measured independent variable (a kind of Eddington bias), selection effects in the response variable (Malmquist bias), and departure from linearity in form of a knee. I tested the method with toy models and simulations and quantified the effect of biases and inefficient modeling. The R-package LIRA (LInear Regression in Astronomy) is made available to perform the regression.
Designing and testing inflationary models with Bayesian networks
Price, Layne C; Frazer, Jonathan; Easther, Richard
2015-01-01
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.
Prior processes and their applications nonparametric Bayesian estimation
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...
Models for Prediction, Explanation and Control: Recursive Bayesian Networks
Directory of Open Access Journals (Sweden)
Lorenzo Casini
2011-01-01
Full Text Available The Recursive Bayesian Net (RBN formalism was originally developed for modelling nested causal relationships. In this paper we argue that the formalism can also be applied to modelling the hierarchical structure of mechanisms. The resulting network contains quantitative information about probabilities, as well as qualitative information about mechanistic structure and causal relations. Since information about probabilities, mechanisms and causal relations is vital for prediction, explanation and control respectively, an RBN can be applied to all these tasks. We show in particular how a simple two-level RBN can be used to model a mechanism in cancer science. The higher level of our model contains variables at the clinical level, while the lower level maps the structure of the cell's mechanism for apoptosis.
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.
Bayesian Analysis of Multiple Populations I: Statistical and Computational Methods
Stenning, D C; Robinson, E; van Dyk, D A; von Hippel, T; Sarajedini, A; Stein, N
2016-01-01
We develop a Bayesian model for globular clusters composed of multiple stellar populations, extending earlier statistical models for open clusters composed of simple (single) stellar populations (vanDyk et al. 2009, Stein et al. 2013). Specifically, we model globular clusters with two populations that differ in helium abundance. Our model assumes a hierarchical structuring of the parameters in which physical properties---age, metallicity, helium abundance, distance, absorption, and initial mass---are common to (i) the cluster as a whole or to (ii) individual populations within a cluster, or are unique to (iii) individual stars. An adaptive Markov chain Monte Carlo (MCMC) algorithm is devised for model fitting that greatly improves convergence relative to its precursor non-adaptive MCMC algorithm. Our model and computational tools are incorporated into an open-source software suite known as BASE-9. We use numerical studies to demonstrate that our method can recover parameters of two-population clusters, and al...
Bayesian multi-scale modeling for aggregated disease mapping data.
Aregay, Mehreteab; Lawson, Andrew B; Faes, Christel; Kirby, Russell S
2015-09-29
In disease mapping, a scale effect due to an aggregation of data from a finer resolution level to a coarser level is a common phenomenon. This article addresses this issue using a hierarchical Bayesian modeling framework. We propose four different multiscale models. The first two models use a shared random effect that the finer level inherits from the coarser level. The third model assumes two independent convolution models at the finer and coarser levels. The fourth model applies a convolution model at the finer level, but the relative risk at the coarser level is obtained by aggregating the estimates at the finer level. We compare the models using the deviance information criterion (DIC) and Watanabe-Akaike information criterion (WAIC) that are applied to real and simulated data. The results indicate that the models with shared random effects outperform the other models on a range of criteria.