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
terms have proven to have strong sparsity-inducing properties. In this work, we design pilot assisted channel estimators for OFDM wireless receivers within the framework of sparse Bayesian learning by defining hierarchical Bayesian prior models that lead to sparsity-inducing penalization terms......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....... 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...
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
A Bayesian hierarchical model for climate change detection and attribution
Katzfuss, Matthias; Hammerling, Dorit; Smith, Richard L.
2017-06-01
Regression-based detection and attribution methods continue to take a central role in the study of climate change and its causes. Here we propose a novel Bayesian hierarchical approach to this problem, which allows us to address several open methodological questions. Specifically, we take into account the uncertainties in the true temperature change due to imperfect measurements, the uncertainty in the true climate signal under different forcing scenarios due to the availability of only a small number of climate model simulations, and the uncertainty associated with estimating the climate variability covariance matrix, including the truncation of the number of empirical orthogonal functions (EOFs) in this covariance matrix. We apply Bayesian model averaging to assign optimal probabilistic weights to different possible truncations and incorporate all uncertainties into the inference on the regression coefficients. We provide an efficient implementation of our method in a software package and illustrate its use with a realistic application.
Landau, Will; Niemi, Jarad
2016-01-01
Markov chain Monte Carlo (MCMC) is the predominant tool used in Bayesian parameter estimation for hierarchical models. When the model expands due to an increasing number of hierarchical levels, number of groups at a particular level, or number of observations in each group, a fully Bayesian analysis via MCMC can easily become computationally demanding, even intractable. We illustrate how the steps in an MCMC for hierarchical models are predominantly one of two types: conditionally independent...
Topics in Bayesian Hierarchical Modeling and its Monte Carlo Computations
Tak, Hyung Suk
The first chapter addresses a Beta-Binomial-Logit model that is a Beta-Binomial conjugate hierarchical model with covariate information incorporated via a logistic regression. Various researchers in the literature have unknowingly used improper posterior distributions or have given incorrect statements about posterior propriety because checking posterior propriety can be challenging due to the complicated functional form of a Beta-Binomial-Logit model. We derive data-dependent necessary and sufficient conditions for posterior propriety within a class of hyper-prior distributions that encompass those used in previous studies. Frequency coverage properties of several hyper-prior distributions are also investigated to see when and whether Bayesian interval estimates of random effects meet their nominal confidence levels. The second chapter deals with a time delay estimation problem in astrophysics. When the gravitational field of an intervening galaxy between a quasar and the Earth is strong enough to split light into two or more images, the time delay is defined as the difference between their travel times. The time delay can be used to constrain cosmological parameters and can be inferred from the time series of brightness data of each image. To estimate the time delay, we construct a Gaussian hierarchical model based on a state-space representation for irregularly observed time series generated by a latent continuous-time Ornstein-Uhlenbeck process. Our Bayesian approach jointly infers model parameters via a Gibbs sampler. We also introduce a profile likelihood of the time delay as an approximation of its marginal posterior distribution. The last chapter specifies a repelling-attracting Metropolis algorithm, a new Markov chain Monte Carlo method to explore multi-modal distributions in a simple and fast manner. This algorithm is essentially a Metropolis-Hastings algorithm with a proposal that consists of a downhill move in density that aims to make local modes
A novel Bayesian hierarchical model for road safety hotspot prediction.
Fawcett, Lee; Thorpe, Neil; Matthews, Joseph; Kremer, Karsten
2017-02-01
In this paper, we propose a Bayesian hierarchical model for predicting accident counts in future years at sites within a pool of potential road safety hotspots. The aim is to inform road safety practitioners of the location of likely future hotspots to enable a proactive, rather than reactive, approach to road safety scheme implementation. A feature of our model is the ability to rank sites according to their potential to exceed, in some future time period, a threshold accident count which may be used as a criterion for scheme implementation. Our model specification enables the classical empirical Bayes formulation - commonly used in before-and-after studies, wherein accident counts from a single before period are used to estimate counterfactual counts in the after period - to be extended to incorporate counts from multiple time periods. This allows site-specific variations in historical accident counts (e.g. locally-observed trends) to offset estimates of safety generated by a global accident prediction model (APM), which itself is used to help account for the effects of global trend and regression-to-mean (RTM). The Bayesian posterior predictive distribution is exploited to formulate predictions and to properly quantify our uncertainty in these predictions. The main contributions of our model include (i) the ability to allow accident counts from multiple time-points to inform predictions, with counts in more recent years lending more weight to predictions than counts from time-points further in the past; (ii) where appropriate, the ability to offset global estimates of trend by variations in accident counts observed locally, at a site-specific level; and (iii) the ability to account for unknown/unobserved site-specific factors which may affect accident counts. We illustrate our model with an application to accident counts at 734 potential hotspots in the German city of Halle; we also propose some simple diagnostics to validate the predictive capability of our
Sparse Event Modeling with Hierarchical Bayesian Kernel Methods
2016-01-05
data, is it equally important to analyze the prediction power of a statistical model if it is going to be used for forecasting purposes. Prediction...Poisson Bayesian Kernel Methods for Modeling Count Data, Computational Statistics and Data Analysis (04 2016) TOTAL: 1 Books Number of Manuscripts...factors into the assessment of a rehabilitation project. Conclusions Bayesian kernel methods are powerful tools in forecasting data. These models make
Directory of Open Access Journals (Sweden)
Robert William Rankin
2016-03-01
Full Text Available We present a Hierarchical Bayesian version of Pollock's Closed Robust Design for studying the survival, temporary-migration, and abundance of marked animals. Through simulations and analyses of a bottlenose dolphin photo-identification dataset, we compare several estimation frameworks, including Maximum Likelihood estimation (ML, model-averaging by AICc, as well as Bayesian and Hierarchical Bayesian (HB procedures. Our results demonstrate a number of advantages of the Bayesian framework over other popular methods. First, for simple fixed-effect models, we show the near-equivalence of Bayesian and ML point-estimates and confidence/credibility intervals. Second, we demonstrate how there is an inherent correlation among temporary-migration and survival parameter estimates in the PCRD, and while this can lead to serious convergence issues and singularities among MLEs, we show that the Bayesian estimates were more reliable. Third, we demonstrate that a Hierarchical Bayesian model with carefully thought-out hyperpriors, can lead to similar parameter estimates and conclusions as multi-model inference by AICc model-averaging. This latter point is especially interesting for mark-recapture practitioners, for whom model-uncertainty and multi-model inference have become a major preoccupation. Lastly, we extend the Hierarchical Bayesian PCRD to include full-capture histories (i.e., by modelling a recruitment process and individual-level heterogeneity in detection probabilities, which can have important consequences for the range of phenomena studied by the PCRD, as well as lead to large differences in abundance estimates. For example, we estimate 8%-24% more bottlenose dolphins in the western gulf of Shark Bay than previously estimated by ML and AICc-based model-averaging. Other important extensions are discussed. Our Bayesian PCRD models are written in the BUGS-like JAGS language for easy dissemination and customization by the community of capture
DEFF Research Database (Denmark)
Kristensen, Anders Ringgaard; Søllested, Thomas Algot
2004-01-01
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 i...
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
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.
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
, 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......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 real EEG data demonstrate that invoking a stochastic forward model leads to improved source estimates....
Directory of Open Access Journals (Sweden)
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.
A Hierarchical Bayesian Model to Predict Self-Thinning Line for Chinese Fir in Southern China.
Directory of Open Access Journals (Sweden)
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.
Directory of Open Access Journals (Sweden)
Fidel Ernesto Castro Morales
2016-03-01
Full Text Available Abstract Objectives: to propose the use of a Bayesian hierarchical model to study the allometric scaling of the fetoplacental weight ratio, including possible confounders. Methods: data from 26 singleton pregnancies with gestational age at birth between 37 and 42 weeks were analyzed. The placentas were collected immediately after delivery and stored under refrigeration until the time of analysis, which occurred within up to 12 hours. Maternal data were collected from medical records. A Bayesian hierarchical model was proposed and Markov chain Monte Carlo simulation methods were used to obtain samples from distribution a posteriori. Results: the model developed showed a reasonable fit, even allowing for the incorporation of variables and a priori information on the parameters used. Conclusions: new variables can be added to the modelfrom the available code, allowing many possibilities for data analysis and indicating the potential for use in research on the subject.
Directory of Open Access Journals (Sweden)
J. P. Werner
2015-03-01
Full Text Available Reconstructions of the late-Holocene climate rely heavily upon proxies that are assumed to be accurately dated by layer counting, such as measurements of tree rings, ice cores, and varved lake sediments. Considerable advances could be achieved if time-uncertain proxies were able to be included within these multiproxy reconstructions, and if time uncertainties were recognized and correctly modeled for proxies commonly treated as free of age model errors. Current approaches for accounting for time uncertainty are generally limited to repeating the reconstruction using each one of an ensemble of age models, thereby inflating the final estimated uncertainty – in effect, each possible age model is given equal weighting. Uncertainties can be reduced by exploiting the inferred space–time covariance structure of the climate to re-weight the possible age models. Here, we demonstrate how Bayesian hierarchical climate reconstruction models can be augmented to account for time-uncertain proxies. Critically, although a priori all age models are given equal probability of being correct, the probabilities associated with the age models are formally updated within the Bayesian framework, thereby reducing uncertainties. Numerical experiments show that updating the age model probabilities decreases uncertainty in the resulting reconstructions, as compared with the current de facto standard of sampling over all age models, provided there is sufficient information from other data sources in the spatial region of the time-uncertain proxy. This approach can readily be generalized to non-layer-counted proxies, such as those derived from marine sediments.
DEFF Research Database (Denmark)
Stahlhut, Carsten; Mørup, Morten; Winther, Ole
2011-01-01
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 approach by comparison with source reconstruction methods that use fixed forward......We present an approach to handle forward model uncertainty for EEG source reconstruction. A stochastic forward model representation is motivated by the many random contributions to the path from sources to measurements including the tissue conductivity distribution, the geometry of the cortical...... models. Analysis of simulated and real EEG data provide evidence that reconstruction of the forward model leads to improved source estimates....
The application of a hierarchical Bayesian spatiotemporal model for ...
Indian Academy of Sciences (India)
The visual validation showed a powerful combination of HBST-GP model with Kriging interpolation technique. The Kriging also produced a good quality of the distribu- tion 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 ...
Directory of Open Access Journals (Sweden)
Hea-Jung Kim
2017-06-01
Full Text Available This paper develops Bayesian inference in reliability of a class of scale mixtures of log-normal failure time (SMLNFT models with stochastic (or uncertain constraint in their reliability measures. The class is comprehensive and includes existing failure time (FT models (such as log-normal, log-Cauchy, and log-logistic FT models as well as new models that are robust in terms of heavy-tailed FT observations. Since classical frequency approaches to reliability analysis based on the SMLNFT model with stochastic constraint are intractable, the Bayesian method is pursued utilizing a Markov chain Monte Carlo (MCMC sampling based approach. This paper introduces a two-stage maximum entropy (MaxEnt prior, which elicits a priori uncertain constraint and develops Bayesian hierarchical SMLNFT model by using the prior. The paper also proposes an MCMC method for Bayesian inference in the SMLNFT model reliability and calls attention to properties of the MaxEnt prior that are useful for method development. Finally, two data sets are used to illustrate how the proposed methodology works.
DEFF Research Database (Denmark)
Kristensen, Anders Ringgaard; Søllested, Thomas Algot
2004-01-01
Recent methodological improvements in replacement models comprising multi-level hierarchical Markov processes and Bayesian updating have hardly been implemented in any replacement model and the aim of this study is to present a sow replacement model that really uses these methodological improveme...
The application of a hierarchical Bayesian spatiotemporal model for ...
Indian Academy of Sciences (India)
30 March 2008 with particle energies as < 30 keV (mep0e1) and < 300 keV ... 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.
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.
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
Tsai, Frank T.-C.; Elshall, Ahmed S.
2013-09-01
Analysts are often faced with competing propositions for each uncertain model component. How can we judge that we select a correct proposition(s) for an uncertain model component out of numerous possible propositions? We introduce the hierarchical Bayesian model averaging (HBMA) method as a multimodel framework for uncertainty analysis. The HBMA allows for segregating, prioritizing, and evaluating different sources of uncertainty and their corresponding competing propositions through a hierarchy of BMA models that forms a BMA tree. We apply the HBMA to conduct uncertainty analysis on the reconstructed hydrostratigraphic architectures of the Baton Rouge aquifer-fault system, Louisiana. Due to uncertainty in model data, structure, and parameters, multiple possible hydrostratigraphic models are produced and calibrated as base models. The study considers four sources of uncertainty. With respect to data uncertainty, the study considers two calibration data sets. With respect to model structure, the study considers three different variogram models, two geological stationarity assumptions and two fault conceptualizations. The base models are produced following a combinatorial design to allow for uncertainty segregation. Thus, these four uncertain model components with their corresponding competing model propositions result in 24 base models. The results show that the systematic dissection of the uncertain model components along with their corresponding competing propositions allows for detecting the robust model propositions and the major sources of uncertainty.
A hierarchical bayesian model to quantify uncertainty of stream water temperature forecasts.
Directory of Open Access Journals (Sweden)
Guillaume Bal
Full Text Available Providing generic and cost effective modelling approaches to reconstruct and forecast freshwater temperature using predictors as air temperature and water discharge is a prerequisite to understanding ecological processes underlying the impact of water temperature and of global warming on continental aquatic ecosystems. Using air temperature as a simple linear predictor of water temperature can lead to significant bias in forecasts as it does not disentangle seasonality and long term trends in the signal. Here, we develop an alternative approach based on hierarchical Bayesian statistical time series modelling of water temperature, air temperature and water discharge using seasonal sinusoidal periodic signals and time varying means and amplitudes. Fitting and forecasting performances of this approach are compared with that of simple linear regression between water and air temperatures using i an emotive simulated example, ii application to three French coastal streams with contrasting bio-geographical conditions and sizes. The time series modelling approach better fit data and does not exhibit forecasting bias in long term trends contrary to the linear regression. This new model also allows for more accurate forecasts of water temperature than linear regression together with a fair assessment of the uncertainty around forecasting. Warming of water temperature forecast by our hierarchical Bayesian model was slower and more uncertain than that expected with the classical regression approach. These new forecasts are in a form that is readily usable in further ecological analyses and will allow weighting of outcomes from different scenarios to manage climate change impacts on freshwater wildlife.
A hierarchical bayesian model to quantify uncertainty of stream water temperature forecasts.
Bal, Guillaume; Rivot, Etienne; Baglinière, Jean-Luc; White, Jonathan; Prévost, Etienne
2014-01-01
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.
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
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.
National Research Council Canada - National Science Library
Dura-Bernal, Salvador; Wennekers, Thomas; Denham, Susan L
2012-01-01
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...
National Research Council Canada - National Science Library
Salvador Dura-Bernal; Thomas Wennekers; Susan L Denham
2012-01-01
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...
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.
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.
Probabilistic daily ILI syndromic surveillance with a spatio-temporal Bayesian hierarchical model.
Directory of Open Access Journals (Sweden)
Ta-Chien Chan
Full Text Available BACKGROUND: For daily syndromic surveillance to be effective, an efficient and sensible algorithm would be expected to detect aberrations in influenza illness, and alert public health workers prior to any impending epidemic. This detection or alert surely contains uncertainty, and thus should be evaluated with a proper probabilistic measure. However, traditional monitoring mechanisms simply provide a binary alert, failing to adequately address this uncertainty. METHODS AND FINDINGS: Based on the Bayesian posterior probability of influenza-like illness (ILI visits, the intensity of outbreak can be directly assessed. The numbers of daily emergency room ILI visits at five community hospitals in Taipei City during 2006-2007 were collected and fitted with a Bayesian hierarchical model containing meteorological factors such as temperature and vapor pressure, spatial interaction with conditional autoregressive structure, weekend and holiday effects, seasonality factors, and previous ILI visits. The proposed algorithm recommends an alert for action if the posterior probability is larger than 70%. External data from January to February of 2008 were retained for validation. The decision rule detects successfully the peak in the validation period. When comparing the posterior probability evaluation with the modified Cusum method, results show that the proposed method is able to detect the signals 1-2 days prior to the rise of ILI visits. CONCLUSIONS: This Bayesian hierarchical model not only constitutes a dynamic surveillance system but also constructs a stochastic evaluation of the need to call for alert. The monitoring mechanism provides earlier detection as well as a complementary tool for current surveillance programs.
Grieve, Richard; Nixon, Richard; Thompson, Simon G
2010-01-01
Cost-effectiveness analyses (CEA) may be undertaken alongside cluster randomized trials (CRTs) where randomization is at the level of the cluster (for example, the hospital or primary care provider) rather than the individual. Costs (and outcomes) within clusters may be correlated so that the assumption made by standard bivariate regression models, that observations are independent, is incorrect. This study develops a flexible modeling framework to acknowledge the clustering in CEA that use CRTs. The authors extend previous Bayesian bivariate models for CEA of multicenter trials to recognize the specific form of clustering in CRTs. They develop new Bayesian hierarchical models (BHMs) that allow mean costs and outcomes, and also variances, to differ across clusters. They illustrate how each model can be applied using data from a large (1732 cases, 70 primary care providers) CRT evaluating alternative interventions for reducing postnatal depression. The analyses compare cost-effectiveness estimates from BHMs with standard bivariate regression models that ignore the data hierarchy. The BHMs show high levels of cost heterogeneity across clusters (intracluster correlation coefficient, 0.17). Compared with standard regression models, the BHMs yield substantially increased uncertainty surrounding the cost-effectiveness estimates, and altered point estimates. The authors conclude that ignoring clustering can lead to incorrect inferences. The BHMs that they present offer a flexible modeling framework that can be applied more generally to CEA that use CRTs.
Directory of Open Access Journals (Sweden)
David Lunn
Full Text Available The advantages of Bayesian statistical approaches, such as flexibility and the ability to acknowledge uncertainty in all parameters, have made them the prevailing method for analysing the spread of infectious diseases in human or animal populations. We introduce a Bayesian approach to experimental host-pathogen systems that shares these attractive features. Since uncertainty in all parameters is acknowledged, existing information can be accounted for through prior distributions, rather than through fixing some parameter values. The non-linear dynamics, multi-factorial design, multiple measurements of responses over time and sampling error that are typical features of experimental host-pathogen systems can also be naturally incorporated. We analyse the dynamics of the free-living protozoan Paramecium caudatum and its specialist bacterial parasite Holospora undulata. Our analysis provides strong evidence for a saturable infection function, and we were able to reproduce the two waves of infection apparent in the data by separating the initial inoculum from the parasites released after the first cycle of infection. In addition, the parameter estimates from the hierarchical model can be combined to infer variations in the parasite's basic reproductive ratio across experimental groups, enabling us to make predictions about the effect of resources and host genotype on the ability of the parasite to spread. Even though the high level of variability between replicates limited the resolution of the results, this Bayesian framework has strong potential to be used more widely in experimental ecology.
Hierarchical Bayesian spatial models for alcohol availability, drug "hot spots" and violent crime
Directory of Open Access Journals (Sweden)
Horel Scott
2006-12-01
Full Text Available Abstract Background Ecologic studies have shown a relationship between alcohol outlet densities, illicit drug use and violence. The present study examined this relationship in the City of Houston, Texas, using a sample of 439 census tracts. Neighborhood sociostructural covariates, alcohol outlet density, drug crime density and violent crime data were collected for the year 2000, and analyzed using hierarchical Bayesian models. Model selection was accomplished by applying the Deviance Information Criterion. Results The counts of violent crime in each census tract were modelled as having a conditional Poisson distribution. Four neighbourhood explanatory variables were identified using principal component analysis. The best fitted model was selected as the one considering both unstructured and spatial dependence random effects. The results showed that drug-law violation explained a greater amount of variance in violent crime rates than alcohol outlet densities. The relative risk for drug-law violation was 2.49 and that for alcohol outlet density was 1.16. Of the neighbourhood sociostructural covariates, males of age 15 to 24 showed an effect on violence, with a 16% decrease in relative risk for each increase the size of its standard deviation. Both unstructured heterogeneity random effect and spatial dependence need to be included in the model. Conclusion The analysis presented suggests that activity around illicit drug markets is more strongly associated with violent crime than is alcohol outlet density. Unique among the ecological studies in this field, the present study not only shows the direction and magnitude of impact of neighbourhood sociostructural covariates as well as alcohol and illicit drug activities in a neighbourhood, it also reveals the importance of applying hierarchical Bayesian models in this research field as both spatial dependence and heterogeneity random effects need to be considered simultaneously.
Wang, Xiao; Gu, Jinghua; Hilakivi-Clarke, Leena; Clarke, Robert; Xuan, Jianhua
2017-01-15
The advent of high-throughput DNA methylation profiling techniques has enabled the possibility of accurate identification of differentially methylated genes for cancer research. The large number of measured loci facilitates whole genome methylation study, yet posing great challenges for differential methylation detection due to the high variability in tumor samples. We have developed a novel probabilistic approach, D: ifferential M: ethylation detection using a hierarchical B: ayesian model exploiting L: ocal D: ependency (DM-BLD), to detect differentially methylated genes based on a Bayesian framework. The DM-BLD approach features a joint model to capture both the local dependency of measured loci and the dependency of methylation change in samples. Specifically, the local dependency is modeled by Leroux conditional autoregressive structure; the dependency of methylation changes is modeled by a discrete Markov random field. A hierarchical Bayesian model is developed to fully take into account the local dependency for differential analysis, in which differential states are embedded as hidden variables. Simulation studies demonstrate that DM-BLD outperforms existing methods for differential methylation detection, particularly when the methylation change is moderate and the variability of methylation in samples is high. DM-BLD has been applied to breast cancer data to identify important methylated genes (such as polycomb target genes and genes involved in transcription factor activity) associated with breast cancer recurrence. A Matlab package of DM-BLD is available at http://www.cbil.ece.vt.edu/software.htm CONTACT: Xuan@vt.eduSupplementary information: Supplementary data are available at Bioinformatics online. © The Author 2016. Published by Oxford University Press. All rights reserved. For Permissions, please e-mail: journals.permissions@oup.com.
Modeling age and nest-specific survival using a hierarchical Bayesian approach.
Cao, Jing; He, Chong Z; Suedkamp Wells, Kimberly M; Millspaugh, Joshua J; Ryan, Mark R
2009-12-01
Recent studies have shown that grassland birds are declining more rapidly than any other group of terrestrial birds. Current methods of estimating avian age-specific nest survival rates require knowing the ages of nests, assuming homogeneous nests in terms of nest survival rates, or treating the hazard function as a piecewise step function. In this article, we propose a Bayesian hierarchical model with nest-specific covariates to estimate age-specific daily survival probabilities without the above requirements. The model provides a smooth estimate of the nest survival curve and identifies the factors that are related to the nest survival. The model can handle irregular visiting schedules and it has the least restrictive assumptions compared to existing methods. Without assuming proportional hazards, we use a multinomial semiparametric logit model to specify a direct relation between age-specific nest failure probability and nest-specific covariates. An intrinsic autoregressive prior is employed for the nest age effect. This nonparametric prior provides a more flexible alternative to the parametric assumptions. The Bayesian computation is efficient because the full conditional posterior distributions either have closed forms or are log concave. We use the method to analyze a Missouri dickcissel dataset and find that (1) nest survival is not homogeneous during the nesting period, and it reaches its lowest at the transition from incubation to nestling; and (2) nest survival is related to grass cover and vegetation height in the study area.
A Bayesian hierarchical model for discrete choice data in health care.
Antonio, Anna Liza M; Weiss, Robert E; Saigal, Christopher S; Dahan, Ely; Crespi, Catherine M
2017-01-01
In discrete choice experiments, patients are presented with sets of health states described by various attributes and asked to make choices from among them. Discrete choice experiments allow health care researchers to study the preferences of individual patients by eliciting trade-offs between different aspects of health-related quality of life. However, many discrete choice experiments yield data with incomplete ranking information and sparsity due to the limited number of choice sets presented to each patient, making it challenging to estimate patient preferences. Moreover, methods to identify outliers in discrete choice data are lacking. We develop a Bayesian hierarchical random effects rank-ordered multinomial logit model for discrete choice data. Missing ranks are accounted for by marginalizing over all possible permutations of unranked alternatives to estimate individual patient preferences, which are modeled as a function of patient covariates. We provide a Bayesian version of relative attribute importance, and adapt the use of the conditional predictive ordinate to identify outlying choice sets and outlying individuals with unusual preferences compared to the population. The model is applied to data from a study using a discrete choice experiment to estimate individual patient preferences for health states related to prostate cancer treatment.
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.
Evaluation of image registration spatial accuracy using a Bayesian hierarchical model.
Liu, Suyu; Yuan, Ying; Castillo, Richard; Guerrero, Thomas; Johnson, Valen E
2014-06-01
To evaluate the utility of automated deformable image registration (DIR) algorithms, it is necessary to evaluate both the registration accuracy of the DIR algorithm itself, as well as the registration accuracy of the human readers from whom the "gold standard" is obtained. We propose a Bayesian hierarchical model to evaluate the spatial accuracy of human readers and automatic DIR methods based on multiple image registration data generated by human readers and automatic DIR methods. To fully account for the locations of landmarks in all images, we treat the true locations of landmarks as latent variables and impose a hierarchical structure on the magnitude of registration errors observed across image pairs. DIR registration errors are modeled using Gaussian processes with reference prior densities on prior parameters that determine the associated covariance matrices. We develop a Gibbs sampling algorithm to efficiently fit our models to high-dimensional data, and apply the proposed method to analyze an image dataset obtained from a 4D thoracic CT study. © 2014, The International Biometric Society.
Ognibene, Dimitri; Giglia, Giuseppe
2015-01-01
An integrative account of MTS could be cast in terms of hierarchical Bayesian inference. It may help to highlight a central role of sensory (tactile) precision could play in MTS. We suggest that anosognosic patients, with anesthetic hemisoma, can also be interpreted as a form of acquired MTS, providing additional data for the model.
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
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.
Wynton, Sarah K A; Anglim, Jeromy
2017-10-01
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).
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...
Cruz-Marcelo, Alejandro; Ensor, Katherine B.; Rosner, Gary L.
2011-01-01
The term structure of interest rates is used to price defaultable bonds and credit derivatives, as well as to infer the quality of bonds for risk management purposes. We introduce a model that jointly estimates term structures by means of a Bayesian hierarchical model with a prior probability model based on Dirichlet process mixtures. The modeling methodology borrows strength across term structures for purposes of estimation. The main advantage of our framework is its ability to produce reliable estimators at the company level even when there are only a few bonds per company. After describing the proposed model, we discuss an empirical application in which the term structure of 197 individual companies is estimated. The sample of 197 consists of 143 companies with only one or two bonds. In-sample and out-of-sample tests are used to quantify the improvement in accuracy that results from approximating the term structure of corporate bonds with estimators by company rather than by credit rating, the latter being a popular choice in the financial literature. A complete description of a Markov chain Monte Carlo (MCMC) scheme for the proposed model is available as Supplementary Material. PMID:21765566
Bayesian hierarchical models for regional climate reconstructions of the last glacial maximum
Weitzel, Nils; Hense, Andreas; Ohlwein, Christian
2017-04-01
Spatio-temporal reconstructions of past climate are important for the understanding of the long term behavior of the climate system and the sensitivity to forcing changes. Unfortunately, they are subject to large uncertainties, have to deal with a complex proxy-climate structure, and a physically reasonable interpolation between the sparse proxy observations is difficult. Bayesian Hierarchical Models (BHMs) are a class of statistical models that is well suited for spatio-temporal reconstructions of past climate because they permit the inclusion of multiple sources of information (e.g. records from different proxy types, uncertain age information, output from climate simulations) and quantify uncertainties in a statistically rigorous way. BHMs in paleoclimatology typically consist of three stages which are modeled individually and are combined using Bayesian inference techniques. The data stage models the proxy-climate relation (often named transfer function), the process stage models the spatio-temporal distribution of the climate variables of interest, and the prior stage consists of prior distributions of the model parameters. For our BHMs, we translate well-known proxy-climate transfer functions for pollen to a Bayesian framework. In addition, we can include Gaussian distributed local climate information from preprocessed proxy records. The process stage combines physically reasonable spatial structures from prior distributions with proxy records which leads to a multivariate posterior probability distribution for the reconstructed climate variables. The prior distributions that constrain the possible spatial structure of the climate variables are calculated from climate simulation output. We present results from pseudoproxy tests as well as new regional reconstructions of temperatures for the last glacial maximum (LGM, ˜ 21,000 years BP). These reconstructions combine proxy data syntheses with information from climate simulations for the LGM that were
Epigenetic change detection and pattern recognition via Bayesian hierarchical hidden Markov models.
Wang, Xinlei; Zang, Miao; Xiao, Guanghua
2013-06-15
Epigenetics is the study of changes to the genome that can switch genes on or off and determine which proteins are transcribed without altering the DNA sequence. Recently, epigenetic changes have been linked to the development and progression of disease such as psychiatric disorders. High-throughput epigenetic experiments have enabled researchers to measure genome-wide epigenetic profiles and yield data consisting of intensity ratios of immunoprecipitation versus reference samples. The intensity ratios can provide a view of genomic regions where protein binding occur under one experimental condition and further allow us to detect epigenetic alterations through comparison between two different conditions. However, such experiments can be expensive, with only a few replicates available. Moreover, epigenetic data are often spatially correlated with high noise levels. In this paper, we develop a Bayesian hierarchical model, combined with hidden Markov processes with four states for modeling spatial dependence, to detect genomic sites with epigenetic changes from two-sample experiments with paired internal control. One attractive feature of the proposed method is that the four states of the hidden Markov process have well-defined biological meanings and allow us to directly call the change patterns based on the corresponding posterior probabilities. In contrast, none of existing methods can offer this advantage. In addition, the proposed method offers great power in statistical inference by spatial smoothing (via hidden Markov modeling) and information pooling (via hierarchical modeling). Both simulation studies and real data analysis in a cocaine addiction study illustrate the reliability and success of this method. Copyright © 2012 John Wiley & Sons, Ltd.
Commeau, Natalie; Cornu, Marie; Albert, Isabelle; Denis, Jean-Baptiste; Parent, Eric
2012-03-01
Assessing within-batch and between-batch variability is of major interest for risk assessors and risk managers in the context of microbiological contamination of food. For example, the ratio between the within-batch variability and the between-batch variability has a large impact on the results of a sampling plan. Here, we designed hierarchical Bayesian models to represent such variability. Compatible priors were built mathematically to obtain sound model comparisons. A numeric criterion is proposed to assess the contamination structure comparing the ability of the models to replicate grouped data at the batch level using a posterior predictive loss approach. Models were applied to two case studies: contamination by Listeria monocytogenes of pork breast used to produce diced bacon and contamination by the same microorganism on cold smoked salmon at the end of the process. In the first case study, a contamination structure clearly exists and is located at the batch level, that is, between batches variability is relatively strong, whereas in the second a structure also exists but is less marked. © 2012 Society for Risk Analysis.
Zhao, Rui; Catalano, Paul; DeGruttola, Victor G; Michor, Franziska
2017-01-01
The dynamics of tumor burden, secreted proteins or other biomarkers over time, is often used to evaluate the effectiveness of therapy and to predict outcomes for patients. Many methods have been proposed to investigate longitudinal trends to better characterize patients and to understand disease progression. However, most approaches assume a homogeneous patient population and a uniform response trajectory over time and across patients. Here, we present a mixture piecewise linear Bayesian hierarchical model, which takes into account both population heterogeneity and nonlinear relationships between biomarkers and time. Simulation results show that our method was able to classify subjects according to their patterns of treatment response with greater than 80% accuracy in the three scenarios tested. We then applied our model to a large randomized controlled phase III clinical trial of multiple myeloma patients. Analysis results suggest that the longitudinal tumor burden trajectories in multiple myeloma patients are heterogeneous and nonlinear, even among patients assigned to the same treatment cohort. In addition, between cohorts, there are distinct differences in terms of the regression parameters and the distributions among categories in the mixture. Those results imply that longitudinal data from clinical trials may harbor unobserved subgroups and nonlinear relationships; accounting for both may be important for analyzing longitudinal data.
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.
Xie, Kun; Wang, Xuesong; Huang, Helai; Chen, Xiaohong
2013-01-01
Most traffic crashes in Chinese cities occur at signalized intersections. Research on the intersection safety problem in China is still in its early stage. The recent development of an advanced traffic information system in Shanghai enables in-depth intersection safety analyses using road design, traffic operation, and crash data. In Shanghai, the road network density is relatively high and the distance between signalized intersections is small, averaging about 200m. Adjacent signalized intersections located along the same corridor share similar traffic flows, and signals are usually coordinated. Therefore, when studying intersection safety in Shanghai, it is essential to account for intersection correlations within corridors. In this study, data for 195 signalized intersections along 22 corridors in the urban areas of Shanghai were collected. Mean speeds and speed variances of corridors were acquired from taxis equipped with Global Positioning Systems (GPS). Bayesian hierarchical models were applied to identify crash risk factors at both the intersection and the corridor levels. Results showed that intersections along corridors with lower mean speeds were associated with fewer crashes than those with higher speeds, and those intersections along two-way roads, under elevated roads, and in close proximity to each other, tended to have higher crash frequencies. Copyright © 2012 Elsevier Ltd. All rights reserved.
Di Giuseppe, Edmondo; Lasinio, Giovanna Jona; Pasqui, Massimiliano; Esposito, Stanislao
2015-01-01
We propose a new statistical protocol for the estimation of precipitation using lightning data. We first identify rainy events using a scan statistics, then we estimate Rainfall Lighting Ratio (RLR) to convert lightning number into rain volume given the storm intensity. Then we build a hierarchical Bayesian model aiming at the prediction of 15- and 30-minutes cumulated precipitation at unobserved locations and time using information on lightning in the same area. More specifically, we build a...
Jiménez, José; García, Emilio J; Llaneza, Luis; Palacios, Vicente; González, Luis Mariano; García-Domínguez, Francisco; Múñoz-Igualada, Jaime; López-Bao, José Vicente
2016-08-01
In many cases, the first step in large-carnivore management is to obtain objective, reliable, and cost-effective estimates of population parameters through procedures that are reproducible over time. However, monitoring predators over large areas is difficult, and the data have a high level of uncertainty. We devised a practical multimethod and multistate modeling approach based on Bayesian hierarchical-site-occupancy models that combined multiple survey methods to estimate different population states for use in monitoring large predators at a regional scale. We used wolves (Canis lupus) as our model species and generated reliable estimates of the number of sites with wolf reproduction (presence of pups). We used 2 wolf data sets from Spain (Western Galicia in 2013 and Asturias in 2004) to test the approach. Based on howling surveys, the naïve estimation (i.e., estimate based only on observations) of the number of sites with reproduction was 9 and 25 sites in Western Galicia and Asturias, respectively. Our model showed 33.4 (SD 9.6) and 34.4 (3.9) sites with wolf reproduction, respectively. The number of occupied sites with wolf reproduction was 0.67 (SD 0.19) and 0.76 (0.11), respectively. This approach can be used to design more cost-effective monitoring programs (i.e., to define the sampling effort needed per site). Our approach should inspire well-coordinated surveys across multiple administrative borders and populations and lead to improved decision making for management of large carnivores on a landscape level. The use of this Bayesian framework provides a simple way to visualize the degree of uncertainty around population-parameter estimates and thus provides managers and stakeholders an intuitive approach to interpreting monitoring results. Our approach can be widely applied to large spatial scales in wildlife monitoring where detection probabilities differ between population states and where several methods are being used to estimate different population
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
2017-09-01
from this PDF . EMOS models also use multiple linear regression to characterize the sensitivity of a univariate weather quantity—that is, the...classical least-squares approach to multivariate multiple linear regression using both measures-oriented and distributions-oriented scoring rules...14. SUBJECT TERMS ensemble model output statistics, statistical post-processing, multivariate multiple linear regression, Bayesian data analysis
Grzegorczyk, Marco; Husmeier, Dirk
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
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.
Maclaren, Oliver J; Parker, Aimée; Pin, Carmen; Carding, Simon R; Watson, Alastair J M; Fletcher, Alexander G; Byrne, Helen M; Maini, Philip K
2017-07-01
Our work addresses two key challenges, one biological and one methodological. First, we aim to understand how proliferation and cell migration rates in the intestinal epithelium are related under healthy, damaged (Ara-C treated) and recovering conditions, and how these relations can be used to identify mechanisms of repair and regeneration. We analyse new data, presented in more detail in a companion paper, in which BrdU/IdU cell-labelling experiments were performed under these respective conditions. Second, in considering how to more rigorously process these data and interpret them using mathematical models, we use a probabilistic, hierarchical approach. This provides a best-practice approach for systematically modelling and understanding the uncertainties that can otherwise undermine the generation of reliable conclusions-uncertainties in experimental measurement and treatment, difficult-to-compare mathematical models of underlying mechanisms, and unknown or unobserved parameters. Both spatially discrete and continuous mechanistic models are considered and related via hierarchical conditional probability assumptions. We perform model checks on both in-sample and out-of-sample datasets and use them to show how to test possible model improvements and assess the robustness of our conclusions. We conclude, for the present set of experiments, that a primarily proliferation-driven model suffices to predict labelled cell dynamics over most time-scales.
Directory of Open Access Journals (Sweden)
Oliver J Maclaren
2017-07-01
Full Text Available Our work addresses two key challenges, one biological and one methodological. First, we aim to understand how proliferation and cell migration rates in the intestinal epithelium are related under healthy, damaged (Ara-C treated and recovering conditions, and how these relations can be used to identify mechanisms of repair and regeneration. We analyse new data, presented in more detail in a companion paper, in which BrdU/IdU cell-labelling experiments were performed under these respective conditions. Second, in considering how to more rigorously process these data and interpret them using mathematical models, we use a probabilistic, hierarchical approach. This provides a best-practice approach for systematically modelling and understanding the uncertainties that can otherwise undermine the generation of reliable conclusions-uncertainties in experimental measurement and treatment, difficult-to-compare mathematical models of underlying mechanisms, and unknown or unobserved parameters. Both spatially discrete and continuous mechanistic models are considered and related via hierarchical conditional probability assumptions. We perform model checks on both in-sample and out-of-sample datasets and use them to show how to test possible model improvements and assess the robustness of our conclusions. We conclude, for the present set of experiments, that a primarily proliferation-driven model suffices to predict labelled cell dynamics over most time-scales.
Gajewski, Byron J; Hart, Sara; Bergquist-Beringer, Sandra; Dunton, Nancy
2007-11-10
This article describes a method for estimating the inter-rater reliability of pressure ulcer (PU) staging (stages I-IV) from raters in National Database of Nursing Quality Indicators (NDNQI) participating hospitals. The method models ordinal spanning data utilizing an ordinal probit Bayesian hierarchical model (BHM) across several hospitals in which raters monitor patient's PUs. An ulcer that cannot be accurately assessed because the base of the wound cannot be seen is defined as unstageable. Our novel approach allows for an unstageable PU rating to be included in the analysis. We compare the ordinal probit BHM to an approximate random-effects (standard approach in the literature) model that assumes that the raw ordinal data are continuous. Copyright 2007 John Wiley & Sons, Ltd.
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.
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.
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Brice X Semmens
Full Text Available 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.
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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.
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Thomas J Rodhouse
Full Text Available Monitoring programs that evaluate restoration and inform adaptive management are important for addressing environmental degradation. These efforts may be well served by spatially explicit hierarchical approaches to modeling because of unavoidable spatial structure inherited from past land use patterns and other factors. We developed bayesian hierarchical models to estimate trends from annual density counts observed in a spatially structured wetland forb (Camassia quamash [camas] population following the cessation of grazing and mowing on the study area, and in a separate reference population of camas. The restoration site was bisected by roads and drainage ditches, resulting in distinct subpopulations ("zones" with different land use histories. We modeled this spatial structure by fitting zone-specific intercepts and slopes. We allowed spatial covariance parameters in the model to vary by zone, as in stratified kriging, accommodating anisotropy and improving computation and biological interpretation. Trend estimates provided evidence of a positive effect of passive restoration, and the strength of evidence was influenced by the amount of spatial structure in the model. Allowing trends to vary among zones and accounting for topographic heterogeneity increased precision of trend estimates. Accounting for spatial autocorrelation shifted parameter coefficients in ways that varied among zones depending on strength of statistical shrinkage, autocorrelation and topographic heterogeneity--a phenomenon not widely described. Spatially explicit estimates of trend from hierarchical models will generally be more useful to land managers than pooled regional estimates and provide more realistic assessments of uncertainty. The ability to grapple with historical contingency is an appealing benefit of this approach.
Scheuerell, Mark D; Buhle, Eric R; Semmens, Brice X; Ford, Michael J; Cooney, Tom; Carmichael, Richard W
2015-05-01
Myriad human activities increasingly threaten the existence of many species. A variety of conservation interventions such as habitat restoration, protected areas, and captive breeding have been used to prevent extinctions. Evaluating the effectiveness of these interventions requires appropriate statistical methods, given the quantity and quality of available data. Historically, analysis of variance has been used with some form of predetermined before-after control-impact design to estimate the effects of large-scale experiments or conservation interventions. However, ad hoc retrospective study designs or the presence of random effects at multiple scales may preclude the use of these tools. We evaluated the effects of a large-scale supplementation program on the density of adult Chinook salmon Oncorhynchus tshawytscha from the Snake River basin in the northwestern United States currently listed under the U.S. Endangered Species Act. We analyzed 43 years of data from 22 populations, accounting for random effects across time and space using a form of Bayesian hierarchical time-series model common in analyses of financial markets. We found that varying degrees of supplementation over a period of 25 years increased the density of natural-origin adults, on average, by 0-8% relative to nonsupplementation years. Thirty-nine of the 43 year effects were at least two times larger in magnitude than the mean supplementation effect, suggesting common environmental variables play a more important role in driving interannual variability in adult density. Additional residual variation in density varied considerably across the region, but there was no systematic difference between supplemented and reference populations. Our results demonstrate the power of hierarchical Bayesian models to detect the diffuse effects of management interventions and to quantitatively describe the variability of intervention success. Nevertheless, our study could not address whether ecological factors
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.
Improving the Calibration of the SN Ia Anchor Datasets with a Bayesian Hierarchal Model
Currie, Miles; Rubin, David
2018-01-01
Inter-survey calibration remains one of the largest systematic uncertainties in SN Ia cosmology today. Ideally, each survey would measure their system throughputs and observe well characterized spectrophotometric standard stars, but many important surveys have not done so. For these surveys, we calibrate using tertiary survey stars tied to SDSS and Pan-STARRS. We improve on previous efforts by taking the spatially variable response of each telescope/camera into account, and using improved color transformations in the surveys’ natural instrumental photometric system. We use a global hierarchical model of the data, automatically providing a covariance matrix of magnitude offsets and bandpass shifts which reduces the systematic uncertainty in inter-survey calibration, thereby providing better cosmological constraints.
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.
Millar, Russell B
2009-09-01
When replicate count data are overdispersed, it is common practice to incorporate this extra-Poisson variability by including latent parameters at the observation level. For example, the negative binomial and Poisson-lognormal (PLN) models are obtained by using gamma and lognormal latent parameters, respectively. Several recent publications have employed the deviance information criterion (DIC) to choose between these two models, with the deviance defined using the Poisson likelihood that is obtained from conditioning on these latent parameters. The results herein show that this use of DIC is inappropriate. Instead, DIC was seen to perform well if calculated using likelihood that was marginalized at the group level by integrating out the observation-level latent parameters. This group-level marginalization is explicit in the case of the negative binomial, but requires numerical integration for the PLN model. Similarly, DIC performed well to judge whether zero inflation was required when calculated using the group-marginalized form of the zero-inflated likelihood. In the context of comparing multilevel hierarchical models, the top-level DIC was obtained using likelihood that was further marginalized by additional integration over the group-level latent parameters, and the marginal densities of the models were calculated for the purpose of providing Bayes' factors. The computational viability and interpretability of these different measures is considered.
A full Bayesian hierarchical mixture model for the variance of gene differential expression
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Walls Rebecca E
2007-04-01
Full Text Available Abstract Background In many laboratory-based high throughput microarray experiments, there are very few replicates of gene expression levels. Thus, estimates of gene variances are inaccurate. Visual inspection of graphical summaries of these data usually reveals that heteroscedasticity is present, and the standard approach to address this is to take a log2 transformation. In such circumstances, it is then common to assume that gene variability is constant when an analysis of these data is undertaken. However, this is perhaps too stringent an assumption. More careful inspection reveals that the simple log2 transformation does not remove the problem of heteroscedasticity. An alternative strategy is to assume independent gene-specific variances; although again this is problematic as variance estimates based on few replications are highly unstable. More meaningful and reliable comparisons of gene expression might be achieved, for different conditions or different tissue samples, where the test statistics are based on accurate estimates of gene variability; a crucial step in the identification of differentially expressed genes. Results We propose a Bayesian mixture model, which classifies genes according to similarity in their variance. The result is that genes in the same latent class share the similar variance, estimated from a larger number of replicates than purely those per gene, i.e. the total of all replicates of all genes in the same latent class. An example dataset, consisting of 9216 genes with four replicates per condition, resulted in four latent classes based on their similarity of the variance. Conclusion The mixture variance model provides a realistic and flexible estimate for the variance of gene expression data under limited replicates. We believe that in using the latent class variances, estimated from a larger number of genes in each derived latent group, the p-values obtained are more robust than either using a constant gene or
Yasmirullah, Septia Devi Prihastuti; Iriawan, Nur; Sipayung, Feronika Rosalinda
2017-11-01
The success of regional economic establishment could be measured by economic growth. Since the Act No. 32 of 2004 has been implemented, unbalance economic among the regency in Indonesia is increasing. This condition is contrary different with the government goal to build society welfare through the economic activity development in each region. This research aims to examine economic growth through the distribution of bank credits to each Indonesia's regency. The data analyzed in this research is hierarchically structured data which follow normal distribution in first level. Two modeling approaches are employed in this research, a global-one level Bayesian approach and two-level hierarchical Bayesian approach. The result shows that hierarchical Bayesian has succeeded to demonstrate a better estimation than a global-one level Bayesian. It proves that the different economic growth in each province is significantly influenced by the variations of micro level characteristics in each province. These variations are significantly affected by cities and province characteristics in second level.
Tang, Yuping; Wang, Daniel; Wilson, Grant; Gutermuth, Robert; Heyer, Mark
2018-01-01
We present the AzTEC/LMT survey of dust continuum at 1.1mm on the central ˜ 200pc (CMZ) of our Galaxy. A joint SED analysis of all existing dust continuum surveys on the CMZ is performed, from 160µm to 1.1mm. Our analysis follows a MCMC sampling strategy incorporating the knowledge of PSFs in different maps, which provides unprecedented spacial resolution on distributions of dust temperature, column density and emissivity index. The dense clumps in the CMZ typically show low dust temperature ( 20K), with no significant sign of buried star formation, and a weak evolution of higher emissivity index toward dense peak. A new model is proposed, allowing for varying dust temperature inside a cloud and self-shielding of dust emission, which leads to similar conclusions on dust temperature and grain properties. We further apply a hierarchical Bayesian analysis to infer the column density probability distribution function (N-PDF), while simultaneously removing the Galactic foreground and background emission. The N-PDF shows a steep power-law profile with α > 3, indicating that formation of dense structures are suppressed.
Oh, Sunghee; Song, Seongho
2017-01-01
In gene expression profile, data analysis pipeline is categorized into four levels, major downstream tasks, i.e., (1) identification of differential expression; (2) clustering co-expression patterns; (3) classification of subtypes of samples; and (4) detection of genetic regulatory networks, are performed posterior to preprocessing procedure such as normalization techniques. To be more specific, temporal dynamic gene expression data has its inherent feature, namely, two neighboring time points (previous and current state) are highly correlated with each other, compared to static expression data which samples are assumed as independent individuals. In this chapter, we demonstrate how HMMs and hierarchical Bayesian modeling methods capture the horizontal time dependency structures in time series expression profiles by focusing on the identification of differential expression. In addition, those differential expression genes and transcript variant isoforms over time detected in core prerequisite steps can be generally further applied in detection of genetic regulatory networks to comprehensively uncover dynamic repertoires in the aspects of system biology as the coupled framework.
Li, Lianfa; Laurent, Olivier; Wu, Jun
2016-02-05
Epidemiological studies suggest that air pollution is adversely associated with pregnancy outcomes. Such associations may be modified by spatially-varying factors including socio-demographic characteristics, land-use patterns and unaccounted exposures. Yet, few studies have systematically investigated the impact of these factors on spatial variability of the air pollution's effects. This study aimed to examine spatial variability of the effects of air pollution on term birth weight across Census tracts and the influence of tract-level factors on such variability. We obtained over 900,000 birth records from 2001 to 2008 in Los Angeles County, California, USA. Air pollution exposure was modeled at individual level for nitrogen dioxide (NO2) and nitrogen oxides (NOx) using spatiotemporal models. Two-stage Bayesian hierarchical non-linear models were developed to (1) quantify the associations between air pollution exposure and term birth weight within each tract; and (2) examine the socio-demographic, land-use, and exposure-related factors contributing to the between-tract variability of the associations between air pollution and term birth weight. Higher air pollution exposure was associated with lower term birth weight (average posterior effects: -14.7 (95 % CI: -19.8, -9.7) g per 10 ppb increment in NO2 and -6.9 (95 % CI: -12.9, -0.9) g per 10 ppb increment in NOx). The variation of the association across Census tracts was significantly influenced by the tract-level socio-demographic, exposure-related and land-use factors. Our models captured the complex non-linear relationship between these factors and the associations between air pollution and term birth weight: we observed the thresholds from which the influence of the tract-level factors was markedly exacerbated or attenuated. Exacerbating factors might reflect additional exposure to environmental insults or lower socio-economic status with higher vulnerability, whereas attenuating factors might indicate reduced
Chen, Cong; Zhang, Guohui; Tian, Zong; Bogus, Susan M; Yang, Yin
2015-12-01
Traffic crashes occurring on rural roadways induce more severe injuries and fatalities than those in urban areas, especially when there are trucks involved. Truck drivers are found to suffer higher potential of crash injuries compared with other occupational labors. Besides, unobserved heterogeneity in crash data analysis is a critical issue that needs to be carefully addressed. In this study, a hierarchical Bayesian random intercept model decomposing cross-level interaction effects as unobserved heterogeneity is developed to examine the posterior probabilities of truck driver injuries in rural truck-involved crashes. The interaction effects contributing to truck driver injury outcomes are investigated based on two-year rural truck-involved crashes in New Mexico from 2010 to 2011. The analysis results indicate that the cross-level interaction effects play an important role in predicting truck driver injury severities, and the proposed model produces comparable performance with the traditional random intercept model and the mixed logit model even after penalization by high model complexity. It is revealed that factors including road grade, number of vehicles involved in a crash, maximum vehicle damage in a crash, vehicle actions, driver age, seatbelt use, and driver under alcohol or drug influence, as well as a portion of their cross-level interaction effects with other variables are significantly associated with truck driver incapacitating injuries and fatalities. These findings are helpful to understand the respective or joint impacts of these attributes on truck driver injury patterns in rural truck-involved crashes. Copyright © 2015 Elsevier Ltd. All rights reserved.
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 z< 0.10. The conventional linear 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.
Wu, Zhen; Liu, Yong; Liang, Zhongyao; Wu, Sifeng; Guo, Huaicheng
2017-06-01
Lake eutrophication is associated with excessive anthropogenic nutrients (mainly nitrogen (N) and phosphorus (P)) and unobserved internal nutrient cycling. Despite the advances in understanding the role of external loadings, the contribution of internal nutrient cycling is still an open question. A dynamic mass-balance model was developed to simulate and measure the contributions of internal cycling and external loading. It was based on the temporal Bayesian Hierarchical Framework (BHM), where we explored the seasonal patterns in the dynamics of nutrient cycling processes and the limitation of N and P on phytoplankton growth in hyper-eutrophic Lake Dianchi, China. The dynamic patterns of the five state variables (Chla, TP, ammonia, nitrate and organic N) were simulated based on the model. Five parameters (algae growth rate, sediment exchange rate of N and P, nitrification rate and denitrification rate) were estimated based on BHM. The model provided a good fit to observations. Our model results highlighted the role of internal cycling of N and P in Lake Dianchi. The internal cycling processes contributed more than external loading to the N and P changes in the water column. Further insights into the nutrient limitation analysis indicated that the sediment exchange of P determined the P limitation. Allowing for the contribution of denitrification to N removal, N was the more limiting nutrient in most of the time, however, P was the more important nutrient for eutrophication management. For Lake Dianchi, it would not be possible to recover solely by reducing the external watershed nutrient load; the mechanisms of internal cycling should also be considered as an approach to inhibit the release of sediments and to enhance denitrification. Copyright © 2017 Elsevier Ltd. All rights reserved.
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. Copyright © 2013 Elsevier Ltd. All rights reserved.
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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
Wahl, E. R.
2008-12-01
as much information as the multi-taxonomic MAT in well-selected regions, the ratio inverse model is used as the starting point for developing a temperature-pollen forward model. Such a forward model can be directly incorporated into a Bayesian hierarchical model (BHM) framework: the reason for seeking a taxonomically simplified pollen model is itself driven by computational considerations within the BHM. The BHM framework thus allows pollen- derived climate information to contribute multi-decadal to centennial information into a simultaneous reconstruction framework that also incorporates annually-resolved climate information from tree ring sources and centennial to multi-centennial information from borehole reconstructions. In the forward model, the pine and oak pollen counts are treated as binomial random variables with expected values (p) and (1-p), conditional on the calibration temperature values and the total counts (n) used to determine the ratios. Model parameters and (p) values have been estimated using a binomial logistic form of the generalized linear model. Comparison of the estimated conditional expected (p) values with the associated calibration ratio/temperature relationships shows good performance for the SW N American test case, with little (but non- 0) bias and good overall tracking (R2 = 0.79). (4) The results from (3) indicate that appropriate forward models can be developed for a suite of sites in North America with temporally dense, well-dated fossil pollen records over the past 2ka, and then incorporated into the BHM. Modeling results for the suite of sites will be presented.
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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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Douglas F Bertram
Full Text Available Species at risk with secretive breeding behaviours, low densities, and wide geographic range pose a significant challenge to conservation actions because population trends are difficult to detect. Such is the case with the Marbled Murrelet (Brachyramphus marmoratus, a seabird listed as 'Threatened' by the Species at Risk Act in Canada largely due to the loss of its old growth forest nesting habitat. We report the first estimates of population trend of Marbled Murrelets in Canada derived from a monitoring program that uses marine radar to detect birds as they enter forest watersheds during 923 dawn surveys at 58 radar monitoring stations within the six Marbled Murrelet Conservation Regions on coastal British Columbia, Canada, 1996-2013. Temporal trends in radar counts were analyzed with a hierarchical Bayesian multivariate modeling approach that controlled for variation in tilt of the radar unit and day of year, included year-specific deviations from the overall trend ('year effects', and allowed for trends to be estimated at three spatial scales. A negative overall trend of -1.6%/yr (95% credibility interval: -3.2%, 0.01% indicated moderate evidence for a coast-wide decline, although trends varied strongly among the six conservation regions. Negative annual trends were detected in East Vancouver Island (-9%/yr and South Mainland Coast (-3%/yr Conservation Regions. Over a quarter of the year effects were significantly different from zero, and the estimated standard deviation in common-shared year effects between sites within each region was about 50% per year. This large common-shared interannual variation in counts may have been caused by regional movements of birds related to changes in marine conditions that affect the availability of prey.
Bertram, Douglas F; Drever, Mark C; McAllister, Murdoch K; Schroeder, Bernard K; Lindsay, David J; Faust, Deborah A
2015-01-01
Species at risk with secretive breeding behaviours, low densities, and wide geographic range pose a significant challenge to conservation actions because population trends are difficult to detect. Such is the case with the Marbled Murrelet (Brachyramphus marmoratus), a seabird listed as 'Threatened' by the Species at Risk Act in Canada largely due to the loss of its old growth forest nesting habitat. We report the first estimates of population trend of Marbled Murrelets in Canada derived from a monitoring program that uses marine radar to detect birds as they enter forest watersheds during 923 dawn surveys at 58 radar monitoring stations within the six Marbled Murrelet Conservation Regions on coastal British Columbia, Canada, 1996-2013. Temporal trends in radar counts were analyzed with a hierarchical Bayesian multivariate modeling approach that controlled for variation in tilt of the radar unit and day of year, included year-specific deviations from the overall trend ('year effects'), and allowed for trends to be estimated at three spatial scales. A negative overall trend of -1.6%/yr (95% credibility interval: -3.2%, 0.01%) indicated moderate evidence for a coast-wide decline, although trends varied strongly among the six conservation regions. Negative annual trends were detected in East Vancouver Island (-9%/yr) and South Mainland Coast (-3%/yr) Conservation Regions. Over a quarter of the year effects were significantly different from zero, and the estimated standard deviation in common-shared year effects between sites within each region was about 50% per year. This large common-shared interannual variation in counts may have been caused by regional movements of birds related to changes in marine conditions that affect the availability of prey.
A hierarchical Bayesian spatio-temporal model for extreme precipitation events
Ghosh, Souparno
2011-03-01
We propose a new approach to model a sequence of spatially distributed time series of extreme values. Unlike common practice, we incorporate spatial dependence directly in the likelihood and allow the temporal component to be captured at the second level of hierarchy. Inferences about the parameters and spatio-temporal predictions are obtained via MCMC technique. The model is fitted to a gridded precipitation data set collected over 99 years across the continental U.S. © 2010 John Wiley & Sons, Ltd..
Wynton, Sarah K. A.; Anglim, Jeromy
2017-01-01
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,…
Savitsky, Terrance D; Paddock, Susan M
2013-06-01
We develop a dependent Dirichlet process (DDP) model for repeated measures multiple membership (MM) data. This data structure arises in studies under which an intervention is delivered to each client through a sequence of elements which overlap with those of other clients on different occasions. Our interest concentrates on study designs for which the overlaps of sequences occur for clients who receive an intervention in a shared or grouped fashion whose memberships may change over multiple treatment events. Our motivating application focuses on evaluation of the effectiveness of a group therapy intervention with treatment delivered through a sequence of cognitive behavioral therapy session blocks, called modules. An open-enrollment protocol permits entry of clients at the beginning of any new module in a manner that may produce unique MM sequences across clients. We begin with a model that composes an addition of client and multiple membership module random effect terms, which are assumed independent. Our MM DDP model relaxes the assumption of conditionally independent client and module random effects by specifying a collection of random distributions for the client effect parameters that are indexed by the unique set of module attendances. We demonstrate how this construction facilitates examining heterogeneity in the relative effectiveness of group therapy modules over repeated measurement occasions.
Bayesian hierarchical models for network meta-analysis incorporating nonignorable missingness.
Zhang, Jing; Chu, Haitao; Hong, Hwanhee; Virnig, Beth A; Carlin, Bradley P
2017-10-01
Network meta-analysis expands the scope of a conventional pairwise meta-analysis to simultaneously compare multiple treatments, synthesizing both direct and indirect information and thus strengthening inference. Since most of trials only compare two treatments, a typical data set in a network meta-analysis managed as a trial-by-treatment matrix is extremely sparse, like an incomplete block structure with significant missing data. Zhang et al. proposed an arm-based method accounting for correlations among different treatments within the same trial and assuming that absent arms are missing at random. However, in randomized controlled trials, nonignorable missingness or missingness not at random may occur due to deliberate choices of treatments at the design stage. In addition, those undertaking a network meta-analysis may selectively choose treatments to include in the analysis, which may also lead to missingness not at random. In this paper, we extend our previous work to incorporate missingness not at random using selection models. The proposed method is then applied to two network meta-analyses and evaluated through extensive simulation studies. We also provide comprehensive comparisons of a commonly used contrast-based method and the arm-based method via simulations in a technical appendix under missing completely at random and missing at random.
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...
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.
Basu, Cynthia; Ahmed, Mariam A.; Kartha, Reena V.; Brundage, Richard C.; Raymond, Gerald V.; Cloyd, James C.; Carlin, Bradley P.
2017-01-01
X-linked adrenoleukodystrophy (X-ALD) is a rare, progressive and typically fatal neurodegenerative disease. Lorenzo’s Oil (LO) is one of the few X-ALD treatments available, but little has been done to establish its clinical efficacy or indications for its use. In this paper, we analyze data on 116 male asymptomatic pediatric patients who were administered LO. We offer a hierarchical Bayesian statistical approach to understanding LO pharmacokinetics (PK) and pharmacodynamics (PD) resulting from an accumulation of very long chain fatty acids. We experiment with individual- and observational-level errors, various choices of prior distributions, and deal with the limitation of having just one observation per administration of the drug, as opposed to the more usual multiple observations per administration. We link LO dose to the plasma erucic acid concentrations by PK modeling, and then link this concentration to a biomarker (C26, a very long chain fatty acid) by PD modeling. Next, we design a Bayesian Phase IIa study to estimate precisely what improvements in the biomarker can arise from various LO doses, while simultaneously modeling a binary toxicity endpoint. Our Bayesian adaptive algorithm emerges as reasonably robust and efficient while still retaining good classical (frequentist) operating characteristics. Future work looks toward using the results of this trial to design a Phase III study linking LO dose to actual improvements in health status, as measured by the appearance of brain lesions observed via magnetic resonance imaging. PMID:27547896
Basu, Cynthia; Ahmed, Mariam A; Kartha, Reena V; Brundage, Richard C; Raymond, Gerald V; Cloyd, James C; Carlin, Bradley P
2016-01-01
X-linked adrenoleukodystrophy (X-ALD) is a rare, progressive, and typically fatal neurodegenerative disease. Lorenzo's oil (LO) is one of the few X-ALD treatments available, but little has been done to establish its clinical efficacy or indications for its use. In this article, we analyze data on 116 male asymptomatic pediatric patients who were administered LO. We offer a hierarchical Bayesian statistical approach to understand LO pharmacokinetics (PK) and pharmacodynamics (PD) resulting from an accumulation of very long-chain fatty acids. We experiment with individual- and observational-level errors and various choices of prior distributions and deal with the limitation of having just one observation per administration of the drug, as opposed to the more usual multiple observations per administration. We link LO dose to the plasma erucic acid concentrations by PK modeling, and then link this concentration to a biomarker (C26, a very long-chain fatty acid) by PD modeling. Next, we design a Bayesian Phase IIa study to estimate precisely what improvements in the biomarker can arise from various LO doses while simultaneously modeling a binary toxicity endpoint. Our Bayesian adaptive algorithm emerges as reasonably robust and efficient while still retaining good classical (frequentist) operating characteristics. Future work looks toward using the results of this trial to design a Phase III study linking LO dose to actual improvements in health status, as measured by the appearance of brain lesions observed via magnetic resonance imaging.
Ganatra, Bela; Gerdts, Caitlin; Rossier, Clémentine; Johnson, Brooke Ronald; Tunçalp, Özge; Assifi, Anisa; Sedgh, Gilda; Singh, Susheela; Bankole, Akinrinola; Popinchalk, Anna; Bearak, Jonathan; Kang, Zhenning; Alkema, Leontine
2017-11-25
Global estimates of unsafe abortions have been produced for 1995, 2003, and 2008. However, reconceptualisation of the framework and methods for estimating abortion safety is needed owing to the increased availability of simple methods for safe abortion (eg, medical abortion), the increasingly widespread use of misoprostol outside formal health systems in contexts where abortion is legally restricted, and the need to account for the multiple factors that affect abortion safety. We used all available empirical data on abortion methods, providers, and settings, and factors affecting safety as covariates within a Bayesian hierarchical model to estimate the global, regional, and subregional distributions of abortion by safety categories. We used a three-tiered categorisation based on the WHO definition of unsafe abortion and WHO guidelines on safe abortion to categorise abortions as safe or unsafe and to further divide unsafe abortions into two categories of less safe and least safe. Of the 55· 7 million abortions that occurred worldwide each year between 2010-14, we estimated that 30·6 million (54·9%, 90% uncertainty interval 49·9-59·4) were safe, 17·1 million (30·7%, 25·5-35·6) were less safe, and 8·0 million (14·4%, 11·5-18·1) were least safe. Thus, 25·1 million (45·1%, 40·6-50·1) abortions each year between 2010 and 2014 were unsafe, with 24·3 million (97%) of these in developing countries. The proportion of unsafe abortions was significantly higher in developing countries than developed countries (49·5% vs 12·5%). When grouped by the legal status of abortion, the proportion of unsafe abortions was significantly higher in countries with highly restrictive abortion laws than in those with less restrictive laws. Increased efforts are needed, especially in developing countries, to ensure access to safe abortion. The paucity of empirical data is a limitation of these findings. Improved in-country data for health services and innovative research to
Liu, Xiangdong; Jessen, Walter J; Sivaganesan, Siva; Aronow, Bruce J; Medvedovic, Mario
2007-08-03
Transcriptional modules (TM) consist of groups of co-regulated genes and transcription factors (TF) regulating their expression. Two high-throughput (HT) experimental technologies, gene expression microarrays and Chromatin Immuno-Precipitation on Chip (ChIP-chip), are capable of producing data informative about expression regulatory mechanism on a genome scale. The optimal approach to joint modeling of data generated by these two complementary biological assays, with the goal of identifying and characterizing TMs, is an important open problem in computational biomedicine. We developed and validated a novel probabilistic model and related computational procedure for identifying TMs by jointly modeling gene expression and ChIP-chip binding data. We demonstrate an improved functional coherence of the TMs produced by the new method when compared to either analyzing expression or ChIP-chip data separately or to alternative approaches for joint analysis. We also demonstrate the ability of the new algorithm to identify novel regulatory relationships not revealed by ChIP-chip data alone. The new computational procedure can be used in more or less the same way as one would use simple hierarchical clustering without performing any special transformation of data prior to the analysis. The R and C-source code for implementing our algorithm is incorporated within the R package gimmR which is freely available at http://eh3.uc.edu/gimm. Our results indicate that, whenever available, ChIP-chip and expression data should be analyzed within the unified probabilistic modeling framework, which will likely result in improved clusters of co-regulated genes and improved ability to detect meaningful regulatory relationships. Given the good statistical properties and the ease of use, the new computational procedure offers a worthy new tool for reconstructing transcriptional regulatory networks.
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 ...
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...... in the ability to characterize variation in immune responses involving larger numbers of functionally differentiated cell subtypes. We describe novel classes of Markov chain Monte Carlo methods for model fitting that exploit distributed GPU (graphics processing unit) implementation. We discuss issues of cellular...... subtype identification in this novel, general model framework, and provide a detailed example using simulated data. We then describe application to a data set from an experimental study of antigen-specific T-cell subtyping using combinatorially encoded assays in human blood samples. Summary comments...
Bayesian Hierarchical Grouping: perceptual grouping as mixture estimation
Froyen, Vicky; Feldman, Jacob; Singh, Manish
2015-01-01
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. PMID:26322548
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 ......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...
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.
Dynamic networks from hierarchical bayesian graph clustering.
Directory of Open Access Journals (Sweden)
Yongjin Park
Full Text Available Biological networks change dynamically as protein components are synthesized and degraded. Understanding the time-dependence and, in a multicellular organism, tissue-dependence of a network leads to insight beyond a view that collapses time-varying interactions into a single static map. Conventional algorithms are limited to analyzing evolving networks by reducing them to a series of unrelated snapshots.Here we introduce an approach that groups proteins according to shared interaction patterns through a dynamical hierarchical stochastic block model. Protein membership in a block is permitted to evolve as interaction patterns shift over time and space, representing the spatial organization of cell types in a multicellular organism. The spatiotemporal evolution of the protein components are inferred from transcript profiles, using Arabidopsis root development (5 tissues, 3 temporal stages as an example.The new model requires essentially no parameter tuning, out-performs existing snapshot-based methods, identifies protein modules recruited to specific cell types and developmental stages, and could have broad application to social networks and other similar dynamic systems.
Morita, Satoshi; Thall, Peter F.; Bekele, B. Nebiyou; Mathew, Paul
2010-01-01
SUMMARY Advances in understanding the biological underpinnings of many cancers have led increasingly to the use of molecularly targeted anti-cancer therapies. Because the platelet-derived growth factor receptor (PDGFR) has been implicated in the progression of prostate cancer bone metastases, it is of great interest to examine possible relationships between PDGFR inhibition and therapeutic outcomes. Here, we analyze the association between change in activated PDGFR (p-PDGFR) and progression free survival (PFS) time based on large within-patient samples of cell-specific p-PDGFR values taken before and after treatment from each of 88 prostate cancer patients. To utilize these paired samples as covariate data in a regression model for PFS time, and because the p-PDGFR distributions are bimodal, we first employ a Bayesian hierarchical mixture model to obtain a deconvolution of the pre-treatment and post-treatment within-patient p-PDGFR distributions. We evaluate fits of the mixture model and a non-mixture model that ignores the bimodality by using a supnorm metric to compare the empirical distribution of each p-PDGFR data set with the corresponding fitted distribution under each model. Our results show that first using the mixture model to account for the bimodality of the within-patient p-PDGFR distributions, and then using the posterior within-patient component mean changes in p-PDGFR so obtained as covariates in the regression model for PFS time provides an improved estimation. PMID:20390057
Coley, Rebecca Yates; Fisher, Aaron J; Mamawala, Mufaddal; Carter, Herbert Ballentine; Pienta, Kenneth J; Zeger, Scott L
2017-06-01
In this article, we present a Bayesian hierarchical model for predicting a latent health state from longitudinal clinical measurements. Model development is motivated by the need to integrate multiple sources of data to improve clinical decisions about whether to remove or irradiate a patient's prostate cancer. Existing modeling approaches are extended to accommodate measurement error in cancer state determinations based on biopsied tissue, clinical measurements possibly not missing at random, and informative partial observation of the true state. The proposed model enables estimation of whether an individual's underlying prostate cancer is aggressive, requiring surgery and/or radiation, or indolent, permitting continued surveillance. These individualized predictions can then be communicated to clinicians and patients to inform decision-making. We demonstrate the model with data from a cohort of low-risk prostate cancer patients at Johns Hopkins University and assess predictive accuracy among a subset for whom true cancer state is observed. Simulation studies confirm model performance and explore the impact of adjusting for informative missingness on true state predictions. R code is provided in an online supplement and at http://github.com/rycoley/prediction-prostate-surveillance. © 2016, The International Biometric Society.
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.
Gerbino, Martina; Lattanzi, Massimiliano; Mena, Olga; Freese, Katherine
2017-12-01
We present a novel approach to derive constraints on neutrino masses, as well as on other cosmological parameters, from cosmological data, while taking into account our ignorance of the neutrino mass ordering. We derive constraints from a combination of current as well as future cosmological datasets on the total neutrino mass Mν and on the mass fractions fν,i =mi /Mν (where the index i = 1 , 2 , 3 indicates the three mass eigenstates) carried by each of the mass eigenstates mi, after marginalizing over the (unknown) neutrino mass ordering, either normal ordering (NH) or inverted ordering (IH). The bounds on all the cosmological parameters, including those on the total neutrino mass, take therefore into account the uncertainty related to our ignorance of the mass hierarchy that is actually realized in nature. This novel approach is carried out in the framework of Bayesian analysis of a typical hierarchical problem, where the distribution of the parameters of the model depends on further parameters, the hyperparameters. In this context, the choice of the neutrino mass ordering is modeled via the discrete hyperparameterhtype, which we introduce in the usual Markov chain analysis. The preference from cosmological data for either the NH or the IH scenarios is then simply encoded in the posterior distribution of the hyperparameter itself. Current cosmic microwave background (CMB) measurements assign equal odds to the two hierarchies, and are thus unable to distinguish between them. However, after the addition of baryon acoustic oscillation (BAO) measurements, a weak preference for the normal hierarchical scenario appears, with odds of 4 : 3 from Planck temperature and large-scale polarization in combination with BAO (3 : 2 if small-scale polarization is also included). Concerning next-generation cosmological experiments, forecasts suggest that the combination of upcoming CMB (COrE) and BAO surveys (DESI) may determine the neutrino mass hierarchy at a high statistical
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.
Poor-data and data-poor species stock assessment using a Bayesian hierarchical approach
Jiao, Y.; Cortes, E; Andrews, K.; Guo, F.
2011-01-01
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-po...
Lee, Whanhee; Hwang, Sung-Hee; Choi, Hayoung; Kim, Ho
2017-01-01
Smoking and passive smoking have been extensively reported as risk factors of cardiovascular morbidity and mortality. Despite the biological mechanisms underlying the impact of hazardous chemical substances contained in tobacco in cardiovascular diseases (CVD), studies investigating the association between smoking and passive smoking with morbidity are at an inchoate stage in Korea. Therefore, this study aimed to estimate the risks of smoking and passive smoking on cardiovascular morbidity at the national and regional levels. This study calculated sex-standardized and age-standardized prevalence of CVD and smoking indices in 253 community health centers (si/gun/gu) in Korea using the 2008-2013 Korea Community Health Survey data. Furthermore, a Bayesian hierarchical model was used to estimate the association of smoking and passive smoking with the prevalence of CVD from the national and regional community health centers. At the national level, smoking was significantly associated with stroke (relative risk [RR], 1.060) and hypertension (RR, 1.016) prevalence, whilst passive smoking at home and work were also significantly associated with prevalence of stroke (RR, 1.037/1.013), angina (RR, 1.016/1.006), and hypertension (RR, 1.010/1.004). Furthermore, the effects of smoking and passive smoking were greater in urban-industrial areas than in rural areas. The findings of this study would provide grounds for national policies that limit smoking and passive smoking, as well as regionally serve as the basis for region-specific healthcare policies in populations with high CVD vulnerability.
Xie, Meiquan; Cheng, Wen; Gill, Gurdiljot Singh; Zhou, Jiao; Jia, Xudong; Choi, Simon
2017-08-24
Most of the extensive research dedicated to identifying the influential factors of hit-and-run (HR) crashes has utilized typical maximum likelihood estimation binary logit models, and none have employed real-time traffic data. To fill this gap, this study focused on investigating factors contributing to HR crashes, as well as the severity levels of HR. This study analyzed 4-year crash and real-time loop detector data by employing hierarchical Bayesian models with random effects within a sequential logit structure. In addition to evaluation of the impact of random effects on model fitness and complexity, the prediction capability of the models was examined. Stepwise incremental sensitivity and specificity were calculated and receiver operating characteristic (ROC) curves were utilized to graphically illustrate the predictive performance of the model. Among the real-time flow variables, the average occupancy and speed from the upstream detector were observed to be positively correlated with HR crash possibility. The average upstream speed and speed difference between upstream and downstream speeds were correlated with the occurrence of severe HR crashes. In addition to real-time factors, other variables found influential for HR and severe HR crashes were length of segment, adverse weather conditions, dark lighting conditions with malfunctioning street lights, driving under the influence of alcohol, width of inner shoulder, and nighttime. This study suggests the potential traffic conditions of HR and severe HR occurrence, which refer to relatively congested upstream traffic conditions with high upstream speed and significant speed deviations on long segments. The above findings suggest that traffic enforcement should be directed toward mitigating risky driving under the aforementioned traffic conditions. Moreover, enforcement agencies may employ alcohol checkpoints to counter driving under the influence (DUI) at night. With regard to engineering improvements, wider
Directory of Open Access Journals (Sweden)
Whanhee Lee
2017-06-01
Full Text Available OBJECTIVES Smoking and passive smoking have been extensively reported as risk factors of cardiovascular morbidity and mortality. Despite the biological mechanisms underlying the impact of hazardous chemical substances contained in tobacco in cardiovascular diseases (CVD, studies investigating the association between smoking and passive smoking with morbidity are at an inchoate stage in Korea. Therefore, this study aimed to estimate the risks of smoking and passive smoking on cardiovascular morbidity at the national and regional levels. METHODS This study calculated sex-standardized and age-standardized prevalence of CVD and smoking indices in 253 community health centers (si/gun/gu in Korea using the 2008-2013 Korea Community Health Survey data. Furthermore, a Bayesian hierarchical model was used to estimate the association of smoking and passive smoking with the prevalence of CVD from the national and regional community health centers. RESULTS At the national level, smoking was significantly associated with stroke (relative risk [RR], 1.060 and hypertension (RR, 1.016 prevalence, whilst passive smoking at home and work were also significantly associated with prevalence of stroke (RR, 1.037/1.013, angina (RR, 1.016/1.006, and hypertension (RR, 1.010/1.004. Furthermore, the effects of smoking and passive smoking were greater in urban-industrial areas than in rural areas. CONCLUSIONS The findings of this study would provide grounds for national policies that limit smoking and passive smoking, as well as regionally serve as the basis for region-specific healthcare policies in populations with high CVD vulnerability.
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
2017-05-01
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. © 2017 John Wiley & Sons Ltd/CNRS.
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.
Hierarchical species distribution models
Hefley, Trevor J.; Hooten, Mevin B.
2016-01-01
Determining the distribution pattern of a species is important to increase scientific knowledge, inform management decisions, and conserve biodiversity. To infer spatial and temporal patterns, species distribution models have been developed for use with many sampling designs and types of data. Recently, it has been shown that count, presence-absence, and presence-only data can be conceptualized as arising from a point process distribution. Therefore, it is important to understand properties of the point process distribution. We examine how the hierarchical species distribution modeling framework has been used to incorporate a wide array of regression and theory-based components while accounting for the data collection process and making use of auxiliary information. The hierarchical modeling framework allows us to demonstrate how several commonly used species distribution models can be derived from the point process distribution, highlight areas of potential overlap between different models, and suggest areas where further research is needed.
Hierarchical models and functional traits
van Loon, E.E.; Shamoun-Baranes, J.; Sierdsema, H.; Bouten, W.; Cramer, W.; Badeck, F.; Krukenberg, B.; Klotz, S.; Kühn, I.; Schweiger, O.; Böhning-Gaese, K.; Schaefer, H.-C.; Kissling, D.; Brandl, R.; Brändle, M.; Fricke, R.; Leuschner, C.; Buschmann, H.; Köckermann, B.; Rose, L.
2006-01-01
Hierarchical models for animal abundance prediction are conceptually elegant. They are generally more parsimonous than non-hierarchical models derived from the same data, give relatively robust predictions and automatically provide consistent output at multiple (spatio-temporal) scales. Another
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
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.
Nutrient pathways and neural tube defects: a semi-Bayesian hierarchical analysis.
Carmichael, Suzan L; Witte, John S; Shaw, Gary M
2009-01-01
We used conventional and hierarchical logistic regression to examine the association of neural tube defects (NTDs) with intake of 26 nutrients that contribute to the mechanistic pathways of methylation, glycemic control, and oxidative stress, all of which have been implicated in NTD etiology. The hierarchical approach produces more plausible, more stable estimates than the conventional approach, while adjusting for potential confounding by other nutrients. Analyses included 386 cases and 408 nonmalformed controls with complete data on nutrients and potential confounders (race/ethnicity, education, obesity, and intake of vitamin supplements) from a population-based case-control study of deliveries in California from 1989 to 1991. Nutrients were specified as continuous, and their units were standardized to have a mean of zero and standard deviation (SD) of 1 for comparability of units across pathways. ORs reflect a 1-SD increase in the corresponding nutrient. Among women who took vitamin supplements, semi-Bayesian hierarchical modeling results suggested no associations between nutrient intake and NTDs. Among women who did not take supplements, both conventional and hierarchical models (HM) suggested an inverse association between lutein intake and NTD risk (HM odds ratio [OR] = 0.6; 95% confidence interval = 0.5-0.9) and a positive association with sucrose (HM OR 1.4; 1.1-1.8) and glycemic index (HM OR 1.3; 1.0-1.6). Our findings for lutein, glycemic index, and sucrose suggest that further study of NTDs and the glycemic control and oxidative stress pathways is warranted.
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.
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...... 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 humble Bayesian: model checking from a fully Bayesian perspective.
Morey, Richard D; Romeijn, Jan-Willem; Rouder, Jeffrey N
2013-02-01
Gelman and Shalizi (2012) criticize what they call the 'usual story' in Bayesian statistics: that the distribution over hypotheses or models is the sole means of statistical inference, thus excluding model checking and revision, and that inference is inductivist rather than deductivist. They present an alternative hypothetico-deductive approach to remedy both shortcomings. We agree with Gelman and Shalizi's criticism of the usual story, but disagree on whether Bayesian confirmation theory should be abandoned. We advocate a humble Bayesian approach, in which Bayesian confirmation theory is the central inferential method. A humble Bayesian checks her models and critically assesses whether the Bayesian statistical inferences can reasonably be called upon to support real-world inferences. © 2012 The British Psychological Society.
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.
He, Ji X.; Bence, James R.; Roseman, Edward F.; Fielder, David G.; Ebener, Mark P.
2015-01-01
We evaluated the ecosystem regime shift in the main basin of Lake Huron that was indicated by the 2003 collapse of alewives, and dramatic declines in Chinook salmon abundance thereafter. We found that the period of 1995-2002 should be considered as the early phase of the final regime shift. We developed two Bayesian hierarchical models to describe time-varying growth based on the von Bertalanffy growth function and the length-mass relationship. We used asymptotic length as an index of growth potential, and predicted body mass at a given length as an index of body condition. Modeling fits to length and body mass at age of lake trout, Chinook salmon, and walleye were excellent. Based on posterior distributions, we evaluated the shifts in among-year geometric means of the growth potential and body condition. For a given top piscivore, one of the two indices responded to the regime shift much earlier than the 2003 collapse of alewives, the other corresponded to the 2003 changes, and which index provided the early signal differed among the three top piscivores.
Bayesian analysis of CCDM models
Jesus, J. F.; Valentim, R.; Andrade-Oliveira, F.
2017-09-01
Creation of Cold Dark Matter (CCDM), in the context of Einstein Field Equations, produces a negative pressure term 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 criteria, in light of SNe Ia data: Akaike Information Criterion (AIC), Bayesian Information Criterion (BIC) and Bayesian Evidence (BE). These criteria allow to compare models considering goodness of fit and number of free parameters, penalizing excess of complexity. We find that JO model is slightly favoured over LJO/ΛCDM model, however, neither of these, nor Γ = 3αH0 model can be discarded from the current analysis. Three other scenarios are discarded either because poor fitting or because of the excess of free parameters. A method of increasing Bayesian evidence through reparameterization in order to reducing parameter degeneracy is also developed.
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.
A guide to Bayesian model checking for ecologists
Conn, Paul; Johnson, Devin; Williams, Perry; Melin, Sharon; Hooten, Mevin
2017-01-01
Checking that models adequately represent data is an essential component of applied statistical inference. Ecologists increasingly use hierarchical Bayesian statistical models in their research. The appeal of this modeling paradigm is undeniable, as researchers can build and fit models that embody complex ecological processes while simultaneously controlling observation error. However, ecologists tend to be less focused on checking model assumptions and assessing potential lack-of-fit when ap...
Bayesian models in cognitive neuroscience: A tutorial
O'Reilly, J.X.; Mars, R.B.
2015-01-01
This chapter provides an introduction to Bayesian models and their application in cognitive neuroscience. The central feature of Bayesian models, as opposed to other classes of models, is that Bayesian models represent the beliefs of an observer as probability distributions, allowing them to
Bayesian dynamic modelling to assess differential treatment effects on panic attack frequencies
Krone, Tanja; Albers, C.J.; Timmerman, M.E.
2016-01-01
To represent the complex structure of intensive longitudinal data of multiple individuals, we propose a hierarchical Bayesian Dynamic Model (BDM). This BDM is a generalized linear hierarchical model where the individual parameters do not necessarily follow a normal distribution. The model parameters
Frecon, Jordan; Pustelnik, Nelly; Dobigeon, Nicolas; Wendt, Herwig; Abry, Patrice
2017-10-01
Piecewise constant denoising can be solved either by deterministic optimization approaches, based on the Potts model, or by stochastic Bayesian procedures. The former lead to low computational time but require the selection of a regularization parameter, whose value significantly impacts the achieved solution, and whose automated selection remains an involved and challenging problem. Conversely, fully Bayesian formalisms encapsulate the regularization parameter selection into hierarchical models, at the price of high computational costs. This contribution proposes an operational strategy that combines hierarchical Bayesian and Potts model formulations, with the double aim of automatically tuning the regularization parameter and of maintaining computational effciency. The proposed procedure relies on formally connecting a Bayesian framework to a l2-Potts functional. Behaviors and performance for the proposed piecewise constant denoising and regularization parameter tuning techniques are studied qualitatively and assessed quantitatively, and shown to compare favorably against those of a fully Bayesian hierarchical procedure, both in accuracy and in computational load.
Bayesian inference for the information gain model.
Stringer, Sven; Borsboom, Denny; Wagenmakers, Eric-Jan
2011-06-01
One of the most popular paradigms to use for studying human reasoning involves the Wason card selection task. In this task, the participant is presented with four cards and a conditional rule (e.g., "If there is an A on one side of the card, there is always a 2 on the other side"). Participants are asked which cards should be turned to verify whether or not the rule holds. In this simple task, participants consistently provide answers that are incorrect according to formal logic. To account for these errors, several models have been proposed, one of the most prominent being the information gain model (Oaksford & Chater, Psychological Review, 101, 608-631, 1994). This model is based on the assumption that people independently select cards based on the expected information gain of turning a particular card. In this article, we present two estimation methods to fit the information gain model: a maximum likelihood procedure (programmed in R) and a bayesian procedure (programmed in WinBUGS). We compare the two procedures and illustrate the flexibility of the bayesian hierarchical procedure by applying it to data from a meta-analysis of the Wason task (Oaksford & Chater, Psychological Review, 101, 608-631, 1994). We also show that the goodness of fit of the information gain model can be assessed by inspecting the posterior predictives of the model. These bayesian procedures make it easy to apply the information gain model to empirical data. Supplemental materials may be downloaded along with this article from www.springerlink.com.
Bayesian Repulsive Gaussian Mixture Model
Xie, Fangzheng; Xu, Yanxun
2017-01-01
We develop a general class of Bayesian repulsive Gaussian mixture models that encourage well-separated clusters, aiming at reducing potentially redundant components produced by independent priors for locations (such as the Dirichlet process). The asymptotic results for the posterior distribution of the proposed models are derived, including posterior consistency and posterior contraction rate in the context of nonparametric density estimation. More importantly, we show that compared to the in...
Bayesian Models of Individual Differences.
Powell, Georgie; Meredith, Zoe; McMillin, Rebecca; Freeman, Tom C A
2016-12-01
According to Bayesian models, perception and cognition depend on the optimal combination of noisy incoming evidence with prior knowledge of the world. Individual differences in perception should therefore be jointly determined by a person's sensitivity to incoming evidence and his or her prior expectations. It has been proposed that individuals with autism have flatter prior distributions than do nonautistic individuals, which suggests that prior variance is linked to the degree of autistic traits in the general population. We tested this idea by studying how perceived speed changes during pursuit eye movement and at low contrast. We found that individual differences in these two motion phenomena were predicted by differences in thresholds and autistic traits when combined in a quantitative Bayesian model. Our findings therefore support the flatter-prior hypothesis and suggest that individual differences in prior expectations are more systematic than previously thought. In order to be revealed, however, individual differences in sensitivity must also be taken into account.
Aldrin, Magne Tommy; Huseby, Ragnar Bang; Stien, Audun; Grøntvedt, Randi Nygaard; Viljugrein, Hildegunn; Jansen, Peder A
2017-01-01
Salmon farming has become a prosperous international industry over the last decades. Along with growth in the production farmed salmon, however, an increasing threat by pathogens has emerged. Of special concern is the propagation and spread of the salmon louse, Lepeophtheirus salmonis. To gain insight into this parasite’s population dynamics in large scale salmon farming system, we present a fully mechanistic stage-structured population model for the salmon louse, also allowing for complexiti...
Bayesian population receptive field modelling.
Zeidman, Peter; Silson, Edward Harry; Schwarzkopf, Dietrich Samuel; Baker, Chris Ian; Penny, Will
2017-09-08
We introduce a probabilistic (Bayesian) framework and associated software toolbox for mapping population receptive fields (pRFs) based on fMRI data. This generic approach is intended to work with stimuli of any dimension and is demonstrated and validated in the context of 2D retinotopic mapping. The framework enables the experimenter to specify generative (encoding) models of fMRI timeseries, in which experimental stimuli enter a pRF model of neural activity, which in turns drives a nonlinear model of neurovascular coupling and Blood Oxygenation Level Dependent (BOLD) response. The neuronal and haemodynamic parameters are estimated together on a voxel-by-voxel or region-of-interest basis using a Bayesian estimation algorithm (variational Laplace). This offers several novel contributions to receptive field modelling. The variance/covariance of parameters are estimated, enabling receptive fields to be plotted while properly representing uncertainty about pRF size and location. Variability in the haemodynamic response across the brain is accounted for. Furthermore, the framework introduces formal hypothesis testing to pRF analysis, enabling competing models to be evaluated based on their log model evidence (approximated by the variational free energy), which represents the optimal tradeoff between accuracy and complexity. Using simulations and empirical data, we found that parameters typically used to represent pRF size and neuronal scaling are strongly correlated, which is taken into account by the Bayesian methods we describe when making inferences. We used the framework to compare the evidence for six variants of pRF model using 7 T functional MRI data and we found a circular Difference of Gaussians (DoG) model to be the best explanation for our data overall. We hope this framework will prove useful for mapping stimulus spaces with any number of dimensions onto the anatomy of the brain. Copyright © 2017 The Authors. Published by Elsevier Inc. All rights reserved.
Bayesian operational risk models
Silvia Figini; Lijun Gao; Paolo Giudici
2013-01-01
Operational risk is hard to quantify, for the presence of heavy tailed loss distributions. Extreme value distributions, used in this context, are very sensitive to the data, and this is a problem in the presence of rare loss data. Self risk assessment questionnaires, if properly modelled, may provide the missing piece of information that is necessary to adequately estimate op- erational risks. In this paper we propose to embody self risk assessment data into suitable prior distributions, and ...
Disease mapping of Leishmaniasis outbreak in Afghanistan: spatial hierarchical Bayesian analysis
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Oyelola A. Adegboye
2012-08-01
Full Text Available Objective: To analyze the spatial pattern of Leishmaniasis disease in Afghanistan, using provincial level geo-referenced data. The disease is contracted through bites from sand flies and is the third most common vector-borne disease. Leishmaniasis is a serious health concern in Afghanistan with about 250 000 estimated new cases of cutaneous infection nationwide and 67,000 cases in Kabul. This makes Kabul the city with the largest incidence of the disease worldwide. Methods: We use a Bayesian hierarchical Poisson model to estimate the influence of hypothesized risk factors on the relative risk of the disease. We use random components to take into account the lack of independence of the risk between adjacent areas. Results: Statistical inference is carried out using Markov Chain Monte Carlo simulation. The final model specification includes altitude, two random components (intercept and slope and utilizes a conditional autoregressive prior with a deviance information criterion of 247.761. Spatial scan statistics confirm disease clusters in the North-Eastern and South-Eastern regions of Afghanistan with a p-value of less than 0.0001. Conclusions: The study confirms disease clusters in the North-Eastern and South-Eastern regions of Afghanistan. Our findings are robust with respect to the specification of the prior distribution and give important insights into the spatial dynamics of Leishmaniasis in Afghanistan.
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
The humble Bayesian : Model checking from a fully Bayesian perspective
Morey, Richard D.; Romeijn, Jan-Willem; Rouder, Jeffrey N.
Gelman and Shalizi (2012) criticize what they call the usual story in Bayesian statistics: that the distribution over hypotheses or models is the sole means of statistical inference, thus excluding model checking and revision, and that inference is inductivist rather than deductivist. They present
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
Post hoc Bayesian model selection.
Friston, Karl; Penny, Will
2011-06-15
This note describes a Bayesian model selection or optimization procedure for post hoc inferences about reduced versions of a full model. The scheme provides the evidence (marginal likelihood) for any reduced model as a function of the posterior density over the parameters of the full model. It rests upon specifying models through priors on their parameters, under the assumption that the likelihood remains the same for all models considered. This provides a quick and efficient scheme for scoring arbitrarily large numbers of models, after inverting a single (full) model. In turn, this enables the selection among discrete models that are distinguished by the presence or absence of free parameters, where free parameters are effectively removed from the model using very precise shrinkage priors. An alternative application of this post hoc model selection considers continuous model spaces, defined in terms of hyperparameters (sufficient statistics) of the prior density over model parameters. In this instance, the prior (model) can be optimized with respect to its evidence. The expressions for model evidence become remarkably simple under the Laplace (Gaussian) approximation to the posterior density. Special cases of this scheme include Savage-Dickey density ratio tests for reduced models and automatic relevance determination in model optimization. We illustrate the approach using general linear models and a more complicated nonlinear state-space model. Copyright © 2011 Elsevier Inc. All rights reserved.
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Rasheda Arman Chowdhury
Full Text Available Localizing the generators of epileptic activity in the brain using Electro-EncephaloGraphy (EEG or Magneto-EncephaloGraphy (MEG signals is of particular interest during the pre-surgical investigation of epilepsy. Epileptic discharges can be detectable from background brain activity, provided they are associated with spatially extended generators. Using realistic simulations of epileptic activity, this study evaluates the ability of distributed source localization methods to accurately estimate the location of the generators and their sensitivity to the spatial extent of such generators when using MEG data. Source localization methods based on two types of realistic models have been investigated: (i brain activity may be modeled using cortical parcels and (ii brain activity is assumed to be locally smooth within each parcel. A Data Driven Parcellization (DDP method was used to segment the cortical surface into non-overlapping parcels and diffusion-based spatial priors were used to model local spatial smoothness within parcels. These models were implemented within the Maximum Entropy on the Mean (MEM and the Hierarchical Bayesian (HB source localization frameworks. We proposed new methods in this context and compared them with other standard ones using Monte Carlo simulations of realistic MEG data involving sources of several spatial extents and depths. Detection accuracy of each method was quantified using Receiver Operating Characteristic (ROC analysis and localization error metrics. Our results showed that methods implemented within the MEM framework were sensitive to all spatial extents of the sources ranging from 3 cm(2 to 30 cm(2, whatever were the number and size of the parcels defining the model. To reach a similar level of accuracy within the HB framework, a model using parcels larger than the size of the sources should be considered.
Modeling Diagnostic Assessments with Bayesian Networks
Almond, Russell G.; DiBello, Louis V.; Moulder, Brad; Zapata-Rivera, Juan-Diego
2007-01-01
This paper defines Bayesian network models and examines their applications to IRT-based cognitive diagnostic modeling. These models are especially suited to building inference engines designed to be synchronous with the finer grained student models that arise in skills diagnostic assessment. Aspects of the theory and use of Bayesian network models…
Multicollinearity in hierarchical linear models.
Yu, Han; Jiang, Shanhe; Land, Kenneth C
2015-09-01
This study investigates an ill-posed problem (multicollinearity) in Hierarchical Linear Models from both the data and the model perspectives. We propose an intuitive, effective approach to diagnosing the presence of multicollinearity and its remedies in this class of models. A simulation study demonstrates the impacts of multicollinearity on coefficient estimates, associated standard errors, and variance components at various levels of multicollinearity for finite sample sizes typical in social science studies. We further investigate the role multicollinearity plays at each level for estimation of coefficient parameters in terms of shrinkage. Based on these analyses, we recommend a top-down method for assessing multicollinearity in HLMs that first examines the contextual predictors (Level-2 in a two-level model) and then the individual predictors (Level-1) and uses the results for data collection, research problem redefinition, model re-specification, variable selection and estimation of a final model. Copyright © 2015 Elsevier Inc. All rights reserved.
Modeling abundance using hierarchical distance sampling
Royle, Andy; Kery, Marc
2016-01-01
In this chapter, we provide an introduction to classical distance sampling ideas for point and line transect data, and for continuous and binned distance data. We introduce the conditional and the full likelihood, and we discuss Bayesian analysis of these models in BUGS using the idea of data augmentation, which we discussed in Chapter 7. We then extend the basic ideas to the problem of hierarchical distance sampling (HDS), where we have multiple point or transect sample units in space (or possibly in time). The benefit of HDS in practice is that it allows us to directly model spatial variation in population size among these sample units. This is a preeminent concern of most field studies that use distance sampling methods, but it is not a problem that has received much attention in the literature. We show how to analyze HDS models in both the unmarked package and in the BUGS language for point and line transects, and for continuous and binned distance data. We provide a case study of HDS applied to a survey of the island scrub-jay on Santa Cruz Island, California.
Bayesian Age-Period-Cohort Modeling and Prediction - BAMP
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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.
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
Zhou, Bo; Konstorum, Anna; Duong, Thao; Tieu, Kinh H.; Wells, William M.; Brown, Gregory G.; Stern, Hal S.; Shahbaba, Babak
2013-01-01
We propose a hierarchical Bayesian model for analyzing multi-site experimental fMRI studies. Our method takes the hierarchical structure of the data (subjects are nested within sites, and there are multiple observations per subject) into account and allows for modeling between-site variation. Using posterior predictive model checking and model…
Hossein Pourghassem
2010-01-01
The ever-increasing number of logo (trademark) in official automation systems for information management, archiving and retrieval application has created greater demand for an automatic detection and recognition logo. In this paper, a classification hierarchical structure based on Bayesian classifier is proposed to logo detection and recognition. In this hierarchical structure, using two measures false accept and false reject, a novel and straightforward training scheme is presented to extrac...
Learning Bayesian Network Model Structure from Data
National Research Council Canada - National Science Library
Margaritis, Dimitris
2003-01-01
In this thesis I address the important problem of the determination of the structure of directed statistical models, with the widely used class of Bayesian network models as a concrete vehicle of my ideas...
Classification using Hierarchical Naive Bayes models
DEFF Research Database (Denmark)
Langseth, Helge; Dyhre Nielsen, Thomas
2006-01-01
Classification problems have a long history in the machine learning literature. One of the simplest, and yet most consistently well-performing set of classifiers is the Naïve Bayes models. However, an inherent problem with these classifiers is the assumption that all attributes used to describe......, termed Hierarchical Naïve Bayes models. Hierarchical Naïve Bayes models extend the modeling flexibility of Naïve Bayes models by introducing latent variables to relax some of the independence statements in these models. We propose a simple algorithm for learning Hierarchical Naïve Bayes models...
Aksoy, Ozan; Weesie, Jeroen
2014-05-01
In this paper, using a within-subjects design, we estimate the utility weights that subjects attach to the outcome of their interaction partners in four decision situations: (1) binary Dictator Games (DG), second player's role in the sequential Prisoner's Dilemma (PD) after the first player (2) cooperated and (3) defected, and (4) first player's role in the sequential Prisoner's Dilemma game. We find that the average weights in these four decision situations have the following order: (1)>(2)>(4)>(3). Moreover, the average weight is positive in (1) but negative in (2), (3), and (4). Our findings indicate the existence of strong negative and small positive reciprocity for the average subject, but there is also high interpersonal variation in the weights in these four nodes. We conclude that the PD frame makes subjects more competitive than the DG frame. Using hierarchical Bayesian modeling, we simultaneously analyze beliefs of subjects about others' utility weights in the same four decision situations. We compare several alternative theoretical models on beliefs, e.g., rational beliefs (Bayesian-Nash equilibrium) and a consensus model. Our results on beliefs strongly support the consensus effect and refute rational beliefs: there is a strong relationship between own preferences and beliefs and this relationship is relatively stable across the four decision situations. Copyright © 2014 Elsevier Inc. All rights reserved.
Directory of Open Access Journals (Sweden)
W David Walter
Full Text Available Bovine tuberculosis is a bacterial disease caused by Mycobacterium bovis in livestock and wildlife with hosts that include Eurasian badgers (Meles meles, brushtail possum (Trichosurus vulpecula, and white-tailed deer (Odocoileus virginianus. Risk-assessment efforts in Michigan have been initiated on farms to minimize interactions of cattle with wildlife hosts but research on M. bovis on cattle farms has not investigated the spatial context of disease epidemiology. To incorporate spatially explicit data, initial likelihood of infection probabilities for cattle farms tested for M. bovis, prevalence of M. bovis in white-tailed deer, deer density, and environmental variables for each farm were modeled in a Bayesian hierarchical framework. We used geo-referenced locations of 762 cattle farms that have been tested for M. bovis, white-tailed deer prevalence, and several environmental variables that may lead to long-term survival and viability of M. bovis on farms and surrounding habitats (i.e., soil type, habitat type. Bayesian hierarchical analyses identified deer prevalence and proportion of sandy soil within our sampling grid as the most supported model. Analysis of cattle farms tested for M. bovis identified that for every 1% increase in sandy soil resulted in an increase in odds of infection by 4%. Our analysis revealed that the influence of prevalence of M. bovis in white-tailed deer was still a concern even after considerable efforts to prevent cattle interactions with white-tailed deer through on-farm mitigation and reduction in the deer population. Cattle farms test positive for M. bovis annually in our study area suggesting that the potential for an environmental source either on farms or in the surrounding landscape may contributing to new or re-infections with M. bovis. Our research provides an initial assessment of potential environmental factors that could be incorporated into additional modeling efforts as more knowledge of deer herd
Bayesian models a statistical primer for ecologists
Hobbs, N Thompson
2015-01-01
Bayesian modeling has become an indispensable tool for ecological research because it is uniquely suited to deal with complexity in a statistically coherent way. This textbook provides a comprehensive and accessible introduction to the latest Bayesian methods-in language ecologists can understand. Unlike other books on the subject, this one emphasizes the principles behind the computations, giving ecologists a big-picture understanding of how to implement this powerful statistical approach. Bayesian Models is an essential primer for non-statisticians. It begins with a definition of probabili
HIERARCHICAL OPTIMIZATION MODEL ON GEONETWORK
Directory of Open Access Journals (Sweden)
Z. Zha
2012-07-01
Full Text Available In existing construction experience of Spatial Data Infrastructure (SDI, GeoNetwork, as the geographical information integrated solution, is an effective way of building SDI. During GeoNetwork serving as an internet application, several shortcomings are exposed. The first one is that the time consuming of data loading has been considerately increasing with the growth of metadata count. Consequently, the efficiency of query and search service becomes lower. Another problem is that stability and robustness are both ruined since huge amount of metadata. The final flaw is that the requirements of multi-user concurrent accessing based on massive data are not effectively satisfied on the internet. A novel approach, Hierarchical Optimization Model (HOM, is presented to solve the incapability of GeoNetwork working with massive data in this paper. HOM optimizes the GeoNetwork from these aspects: internal procedure, external deployment strategies, etc. This model builds an efficient index for accessing huge metadata and supporting concurrent processes. In this way, the services based on GeoNetwork can maintain stable while running massive metadata. As an experiment, we deployed more than 30 GeoNetwork nodes, and harvest nearly 1.1 million metadata. From the contrast between the HOM-improved software and the original one, the model makes indexing and retrieval processes more quickly and keeps the speed stable on metadata amount increasing. It also shows stable on multi-user concurrent accessing to system services, the experiment achieved good results and proved that our optimization model is efficient and reliable.
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.
Raghavan, Ram K; Goodin, Douglas G; Neises, Daniel; Anderson, Gary A; Ganta, Roman R
2016-01-01
This study aims to examine the spatio-temporal dynamics of Rocky Mountain spotted fever (RMSF) prevalence in four contiguous states of Midwestern United States, and to determine the impact of environmental and socio-economic factors associated with this disease. Bayesian hierarchical models were used to quantify space and time only trends and spatio-temporal interaction effect in the case reports submitted to the state health departments in the region. Various socio-economic, environmental and climatic covariates screened a priori in a bivariate procedure were added to a main-effects Bayesian model in progressive steps to evaluate important drivers of RMSF space-time patterns in the region. Our results show a steady increase in RMSF incidence over the study period to newer geographic areas, and the posterior probabilities of county-specific trends indicate clustering of high risk counties in the central and southern parts of the study region. At the spatial scale of a county, the prevalence levels of RMSF is influenced by poverty status, average relative humidity, and average land surface temperature (>35°C) in the region, and the relevance of these factors in the context of climate-change impacts on tick-borne diseases are discussed.
Bayesian modeling 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
Bayesian modeling of ChIP-chip data using latent variables
Directory of Open Access Journals (Sweden)
Tian Yanan
2009-10-01
Full Text Available Abstract 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
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. © 2010 The Authors, Animal Genetics © 2010 Stichting International Foundation for Animal Genetics.
Hierarchical modeling and analysis for spatial data
Banerjee, Sudipto; Gelfand, Alan E
2003-01-01
Among the many uses of hierarchical modeling, their application to the statistical analysis of spatial and spatio-temporal data from areas such as epidemiology And environmental science has proven particularly fruitful. Yet to date, the few books that address the subject have been either too narrowly focused on specific aspects of spatial analysis, or written at a level often inaccessible to those lacking a strong background in mathematical statistics.Hierarchical Modeling and Analysis for Spatial Data is the first accessible, self-contained treatment of hierarchical methods, modeling, and dat
Fast and accurate Bayesian model criticism and conflict diagnostics using R-INLA
Ferkingstad, Egil
2017-10-16
Bayesian hierarchical models are increasingly popular for realistic modelling and analysis of complex data. This trend is accompanied by the need for flexible, general and computationally efficient methods for model criticism and conflict detection. Usually, a Bayesian hierarchical model incorporates a grouping of the individual data points, as, for example, with individuals in repeated measurement data. In such cases, the following question arises: Are any of the groups “outliers,” or in conflict with the remaining groups? Existing general approaches aiming to answer such questions tend to be extremely computationally demanding when model fitting is based on Markov chain Monte Carlo. We show how group-level model criticism and conflict detection can be carried out quickly and accurately through integrated nested Laplace approximations (INLA). The new method is implemented as a part of the open-source R-INLA package for Bayesian computing (http://r-inla.org).
Bayesian Model Checking for Multivariate Outcome Data.
Crespi, Catherine M; Boscardin, W John
2009-09-01
Bayesian models are increasingly used to analyze complex multivariate outcome data. However, diagnostics for such models have not been well-developed. We present a diagnostic method of evaluating the fit of Bayesian models for multivariate data based on posterior predictive model checking (PPMC), a technique in which observed data are compared to replicated data generated from model predictions. Most previous work on PPMC has focused on the use of test quantities that are scalar summaries of the data and parameters. However, scalar summaries are unlikely to capture the rich features of multivariate data. We introduce the use of dissimilarity measures for checking Bayesian models for multivariate outcome data. This method has the advantage of checking the fit of the model to the complete data vectors or vector summaries with reduced dimension, providing a comprehensive picture of model fit. An application with longitudinal binary data illustrates the methods.
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.
Bayesian models for astrophysical data using R, JAGS, Python, and Stan
Hilbe, Joseph M; Ishida, Emille E O
2017-01-01
This comprehensive guide to Bayesian methods in astronomy enables hands-on work by supplying complete R, JAGS, Python, and Stan code, to use directly or to adapt. It begins by examining the normal model from both frequentist and Bayesian perspectives and then progresses to a full range of Bayesian generalized linear and mixed or hierarchical models, as well as additional types of models such as ABC and INLA. The book provides code that is largely unavailable elsewhere and includes details on interpreting and evaluating Bayesian models. Initial discussions offer models in synthetic form so that readers can easily adapt them to their own data; later the models are applied to real astronomical data. The consistent focus is on hands-on modeling, analysis of data, and interpretations that address scientific questions. A must-have for astronomers, its concrete approach will also be attractive to researchers in the sciences more generally.
Hierarchical Model of Container Ports Throughput
Directory of Open Access Journals (Sweden)
Monika Rozmarynowska
2015-12-01
Full Text Available In this article the attempt has been made to construct hierarchical model of container ports throughput development. The presented hierarchical approach uses the relationships of development of global economy and container flows at different geographical levels: global (container throughput in all seaport on the world, regional (container throughput in the Baltic seaports and national (container throughput in Polish seaports. Model have been evaluated for their fit and usefulness for predictive purposes.
Posterior Predictive Model Checking in Bayesian Networks
Crawford, Aaron
2014-01-01
This simulation study compared the utility of various discrepancy measures within a posterior predictive model checking (PPMC) framework for detecting different types of data-model misfit in multidimensional Bayesian network (BN) models. The investigated conditions were motivated by an applied research program utilizing an operational complex…
Bayesian modeling of flexible cognitive control.
Jiang, Jiefeng; Heller, Katherine; Egner, Tobias
2014-10-01
"Cognitive control" describes endogenous guidance of behavior in situations where routine stimulus-response associations are suboptimal for achieving a desired goal. The computational and neural mechanisms underlying this capacity remain poorly understood. We examine recent advances stemming from the application of a Bayesian learner perspective that provides optimal prediction for control processes. In reviewing the application of Bayesian models to cognitive control, we note that an important limitation in current models is a lack of a plausible mechanism for the flexible adjustment of control over conflict levels changing at varying temporal scales. We then show that flexible cognitive control can be achieved by a Bayesian model with a volatility-driven learning mechanism that modulates dynamically the relative dependence on recent and remote experiences in its prediction of future control demand. We conclude that the emergent Bayesian perspective on computational mechanisms of cognitive control holds considerable promise, especially if future studies can identify neural substrates of the variables encoded by these models, and determine the nature (Bayesian or otherwise) of their neural implementation. Copyright © 2014 Elsevier Ltd. All rights reserved.
Wang, Qiu; Diemer, Matthew A.; Maier, Kimberly S.
2013-01-01
This study integrated Bayesian hierarchical modeling and receiver operating characteristic analysis (BROCA) to evaluate how interest strength (IS) and interest differentiation (ID) predicted low–socioeconomic status (SES) youth's interest-major congruence (IMC). Using large-scale Kuder Career Search online-assessment data, this study fit three…
Robust bayesian analysis of an autoregressive model with ...
African Journals Online (AJOL)
In this work, robust Bayesian analysis of the Bayesian estimation of an autoregressive model with exponential innovations is performed. Using a Bayesian robustness methodology, we show that, using a suitable generalized quadratic loss, we obtain optimal Bayesian estimators of the parameters corresponding to the ...
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 mixture models for partially verified data
DEFF Research Database (Denmark)
Kostoulas, Polychronis; Browne, William J.; Nielsen, Søren Saxmose
2013-01-01
Bayesian mixture models can be used to discriminate between the distributions of continuous test responses for different infection stages. These models are particularly useful in case of chronic infections with a long latent period, like Mycobacterium avium subsp. paratuberculosis (MAP) infection...
Dynamic Bayesian Networks for Student Modeling
Kaser, Tanja; Klingler, Severin; Schwing, Alexander G.; Gross, Markus
2017-01-01
Intelligent tutoring systems adapt the curriculum to the needs of the individual student. Therefore, an accurate representation and prediction of student knowledge is essential. Bayesian Knowledge Tracing (BKT) is a popular approach for student modeling. The structure of BKT models, however, makes it impossible to represent the hierarchy and…
Survey of Bayesian Models for Modelling of Stochastic Temporal Processes
Energy Technology Data Exchange (ETDEWEB)
Ng, B
2006-10-12
This survey gives an overview of popular generative models used in the modeling of stochastic temporal systems. In particular, this survey is organized into two parts. The first part discusses the discrete-time representations of dynamic Bayesian networks and dynamic relational probabilistic models, while the second part discusses the continuous-time representation of continuous-time Bayesian networks.
Improved Bayesian multimodeling: Integration of copulas and Bayesian model averaging
Madadgar, Shahrbanou; Moradkhani, Hamid
2014-12-01
Bayesian model averaging (BMA) is a popular approach to combine hydrologic forecasts from individual models and characterize the uncertainty induced by model structure. In the original form of BMA, the conditional probability density function (PDF) of each model is assumed to be a particular probability distribution (e.g., Gaussian, gamma, etc.). If the predictions of any hydrologic model do not follow certain distribution, a data transformation procedure is required prior to model averaging. Moreover, it is strongly recommended to apply BMA on unbiased forecasts, whereas it is sometimes difficult to effectively remove bias from the predictions of complex hydrologic models. To overcome these limitations, we develop an approach to integrate a group of multivariate functions, the so-called copula functions, into BMA. Here we introduce a copula-embedded BMA (Cop-BMA) method that relaxes any assumption on the shape of conditional PDFs. Copula functions have a flexible structure and do not restrict the shape of posterior distributions. Furthermore, copulas are effective tools in removing bias from hydrologic forecasts. To compare the performance of BMA with Cop-BMA, they are applied to hydrologic forecasts from different rainfall-runoff and land-surface models. We consider the streamflow observation and simulations for 10 river basins provided by the Model Parameter Estimation Experiment (MOPEX) project. Results demonstrate that the predictive distributions are more accurate and reliable, less biased, and more confident with small uncertainty after Cop-BMA application. It is also shown that the postprocessed forecasts have better correlation with observation after Cop-BMA application.
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
Czech Academy of Sciences Publication Activity Database
Górecki, J.; Hofert, M.; Holeňa, Martin
2016-01-01
Roč. 46, č. 1 (2016), s. 21-59 ISSN 0925-9902 R&D Projects: GA ČR GA13-17187S Grant - others:Slezská univerzita v Opavě(CZ) SGS/21/2014 Institutional support: RVO:67985807 Keywords : Copula * Hierarchical archimedean copula * Copula estimation * Structure determination * Kendall’s tau * Bayesian classification Subject RIV: IN - Informatics, Computer Science Impact factor: 1.294, year: 2016
A Bayesian framework for simultaneously modeling neural and behavioral data.
Turner, Brandon M; Forstmann, Birte U; Wagenmakers, Eric-Jan; Brown, Scott D; Sederberg, Per B; Steyvers, Mark
2013-05-15
Scientists who study cognition infer underlying processes either by observing behavior (e.g., response times, percentage correct) or by observing neural activity (e.g., the BOLD response). These two types of observations have traditionally supported two separate lines of study. The first is led by cognitive modelers, who rely on behavior alone to support their computational theories. The second is led by cognitive neuroimagers, who rely on statistical models to link patterns of neural activity to experimental manipulations, often without any attempt to make a direct connection to an explicit computational theory. Here we present a flexible Bayesian framework for combining neural and cognitive models. Joining neuroimaging and computational modeling in a single hierarchical framework allows the neural data to influence the parameters of the cognitive model and allows behavioral data, even in the absence of neural data, to constrain the neural model. Critically, our Bayesian approach can reveal interactions between behavioral and neural parameters, and hence between neural activity and cognitive mechanisms. We demonstrate the utility of our approach with applications to simulated fMRI data with a recognition model and to diffusion-weighted imaging data with a response time model of perceptual choice. Copyright © 2013 Elsevier Inc. All rights reserved.
A Bayesian framework for simultaneously modeling neural and behavioral data✩
Turner, Brandon M.; Forstmann, Birte U.; Wagenmakers, Eric-Jan; Brown, Scott D.; Sederberg, Per B.; Steyvers, Mark
2013-01-01
Scientists who study cognition infer underlying processes either by observing behavior (e.g., response times, percentage correct) or by observing neural activity (e.g., the BOLD response). These two types of observations have traditionally supported two separate lines of study. The first is led by cognitive modelers, who rely on behavior alone to support their computational theories. The second is led by cognitive neuroimagers, who rely on statistical models to link patterns of neural activity to experimental manipulations, often without any attempt to make a direct connection to an explicit computational theory. Here we present a flexible Bayesian framework for combining neural and cognitive models. Joining neuroimaging and computational modeling in a single hierarchical framework allows the neural data to influence the parameters of the cognitive model and allows behavioral data, even in the absence of neural data, to constrain the neural model. Critically, our Bayesian approach can reveal interactions between behavioral and neural parameters, and hence between neural activity and cognitive mechanisms. We demonstrate the utility of our approach with applications to simulated fMRI data with a recognition model and to diffusion-weighted imaging data with a response time model of perceptual choice. PMID:23370060
Modelling crime linkage with Bayesian networks
de Zoete, J.; Sjerps, M.; Lagnado, D.; Fenton, N.
2015-01-01
When two or more crimes show specific similarities, such as a very distinct modus operandi, the probability that they were committed by the same offender becomes of interest. This probability depends on the degree of similarity and distinctiveness. We show how Bayesian networks can be used to model
Bayesian statistical approaches to evaluating cognitive models.
Annis, Jeffrey; Palmeri, Thomas J
2017-11-28
Cognitive models aim to explain complex human behavior in terms of hypothesized mechanisms of the mind. These mechanisms can be formalized in terms of mathematical structures containing parameters that are theoretically meaningful. For example, in the case of perceptual decision making, model parameters might correspond to theoretical constructs like response bias, evidence quality, response caution, and the like. Formal cognitive models go beyond verbal models in that cognitive mechanisms are instantiated in terms of mathematics and they go beyond statistical models in that cognitive model parameters are psychologically interpretable. We explore three key elements used to formally evaluate cognitive models: parameter estimation, model prediction, and model selection. We compare and contrast traditional approaches with Bayesian statistical approaches to performing each of these three elements. Traditional approaches rely on an array of seemingly ad hoc techniques, whereas Bayesian statistical approaches rely on a single, principled, internally consistent system. We illustrate the Bayesian statistical approach to evaluating cognitive models using a running example of the Linear Ballistic Accumulator model of decision making (Brown SD, Heathcote A. The simplest complete model of choice response time: linear ballistic accumulation. Cogn Psychol 2008, 57:153-178). This article is categorized under: Neuroscience > Computation Psychology > Reasoning and Decision Making Psychology > Theory and Methods. © 2017 Wiley Periodicals, Inc.
Bayesian Modelling of Functional Whole Brain Connectivity
DEFF Research Database (Denmark)
Røge, Rasmus
the prevalent strategy of standardizing of fMRI time series and model data using directional statistics or we model the variability in the signal across the brain and across multiple subjects. In either case, we use Bayesian nonparametric modeling to automatically learn from the fMRI data the number......This thesis deals with parcellation of whole-brain functional magnetic resonance imaging (fMRI) using Bayesian inference with mixture models tailored to the fMRI data. In the three included papers and manuscripts, we analyze two different approaches to modeling fMRI signal; either we accept...... of funcional units, i.e. parcels. We benchmark the proposed mixture models against state of the art methods of brain parcellation, both probabilistic and non-probabilistic. The time series of each voxel are most often standardized using z-scoring which projects the time series data onto a hypersphere...
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.
Tractography Segmentation Using a Hierarchical Dirichlet Processes Mixture Model
Wang, Xiaogang; Grimson, W. Eric L.; Westin, Carl-Fredrik
2010-01-01
In this paper, we propose a new nonparametric Bayesian framework to cluster white matter fiber tracts into bundles using a hierarchical Dirichlet processes mixture (HDPM) model. The number of clusters is automatically learnt from data with a Dirichlet process (DP) prior instead of being manually specified. After the models of bundles have been learnt from training data without supervision, they can be used as priors to cluster/classify fibers of new subjects. When clustering fibers of new subjects, new clusters can be created for structures not observed in the training data. Our approach does not require computing pairwise distances between fibers and can cluster a huge set of fibers across multiple subjects without subsampling. We present results on multiple data sets, the largest of which has more than 120, 000 fibers. PMID:19694256
Posterior Predictive Bayesian Phylogenetic Model Selection
Lewis, Paul O.; Xie, Wangang; Chen, Ming-Hui; Fan, Yu; Kuo, Lynn
2014-01-01
We present two distinctly different posterior predictive approaches to Bayesian phylogenetic model selection and illustrate these methods using examples from green algal protein-coding cpDNA sequences and flowering plant rDNA sequences. The Gelfand–Ghosh (GG) approach allows dissection of an overall measure of model fit into components due to posterior predictive variance (GGp) and goodness-of-fit (GGg), which distinguishes this method from the posterior predictive P-value approach. The conditional predictive ordinate (CPO) method provides a site-specific measure of model fit useful for exploratory analyses and can be combined over sites yielding the log pseudomarginal likelihood (LPML) which is useful as an overall measure of model fit. CPO provides a useful cross-validation approach that is computationally efficient, requiring only a sample from the posterior distribution (no additional simulation is required). Both GG and CPO add new perspectives to Bayesian phylogenetic model selection based on the predictive abilities of models and complement the perspective provided by the marginal likelihood (including Bayes Factor comparisons) based solely on the fit of competing models to observed data. [Bayesian; conditional predictive ordinate; CPO; L-measure; LPML; model selection; phylogenetics; posterior predictive.] PMID:24193892
Distributed Bayesian Networks for User Modeling
DEFF Research Database (Denmark)
Tedesco, Roberto; Dolog, Peter; Nejdl, Wolfgang
2006-01-01
The World Wide Web is a popular platform for providing eLearning applications to a wide spectrum of users. However – as users differ in their preferences, background, requirements, and goals – applications should provide personalization mechanisms. In the Web context, user models used...... of Web-based eLearning platforms. The scenario we are tackling assumes learners who use several systems over time, which are able to create partial Bayesian Networks for user models based on the local system context. In particular, we focus on how to merge these partial user models. Our merge mechanism...... efficiently combines distributed learner models without the need to exchange internal structure of local Bayesian networks, nor local evidence between the involved platforms....
Hierarchical models in the brain.
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Karl Friston
2008-11-01
Full Text Available This paper describes a general model that subsumes many parametric models for continuous data. The model comprises hidden layers of state-space or dynamic causal models, arranged so that the output of one provides input to another. The ensuing hierarchy furnishes a model for many types of data, of arbitrary complexity. Special cases range from the general linear model for static data to generalised convolution models, with system noise, for nonlinear time-series analysis. Crucially, all of these models can be inverted using exactly the same scheme, namely, dynamic expectation maximization. This means that a single model and optimisation scheme can be used to invert a wide range of models. We present the model and a brief review of its inversion to disclose the relationships among, apparently, diverse generative models of empirical data. We then show that this inversion can be formulated as a simple neural network and may provide a useful metaphor for inference and learning in the brain.
Bayesian modeling of the mass and density of asteroids
Dotson, Jessie L.; Mathias, Donovan
2017-10-01
Mass and density are two of the fundamental properties of any object. In the case of near earth asteroids, knowledge about the mass of an asteroid is essential for estimating the risk due to (potential) impact and planning possible mitigation options. The density of an asteroid can illuminate the structure of the asteroid. A low density can be indicative of a rubble pile structure whereas a higher density can imply a monolith and/or higher metal content. The damage resulting from an impact of an asteroid with Earth depends on its interior structure in addition to its total mass, and as a result, density is a key parameter to understanding the risk of asteroid impact. Unfortunately, measuring the mass and density of asteroids is challenging and often results in measurements with large uncertainties. In the absence of mass / density measurements for a specific object, understanding the range and distribution of likely values can facilitate probabilistic assessments of structure and impact risk. Hierarchical Bayesian models have recently been developed to investigate the mass - radius relationship of exoplanets (Wolfgang, Rogers & Ford 2016) and to probabilistically forecast the mass of bodies large enough to establish hydrostatic equilibrium over a range of 9 orders of magnitude in mass (from planemos to main sequence stars; Chen & Kipping 2017). Here, we extend this approach to investigate the mass and densities of asteroids. Several candidate Bayesian models are presented, and their performance is assessed relative to a synthetic asteroid population. In addition, a preliminary Bayesian model for probablistically forecasting masses and densities of asteroids is presented. The forecasting model is conditioned on existing asteroid data and includes observational errors, hyper-parameter uncertainties and intrinsic scatter.
A neural model of hierarchical reinforcement learning.
Rasmussen, Daniel; Voelker, Aaron; Eliasmith, Chris
2017-01-01
We develop a novel, biologically detailed neural model of reinforcement learning (RL) processes in the brain. This model incorporates a broad range of biological features that pose challenges to neural RL, such as temporally extended action sequences, continuous environments involving unknown time delays, and noisy/imprecise computations. Most significantly, we expand the model into the realm of hierarchical reinforcement learning (HRL), which divides the RL process into a hierarchy of actions at different levels of abstraction. Here we implement all the major components of HRL in a neural model that captures a variety of known anatomical and physiological properties of the brain. We demonstrate the performance of the model in a range of different environments, in order to emphasize the aim of understanding the brain's general reinforcement learning ability. These results show that the model compares well to previous modelling work and demonstrates improved performance as a result of its hierarchical ability. We also show that the model's behaviour is consistent with available data on human hierarchical RL, and generate several novel predictions.
Bayesian Recurrent Neural Network for Language Modeling.
Chien, Jen-Tzung; Ku, Yuan-Chu
2016-02-01
A language model (LM) is calculated as the probability of a word sequence that provides the solution to word prediction for a variety of information systems. A recurrent neural network (RNN) is powerful to learn the large-span dynamics of a word sequence in the continuous space. However, the training of the RNN-LM is an ill-posed problem because of too many parameters from a large dictionary size and a high-dimensional hidden layer. This paper presents a Bayesian approach to regularize the RNN-LM and apply it for continuous speech recognition. We aim to penalize the too complicated RNN-LM by compensating for the uncertainty of the estimated model parameters, which is represented by a Gaussian prior. The objective function in a Bayesian classification network is formed as the regularized cross-entropy error function. The regularized model is constructed not only by calculating the regularized parameters according to the maximum a posteriori criterion but also by estimating the Gaussian hyperparameter by maximizing the marginal likelihood. A rapid approximation to a Hessian matrix is developed to implement the Bayesian RNN-LM (BRNN-LM) by selecting a small set of salient outer-products. The proposed BRNN-LM achieves a sparser model than the RNN-LM. Experiments on different corpora show the robustness of system performance by applying the rapid BRNN-LM under different conditions.
AN INTEGER PROGRAMMING MODEL FOR HIERARCHICAL WORKFORCE
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BANU SUNGUR
2013-06-01
Full Text Available The model presented in this paper is based on the model developed by Billionnet for the hierarchical workforce problem. In Billionnet’s Model, while determining the workers’ weekly costs, weekly working hours of workers are not taken into consideration. In our model, the weekly costs per worker are reduced in proportion to the working hours per week. Our model is illustrated on the Billionnet’s Example. The models in question are compared and evaluated on the basis of the results obtained from the example problem. A reduction is achieved in the total cost by the proposed model.
Bayesian Inference of a Multivariate Regression Model
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Marick S. Sinay
2014-01-01
Full Text Available We explore Bayesian inference of a multivariate linear regression model with use of a flexible prior for the covariance structure. The commonly adopted Bayesian setup involves the conjugate prior, multivariate normal distribution for the regression coefficients and inverse Wishart specification for the covariance matrix. Here we depart from this approach and propose a novel Bayesian estimator for the covariance. A multivariate normal prior for the unique elements of the matrix logarithm of the covariance matrix is considered. Such structure allows for a richer class of prior distributions for the covariance, with respect to strength of beliefs in prior location hyperparameters, as well as the added ability, to model potential correlation amongst the covariance structure. The posterior moments of all relevant parameters of interest are calculated based upon numerical results via a Markov chain Monte Carlo procedure. The Metropolis-Hastings-within-Gibbs algorithm is invoked to account for the construction of a proposal density that closely matches the shape of the target posterior distribution. As an application of the proposed technique, we investigate a multiple regression based upon the 1980 High School and Beyond Survey.
Internet advertising effectiveness by using hierarchical model
Rahmani, Samaneh
2015-01-01
Abstract. Present paper has been developed with the title of internet advertising effectiveness by using hierarchical model. Presenting the question: Today Internet is an important channel in marketing and advertising. The reason for this could be the ability of the Internet to reduce costs and people’s access to online services[1]. Also advertisers can easily access a multitude of users and communicate with them at low cost [9]. On the other hand, compared to traditional advertising, interne...
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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
A hierarchical nest survival model integrating incomplete temporally varying covariates
Converse, Sarah J.; Royle, J. Andrew; Adler, Peter H.; Urbanek, Richard P.; Barzan, Jeb A.
2013-01-01
Nest success is a critical determinant of the dynamics of avian populations, and nest survival modeling has played a key role in advancing avian ecology and management. Beginning with the development of daily nest survival models, and proceeding through subsequent extensions, the capacity for modeling the effects of hypothesized factors on nest survival has expanded greatly. We extend nest survival models further by introducing an approach to deal with incompletely observed, temporally varying covariates using a hierarchical model. Hierarchical modeling offers a way to separate process and observational components of demographic models to obtain estimates of the parameters of primary interest, and to evaluate structural effects of ecological and management interest. We built a hierarchical model for daily nest survival to analyze nest data from reintroduced whooping cranes (Grus americana) in the Eastern Migratory Population. This reintroduction effort has been beset by poor reproduction, apparently due primarily to nest abandonment by breeding birds. We used the model to assess support for the hypothesis that nest abandonment is caused by harassment from biting insects. We obtained indices of blood-feeding insect populations based on the spatially interpolated counts of insects captured in carbon dioxide traps. However, insect trapping was not conducted daily, and so we had incomplete information on a temporally variable covariate of interest. We therefore supplemented our nest survival model with a parallel model for estimating the values of the missing insect covariates. We used Bayesian model selection to identify the best predictors of daily nest survival. Our results suggest that the black fly Simulium annulus may be negatively affecting nest survival of reintroduced whooping cranes, with decreasing nest survival as abundance of S. annulus increases. The modeling framework we have developed will be applied in the future to a larger data set to evaluate the
The traveling salesman problem: a hierarchical model.
Graham, S M; Joshi, A; Pizlo, Z
2000-10-01
Our review of prior literature on spatial information processing in perception, attention, and memory indicates that these cognitive functions involve similar mechanisms based on a hierarchical architecture. The present study extends the application of hierarchical models to the area of problem solving. First, we report results of an experiment in which human subjects were tested on a Euclidean traveling salesman problem (TSP) with 6 to 30 cities. The subject's solutions were either optimal or near-optimal in length and were produced in a time that was, on average, a linear function of the number of cities. Next, the performance of the subjects is compared with that of five representative artificial intelligence and operations research algorithms, that produce approximate solutions for Euclidean problems. None of these algorithms was found to be an adequate psychological model. Finally, we present a new algorithm for solving the TSP, which is based on a hierarchical pyramid architecture. The performance of this new algorithm is quite similar to the performance of the subjects.
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 10th 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. PMID:21912670
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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.
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.
Bayesian Discovery of Linear Acyclic Causal Models
Hoyer, Patrik O
2012-01-01
Methods for automated discovery of causal relationships from non-interventional data have received much attention recently. A widely used and well understood model family is given by linear acyclic causal models (recursive structural equation models). For Gaussian data both constraint-based methods (Spirtes et al., 1993; Pearl, 2000) (which output a single equivalence class) and Bayesian score-based methods (Geiger and Heckerman, 1994) (which assign relative scores to the equivalence classes) are available. On the contrary, all current methods able to utilize non-Gaussianity in the data (Shimizu et al., 2006; Hoyer et al., 2008) always return only a single graph or a single equivalence class, and so are fundamentally unable to express the degree of certainty attached to that output. In this paper we develop a Bayesian score-based approach able to take advantage of non-Gaussianity when estimating linear acyclic causal models, and we empirically demonstrate that, at least on very modest size networks, its accur...
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.
An accessible method for implementing hierarchical models with spatio-temporal abundance data.
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Beth E Ross
Full Text Available 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.
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,…
Miller, S L; Richardson, K; Edwards, P A
2014-11-15
Terrestrial sediments are a significant stressor on coastal ecosystems, with both suspended and deposited sediment having adverse effects on aquatic organisms. However, information on the effect of suspended sediments on fertilization success for urchin species is lacking. Using sediment levels similar to those encountered in situ, a controlled experiment was conducted to test whether suspended sediment affects fertilization success in the urchin Evechinus chloroticus. Analyses used generalized linear mixed models (GLMMs) and hierarchical Bayesian (HB) regression. Both approaches showed a significant decrease in fertilization success with increased suspended sediment levels. Uncertainties in estimates were narrower for HB models, suggesting that this approach has advantages over GLMMs for sparse data problems sometimes encountered in laboratory experiments. Given future global change scenarios, this work is important for predicting the effects of stressors such as sedimentation that may ultimately impact marine populations. Copyright © 2014 Elsevier Ltd. All rights reserved.
Bayesian inference with information content model check for Langevin equations
Krog, Jens; Lomholt, Michael A.
2017-12-01
The Bayesian data analysis framework has been proven to be a systematic and effective method of parameter inference and model selection for stochastic processes. In this work, we introduce an information content model check that may serve as a goodness-of-fit, like the χ2 procedure, to complement conventional Bayesian analysis. We demonstrate this extended Bayesian framework on a system of Langevin equations, where coordinate-dependent mobilities and measurement noise hinder the normal mean-squared displacement approach.
Bayesian extreme quantile regression for hidden Markov models
Koutsourelis, Antonios
2012-01-01
This thesis was submitted for the degree of Doctor of Philosophy and was awarded by Brunel University The main contribution of this thesis is the introduction of Bayesian quantile regression for hidden Markov models, especially when we have to deal with extreme quantile regression analysis, as there is a limited research to inference conditional quantiles for hidden Markov models, under a Bayesian approach. The first objective is to compare Bayesian extreme quantile regression and th...
Kinematic Structural Modelling in Bayesian Networks
Schaaf, Alexander; de la Varga, Miguel; Florian Wellmann, J.
2017-04-01
We commonly capture our knowledge about the spatial distribution of distinct geological lithologies in the form of 3-D geological models. Several methods exist to create these models, each with its own strengths and limitations. We present here an approach to combine the functionalities of two modeling approaches - implicit interpolation and kinematic modelling methods - into one framework, while explicitly considering parameter uncertainties and thus model uncertainty. In recent work, we proposed an approach to implement implicit modelling algorithms into Bayesian networks. This was done to address the issues of input data uncertainty and integration of geological information from varying sources in the form of geological likelihood functions. However, one general shortcoming of implicit methods is that they usually do not take any physical constraints into consideration, which can result in unrealistic model outcomes and artifacts. On the other hand, kinematic structural modelling intends to reconstruct the history of a geological system based on physically driven kinematic events. This type of modelling incorporates simplified, physical laws into the model, at the cost of a substantial increment of usable uncertain parameters. In the work presented here, we show an integration of these two different modelling methodologies, taking advantage of the strengths of both of them. First, we treat the two types of models separately, capturing the information contained in the kinematic models and their specific parameters in the form of likelihood functions, in order to use them in the implicit modelling scheme. We then go further and combine the two modelling approaches into one single Bayesian network. This enables the direct flow of information between the parameters of the kinematic modelling step and the implicit modelling step and links the exclusive input data and likelihoods of the two different modelling algorithms into one probabilistic inference framework. In
Spatially-dependent Bayesian model selection for disease mapping.
Carroll, Rachel; Lawson, Andrew B; Faes, Christel; Kirby, Russell S; Aregay, Mehreteab; Watjou, Kevin
2018-01-01
In disease mapping where predictor effects are to be modeled, it is often the case that sets of predictors are fixed, and the aim is to choose between fixed model sets. Model selection methods, both Bayesian model selection and Bayesian model averaging, are approaches within the Bayesian paradigm for achieving this aim. In the spatial context, model selection could have a spatial component in the sense that some models may be more appropriate for certain areas of a study region than others. In this work, we examine the use of spatially referenced Bayesian model averaging and Bayesian model selection via a large-scale simulation study accompanied by a small-scale case study. Our results suggest that BMS performs well when a strong regression signature is found.
Improving randomness characterization through Bayesian model selection.
Díaz Hernández Rojas, Rafael; Solís, Aldo; Angulo Martínez, Alí M; U'Ren, Alfred B; Hirsch, Jorge G; Marsili, Matteo; Pérez Castillo, Isaac
2017-06-08
Random number generation plays an essential role in technology with important applications in areas ranging from cryptography to Monte Carlo methods, and other probabilistic algorithms. All such applications require high-quality sources of random numbers, yet effective methods for assessing whether a source produce truly random sequences are still missing. Current methods either do not rely on a formal description of randomness (NIST test suite) on the one hand, or are inapplicable in principle (the characterization derived from the Algorithmic Theory of Information), on the other, for they require testing all the possible computer programs that could produce the sequence to be analysed. Here we present a rigorous method that overcomes these problems based on Bayesian model selection. We derive analytic expressions for a model's likelihood which is then used to compute its posterior distribution. Our method proves to be more rigorous than NIST's suite and Borel-Normality criterion and its implementation is straightforward. We applied our method to an experimental device based on the process of spontaneous parametric downconversion to confirm it behaves as a genuine quantum random number generator. As our approach relies on Bayesian inference our scheme transcends individual sequence analysis, leading to a characterization of the source itself.
Modelling complex networks by random hierarchical graphs
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M.Wróbel
2008-06-01
Full Text Available Numerous complex networks contain special patterns, called network motifs. These are specific subgraphs, which occur oftener than in randomized networks of Erdős-Rényi type. We choose one of them, the triangle, and build a family of random hierarchical graphs, being Sierpiński gasket-based graphs with random "decorations". We calculate the important characteristics of these graphs - average degree, average shortest path length, small-world graph family characteristics. They depend on probability of decorations. We analyze the Ising model on our graphs and describe its critical properties using a renormalization-group technique.
MERGING DIGITAL SURFACE MODELS IMPLEMENTING BAYESIAN APPROACHES
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H. Sadeq
2016-06-01
Full Text Available In this research different DSMs from different sources have been merged. The merging is based on a probabilistic model using a Bayesian Approach. The implemented data have been sourced from very high resolution satellite imagery sensors (e.g. WorldView-1 and Pleiades. It is deemed preferable to use a Bayesian Approach when the data obtained from the sensors are limited and it is difficult to obtain many measurements or it would be very costly, thus the problem of the lack of data can be solved by introducing a priori estimations of data. To infer the prior data, it is assumed that the roofs of the buildings are specified as smooth, and for that purpose local entropy has been implemented. In addition to the a priori estimations, GNSS RTK measurements have been collected in the field which are used as check points to assess the quality of the DSMs and to validate the merging result. The model has been applied in the West-End of Glasgow containing different kinds of buildings, such as flat roofed and hipped roofed buildings. Both quantitative and qualitative methods have been employed to validate the merged DSM. The validation results have shown that the model was successfully able to improve the quality of the DSMs and improving some characteristics such as the roof surfaces, which consequently led to better representations. In addition to that, the developed model has been compared with the well established Maximum Likelihood model and showed similar quantitative statistical results and better qualitative results. Although the proposed model has been applied on DSMs that were derived from satellite imagery, it can be applied to any other sourced DSMs.
Regulator Loss Functions and Hierarchical Modeling for Safety Decision Making.
Hatfield, Laura A; Baugh, Christine M; Azzone, Vanessa; Normand, Sharon-Lise T
2017-07-01
Regulators must act to protect the public when evidence indicates safety problems with medical devices. This requires complex tradeoffs among risks and benefits, which conventional safety surveillance methods do not incorporate. To combine explicit regulator loss functions with statistical evidence on medical device safety signals to improve decision making. In the Hospital Cost and Utilization Project National Inpatient Sample, we select pediatric inpatient admissions and identify adverse medical device events (AMDEs). We fit hierarchical Bayesian models to the annual hospital-level AMDE rates, accounting for patient and hospital characteristics. These models produce expected AMDE rates (a safety target), against which we compare the observed rates in a test year to compute a safety signal. We specify a set of loss functions that quantify the costs and benefits of each action as a function of the safety signal. We integrate the loss functions over the posterior distribution of the safety signal to obtain the posterior (Bayes) risk; the preferred action has the smallest Bayes risk. Using simulation and an analysis of AMDE data, we compare our minimum-risk decisions to a conventional Z score approach for classifying safety signals. The 2 rules produced different actions for nearly half of hospitals (45%). In the simulation, decisions that minimize Bayes risk outperform Z score-based decisions, even when the loss functions or hierarchical models are misspecified. Our method is sensitive to the choice of loss functions; eliciting quantitative inputs to the loss functions from regulators is challenging. A decision-theoretic approach to acting on safety signals is potentially promising but requires careful specification of loss functions in consultation with subject matter experts.
Bayesian generalized linear mixed modeling of Tuberculosis using informative priors
Ojo, Oluwatobi Blessing; Lougue, Siaka; Woldegerima, Woldegebriel Assefa
2017-01-01
TB is rated as one of the world's deadliest diseases and South Africa ranks 9th out of the 22 countries with hardest hit of TB. Although many pieces of research have been carried out on this subject, this paper steps further by inculcating past knowledge into the model, using Bayesian approach with informative prior. Bayesian statistics approach is getting popular in data analyses. But, most applications of Bayesian inference technique are limited to situations of non-informative prior, where...
Bayesian spatio-temporal modeling of particulate matter concentrations in Peninsular Malaysia
Manga, Edna; Awang, Norhashidah
2016-06-01
This article presents an application of a Bayesian spatio-temporal Gaussian process (GP) model on particulate matter concentrations from Peninsular Malaysia. We analyze daily PM10 concentration levels from 35 monitoring sites in June and July 2011. The spatiotemporal model set in a Bayesian hierarchical framework allows for inclusion of informative covariates, meteorological variables and spatiotemporal interactions. Posterior density estimates of the model parameters are obtained by Markov chain Monte Carlo methods. Preliminary data analysis indicate information on PM10 levels at sites classified as industrial locations could explain part of the space time variations. We include the site-type indicator in our modeling efforts. Results of the parameter estimates for the fitted GP model show significant spatio-temporal structure and positive effect of the location-type explanatory variable. We also compute some validation criteria for the out of sample sites that show the adequacy of the model for predicting PM10 at unmonitored sites.
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.
Modelling crime linkage with Bayesian networks.
de Zoete, Jacob; Sjerps, Marjan; Lagnado, David; Fenton, Norman
2015-05-01
When two or more crimes show specific similarities, such as a very distinct modus operandi, the probability that they were committed by the same offender becomes of interest. This probability depends on the degree of similarity and distinctiveness. We show how Bayesian networks can be used to model different evidential structures that can occur when linking crimes, and how they assist in understanding the complex underlying dependencies. That is, how evidence that is obtained in one case can be used in another and vice versa. The flip side of this is that the intuitive decision to "unlink" a case in which exculpatory evidence is obtained leads to serious overestimation of the strength of the remaining cases. Copyright © 2014 Forensic Science Society. Published by Elsevier Ireland Ltd. All rights reserved.
Illustrating bayesian evaluation of informative hypotheses for regression models.
Kluytmans, A.; Schoot, R. van de; Mulder, J.; Hoijtink, H.
2012-01-01
In the present article we illustrate a Bayesian method of evaluating informative hypotheses for regression models. Our main aim is to make this method accessible to psychological researchers without a mathematical or Bayesian background. The use of informative hypotheses is illustrated using two
Bayesian analysis. II. Signal detection and model selection
Bretthorst, G. Larry
In the preceding. paper, Bayesian analysis was applied to the parameter estimation problem, given quadrature NMR data. Here Bayesian analysis is extended to the problem of selecting the model which is most probable in view of the data and all the prior information. In addition to the analytic calculation, two examples are given. The first example demonstrates how to use Bayesian probability theory to detect small signals in noise. The second example uses Bayesian probability theory to compute the probability of the number of decaying exponentials in simulated T1 data. The Bayesian answer to this question is essentially a microcosm of the scientific method and a quantitative statement of Ockham's razor: theorize about possible models, compare these to experiment, and select the simplest model that "best" fits the data.
Entrepreneurial intention modeling using hierarchical multiple regression
Directory of Open Access Journals (Sweden)
Marina Jeger
2014-12-01
Full Text Available The goal of this study is to identify the contribution of effectuation dimensions to the predictive power of the entrepreneurial intention model over and above that which can be accounted for by other predictors selected and confirmed in previous studies. As is often the case in social and behavioral studies, some variables are likely to be highly correlated with each other. Therefore, the relative amount of variance in the criterion variable explained by each of the predictors depends on several factors such as the order of variable entry and sample specifics. The results show the modest predictive power of two dimensions of effectuation prior to the introduction of the theory of planned behavior elements. The article highlights the main advantages of applying hierarchical regression in social sciences as well as in the specific context of entrepreneurial intention formation, and addresses some of the potential pitfalls that this type of analysis entails.
Royle, J. Andrew; Converse, Sarah J.
2014-01-01
Capture–recapture studies are often conducted on populations that are stratified by space, time or other factors. In this paper, we develop a Bayesian spatial capture–recapture (SCR) modelling framework for stratified populations – when sampling occurs within multiple distinct spatial and temporal strata.We describe a hierarchical model that integrates distinct models for both the spatial encounter history data from capture–recapture sampling, and also for modelling variation in density among strata. We use an implementation of data augmentation to parameterize the model in terms of a latent categorical stratum or group membership variable, which provides a convenient implementation in popular BUGS software packages.We provide an example application to an experimental study involving small-mammal sampling on multiple trapping grids over multiple years, where the main interest is in modelling a treatment effect on population density among the trapping grids.Many capture–recapture studies involve some aspect of spatial or temporal replication that requires some attention to modelling variation among groups or strata. We propose a hierarchical model that allows explicit modelling of group or strata effects. Because the model is formulated for individual encounter histories and is easily implemented in the BUGS language and other free software, it also provides a general framework for modelling individual effects, such as are present in SCR models.
DEFF Research Database (Denmark)
Mantzouni, Irene; Sørensen, Helle; O'Hara, Robert B.
2010-01-01
Understanding how temperature affects cod (Gadus morhua) ecology is important for forecasting how populations will develop as climate changes in future. The effects of spawning-season temperature and habitat size on cod recruitment dynamics have been investigated across the North Atlantic. Ricker...... 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...
Hierarchical Data Structures, Institutional Research, and Multilevel Modeling
O'Connell, Ann A.; Reed, Sandra J.
2012-01-01
Multilevel modeling (MLM), also referred to as hierarchical linear modeling (HLM) or mixed models, provides a powerful analytical framework through which to study colleges and universities and their impact on students. Due to the natural hierarchical structure of data obtained from students or faculty in colleges and universities, MLM offers many…
Gene function classification using Bayesian models with hierarchy-based priors
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Neal Radford M
2006-10-01
Full Text Available Abstract Background We investigate whether annotation of gene function can be improved using a classification scheme that is aware that functional classes are organized in a hierarchy. The classifiers look at phylogenic descriptors, sequence based attributes, and predicted secondary structure. We discuss three Bayesian models and compare their performance in terms of predictive accuracy. These models are the ordinary multinomial logit (MNL model, a hierarchical model based on a set of nested MNL models, and an MNL model with a prior that introduces correlations between the parameters for classes that are nearby in the hierarchy. We also provide a new scheme for combining different sources of information. We use these models to predict the functional class of Open Reading Frames (ORFs from the E. coli genome. Results The results from all three models show substantial improvement over previous methods, which were based on the C5 decision tree algorithm. The MNL model using a prior based on the hierarchy outperforms both the non-hierarchical MNL model and the nested MNL model. In contrast to previous attempts at combining the three sources of information in this dataset, our new approach to combining data sources produces a higher accuracy rate than applying our models to each data source alone. Conclusion Together, these results show that gene function can be predicted with higher accuracy than previously achieved, using Bayesian models that incorporate suitable prior information.
Stochastic model updating utilizing Bayesian approach and Gaussian process model
Wan, Hua-Ping; Ren, Wei-Xin
2016-03-01
Stochastic model updating (SMU) has been increasingly applied in quantifying structural parameter uncertainty from responses variability. SMU for parameter uncertainty quantification refers to the problem of inverse uncertainty quantification (IUQ), which is a nontrivial task. Inverse problem solved with optimization usually brings about the issues of gradient computation, ill-conditionedness, and non-uniqueness. Moreover, the uncertainty present in response makes the inverse problem more complicated. In this study, Bayesian approach is adopted in SMU for parameter uncertainty quantification. The prominent strength of Bayesian approach for IUQ problem is that it solves IUQ problem in a straightforward manner, which enables it to avoid the previous issues. However, when applied to engineering structures that are modeled with a high-resolution finite element model (FEM), Bayesian approach is still computationally expensive since the commonly used Markov chain Monte Carlo (MCMC) method for Bayesian inference requires a large number of model runs to guarantee the convergence. Herein we reduce computational cost in two aspects. On the one hand, the fast-running Gaussian process model (GPM) is utilized to approximate the time-consuming high-resolution FEM. On the other hand, the advanced MCMC method using delayed rejection adaptive Metropolis (DRAM) algorithm that incorporates local adaptive strategy with global adaptive strategy is employed for Bayesian inference. In addition, we propose the use of the powerful variance-based global sensitivity analysis (GSA) in parameter selection to exclude non-influential parameters from calibration parameters, which yields a reduced-order model and thus further alleviates the computational burden. A simulated aluminum plate and a real-world complex cable-stayed pedestrian bridge are presented to illustrate the proposed framework and verify its feasibility.
A guide to Bayesian model selection for ecologists
Hooten, Mevin B.; Hobbs, N.T.
2015-01-01
The steady upward trend in the use of model selection and Bayesian methods in ecological research has made it clear that both approaches to inference are important for modern analysis of models and data. However, in teaching Bayesian methods and in working with our research colleagues, we have noticed a general dissatisfaction with the available literature on Bayesian model selection and multimodel inference. Students and researchers new to Bayesian methods quickly find that the published advice on model selection is often preferential in its treatment of options for analysis, frequently advocating one particular method above others. The recent appearance of many articles and textbooks on Bayesian modeling has provided welcome background on relevant approaches to model selection in the Bayesian framework, but most of these are either very narrowly focused in scope or inaccessible to ecologists. Moreover, the methodological details of Bayesian model selection approaches are spread thinly throughout the literature, appearing in journals from many different fields. Our aim with this guide is to condense the large body of literature on Bayesian approaches to model selection and multimodel inference and present it specifically for quantitative ecologists as neutrally as possible. We also bring to light a few important and fundamental concepts relating directly to model selection that seem to have gone unnoticed in the ecological literature. Throughout, we provide only a minimal discussion of philosophy, preferring instead to examine the breadth of approaches as well as their practical advantages and disadvantages. This guide serves as a reference for ecologists using Bayesian methods, so that they can better understand their options and can make an informed choice that is best aligned with their goals for inference.
Nonlinear hierarchical modeling of experimental infection data.
Singleton, Michael D; Breheny, Patrick J
2016-08-01
In this paper, we propose a nonlinear hierarchical model (NLHM) for analyzing longitudinal experimental infection (EI) data. The NLHM offers several improvements over commonly used alternatives such as repeated measures analysis of variance (RM-ANOVA) and the linear mixed model (LMM). It enables comparison of relevant biological properties of the course of infection including peak intensity, duration and time to peak, rather than simply comparing mean responses at each observation time. We illustrate the practical benefits of this model and the insights it yields using data from experimental infection studies on equine arteritis virus. Finally, we demonstrate via simulation studies that the NLHM substantially reduces bias and improves the power to detect differences in relevant features of the infection response between two populations. For example, to detect a 20% difference in response duration between two groups (n=15) in which the peak time and peak intensity were identical, the RM-ANOVA test had a power of just 11%, and LMM a power of just 12%. By comparison, the nonlinear model we propose had a power of 58% in the same scenario, while controlling the Type I error rate better than the other two methods. Copyright © 2016 Elsevier B.V. All rights reserved.
Testing Adaptive Toolbox Models: A Bayesian Hierarchical Approach
Scheibehenne, Benjamin; Rieskamp, Jorg; Wagenmakers, Eric-Jan
2013-01-01
Many theories of human cognition postulate that people are equipped with a repertoire of strategies to solve the tasks they face. This theoretical framework of a cognitive toolbox provides a plausible account of intra- and interindividual differences in human behavior. Unfortunately, it is often unclear how to rigorously test the toolbox…
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...
Cassese, Alberto; Guindani, Michele; Antczak, Philipp; Falciani, Francesco; Vannucci, Marina
2015-01-01
In this paper we propose a Bayesian hierarchical model for the identification of differentially expressed genes in Daphnia Magna organisms exposed to chemical compounds, specifically munition pollutants in water. The model we propose constitutes one of the very first attempts at a rigorous modeling of the biological effects of water purification. We have data acquired from a purification system that comprises four consecutive purification stages, which we refer to as “ponds”, of progressively...
Covariance Kernels from Bayesian Generative Models
Seeger, Matthias
2002-01-01
We propose the framework of mutual information kernels for learning covariance kernels, as used in Support Vector machines and Gaussian process classifiers, from unlabeled task data using Bayesian techniques. We describe an implementation of this framework which uses variational Bayesian mixtures of factor analyzers in order to attack classification problems in high-dimensional spaces where labeled data is sparse, but unlabeled data is abundant.
Semiparametric Bayesian Estimation of Random Coefficients Discrete Choice Models
Tchumtchoua, Sylvie; Dey, Dipak
2007-01-01
Heterogeneity in choice models is typically assumed to have a normal distribution in both Bayesian and classical setups. In this paper, we propose a semiparametric Bayesian framework for the analysis of random coefficients discrete choice models that can be applied to both individual as well as aggregate data. Heterogeneity is modeled using a Dirichlet process prior which varies with consumers characteristics through covariates. We develop a Markov chain Monte Carlo algorithm for fitting such...
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.
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 hierarchical stochastic model for bistable perception.
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Stefan Albert
2017-11-01
Full Text Available Viewing of ambiguous stimuli can lead to bistable perception alternating between the possible percepts. During continuous presentation of ambiguous stimuli, percept changes occur as single events, whereas during intermittent presentation of ambiguous stimuli, percept changes occur at more or less regular intervals either as single events or bursts. Response patterns can be highly variable and have been reported to show systematic differences between patients with schizophrenia and healthy controls. Existing models of bistable perception often use detailed assumptions and large parameter sets which make parameter estimation challenging. Here we propose a parsimonious stochastic model that provides a link between empirical data analysis of the observed response patterns and detailed models of underlying neuronal processes. Firstly, we use a Hidden Markov Model (HMM for the times between percept changes, which assumes one single state in continuous presentation and a stable and an unstable state in intermittent presentation. The HMM captures the observed differences between patients with schizophrenia and healthy controls, but remains descriptive. Therefore, we secondly propose a hierarchical Brownian model (HBM, which produces similar response patterns but also provides a relation to potential underlying mechanisms. The main idea is that neuronal activity is described as an activity difference between two competing neuronal populations reflected in Brownian motions with drift. This differential activity generates switching between the two conflicting percepts and between stable and unstable states with similar mechanisms on different neuronal levels. With only a small number of parameters, the HBM can be fitted closely to a high variety of response patterns and captures group differences between healthy controls and patients with schizophrenia. At the same time, it provides a link to mechanistic models of bistable perception, linking the group
Robust Medical Test Evaluation Using Flexible Bayesian Semiparametric Regression Models
Directory of Open Access Journals (Sweden)
Adam J. Branscum
2013-01-01
Full Text Available The application of Bayesian methods is increasing in modern epidemiology. Although parametric Bayesian analysis has penetrated the population health sciences, flexible nonparametric Bayesian methods have received less attention. A goal in nonparametric Bayesian analysis is to estimate unknown functions (e.g., density or distribution functions rather than scalar parameters (e.g., means or proportions. For instance, ROC curves are obtained from the distribution functions corresponding to continuous biomarker data taken from healthy and diseased populations. Standard parametric approaches to Bayesian analysis involve distributions with a small number of parameters, where the prior specification is relatively straight forward. In the nonparametric Bayesian case, the prior is placed on an infinite dimensional space of all distributions, which requires special methods. A popular approach to nonparametric Bayesian analysis that involves Polya tree prior distributions is described. We provide example code to illustrate how models that contain Polya tree priors can be fit using SAS software. The methods are used to evaluate the covariate-specific accuracy of the biomarker, soluble epidermal growth factor receptor, for discerning lung cancer cases from controls using a flexible ROC regression modeling framework. The application highlights the usefulness of flexible models over a standard parametric method for estimating ROC curves.
Modelling modal gating of ion channels with hierarchical Markov models.
Siekmann, Ivo; Fackrell, Mark; Crampin, Edmund J; Taylor, Peter
2016-08-01
Many ion channels spontaneously switch between different levels of activity. Although this behaviour known as modal gating has been observed for a long time it is currently not well understood. Despite the fact that appropriately representing activity changes is essential for accurately capturing time course data from ion channels, systematic approaches for modelling modal gating are currently not available. In this paper, we develop a modular approach for building such a model in an iterative process. First, stochastic switching between modes and stochastic opening and closing within modes are represented in separate aggregated Markov models. Second, the continuous-time hierarchical Markov model, a new modelling framework proposed here, then enables us to combine these components so that in the integrated model both mode switching as well as the kinetics within modes are appropriately represented. A mathematical analysis reveals that the behaviour of the hierarchical Markov model naturally depends on the properties of its components. We also demonstrate how a hierarchical Markov model can be parametrized using experimental data and show that it provides a better representation than a previous model of the same dataset. Because evidence is increasing that modal gating reflects underlying molecular properties of the channel protein, it is likely that biophysical processes are better captured by our new approach than in earlier models.
Classifying hospitals as mortality outliers: logistic versus hierarchical logistic models.
Alexandrescu, Roxana; Bottle, Alex; Jarman, Brian; Aylin, Paul
2014-05-01
The use of hierarchical logistic regression for provider profiling has been recommended due to the clustering of patients within hospitals, but has some associated difficulties. We assess changes in hospital outlier status based on standard logistic versus hierarchical logistic modelling of mortality. The study population consisted of all patients admitted to acute, non-specialist hospitals in England between 2007 and 2011 with a primary diagnosis of acute myocardial infarction, acute cerebrovascular disease or fracture of neck of femur or a primary procedure of coronary artery bypass graft or repair of abdominal aortic aneurysm. We compared standardised mortality ratios (SMRs) from non-hierarchical models with SMRs from hierarchical models, without and with shrinkage estimates of the predicted probabilities (Model 1 and Model 2). The SMRs from standard logistic and hierarchical models were highly statistically significantly correlated (r > 0.91, p = 0.01). More outliers were recorded in the standard logistic regression than hierarchical modelling only when using shrinkage estimates (Model 2): 21 hospitals (out of a cumulative number of 565 pairs of hospitals under study) changed from a low outlier and 8 hospitals changed from a high outlier based on the logistic regression to a not-an-outlier based on shrinkage estimates. Both standard logistic and hierarchical modelling have identified nearly the same hospitals as mortality outliers. The choice of methodological approach should, however, also consider whether the modelling aim is judgment or improvement, as shrinkage may be more appropriate for the former than the latter.
Non-perturbative Methods For Hierarchical Models
Oktay, M B
2001-01-01
The goal of this thesis is to provide a practical method to calculate, in scalar field theory, accurate numerical values of the renormalized quantities which could be used to test any kind of approximate calculation. We use finite truncations of the Fourier transform of the recursion formula for Dyson's hierarchical model in the symmetric and broken phases to perform high precision calculations of the Green's functions at zero momentum. We use the well-known correspondence between statistical mechanics and field theory in which the large cut-off limit is obtained by letting β reach a critical value βc. We show that the round-off errors on the magnetic susceptibility grow like (βc − β) −1 near criticality. We show that the systematic errors (finite truncation and volume) can be controlled with an exponential precision and reduced to a level lower than numerical errors. We probe the numerical errors made in Renormalization Group (RG) calculations by varyin...
Higher-Order Item Response Models for Hierarchical Latent Traits
Huang, Hung-Yu; Wang, Wen-Chung; Chen, Po-Hsi; Su, Chi-Ming
2013-01-01
Many latent traits in the human sciences have a hierarchical structure. This study aimed to develop a new class of higher order item response theory models for hierarchical latent traits that are flexible in accommodating both dichotomous and polytomous items, to estimate both item and person parameters jointly, to allow users to specify…
Data analysis using regression and multilevel/hierarchical models
National Research Council Canada - National Science Library
Gelman, Andrew; Hill, Jennifer
2007-01-01
"Data Analysis Using Regression and Multilevel/Hierarchical Models is a comprehensive manual for the applied researcher who wants to perform data analysis using linear and nonlinear regression and multilevel models...
Anders, R; Oravecz, Z; Alario, F-X
2017-07-11
Cognitive process models are fit to observed data to infer how experimental manipulations modify the assumed underlying cognitive process. They are alternatives to descriptive models, which only capture differences on the observed data level, and do not make assumptions about the underlying cognitive process. Process models may require more observations than descriptive models however, and as a consequence, usually fewer conditions can be simultaneously modeled with them. Unfortunately, it is known that the predictive validity of a model may be compromised when fewer experimental conditions are jointly accounted for (e.g., overestimation of predictor effects, or their incorrect assignment). We develop a hierarchical and covaried multiple regression approach to address this problem. Specifically, we show how to map the recurrences of all conditions, participants, items, and/or traits across experimental design cells to the process model parameters. This systematic pooling of information can facilitate parameter estimation. The proposed approach is particularly relevant for multi-factor experimental designs, and for mixture models that parameterize per cell to assess predictor effects. This hierarchical framework provides the capacity to model more conditions jointly to improve parameter recovery at low observation numbers (e.g., using only 1/6 of trials, recovering as well as standard hierarchical Bayesian methods), and to directly model predictor and covariate effects on the process parameters, without the need for post hoc analyses (e.g., ANOVA). An example application to real data is also provided.
Hierarchical microcrack model for materials exemplified at enamel.
Özcoban, H; Yilmaz, E D; Schneider, G A
2018-01-01
This article investigates the mechanical properties of a material with hierarchically arranged microcracks. Hierarchically structured biomaterials such as enamel exhibit superior mechanical properties as being stiff and damage tolerant at the same time. The common mechanical explanation for this behavior is based on the hierarchically structured arrangement of hard minerals and soft organics and their cooperative deformation mechanisms. In situ mechanical experiments with mm-sized bovine enamel bending bars an scanning electron microscope reveal that enamel is able to withstand mechanical loading even if it contains microcracks on different lengths scales. To clarify this issue an analytical hierarchical microcrack model of non-interacting cracks is presented. The model predicts a decrease of the elastic modulus and the fracture strength with increasing levels of hierarchy. The fracture strain on the other hand may decrease or increase with the number of hierarchical levels, depending on the microcrack density. This simple hierarchical microcrack model is able to explain already published experiments with focused ion beam prepared μm-sized enamel cantilevers on different hierarchical levels. In addition it is shown that microcracking during loading in hierarchical materials may lead to substantial pseudoplastic behavior. Copyright © 2017 The Academy of Dental Materials. Published by Elsevier Ltd. All rights reserved.
Inferring the Growth of Massive Galaxies Using Bayesian Spectral Synthesis Modeling
Stillman, Coley Michael; Poremba, Megan R.; Moustakas, John
2018-01-01
The most massive galaxies in the universe are typically found at the centers of massive galaxy clusters. Studying these galaxies can provide valuable insight into the hierarchical growth of massive dark matter halos. One of the key challenges of measuring the stellar mass growth of massive galaxies is converting the measured light profiles into stellar mass. We use Prospector, a state-of-the-art Bayesian spectral synthesis modeling code, to infer the total stellar masses of a pilot sample of massive central galaxies selected from the Sloan Digital Sky Survey. We compare our stellar mass estimates to previous measurements, and present some of the quantitative diagnostics provided by Prospector.
Bayesian model evidence as a model evaluation metric
Guthke, Anneli; Höge, Marvin; Nowak, Wolfgang
2017-04-01
When building environmental systems models, we are typically confronted with the questions of how to choose an appropriate model (i.e., which processes to include or neglect) and how to measure its quality. Various metrics have been proposed that shall guide the modeller towards a most robust and realistic representation of the system under study. Criteria for evaluation often address aspects of accuracy (absence of bias) or of precision (absence of unnecessary variance) and need to be combined in a meaningful way in order to address the inherent bias-variance dilemma. We suggest using Bayesian model evidence (BME) as a model evaluation metric that implicitly performs a tradeoff between bias and variance. BME is typically associated with model weights in the context of Bayesian model averaging (BMA). However, it can also be seen as a model evaluation metric in a single-model context or in model comparison. It combines a measure for goodness of fit with a penalty for unjustifiable complexity. Unjustifiable refers to the fact that the appropriate level of model complexity is limited by the amount of information available for calibration. Derived in a Bayesian context, BME naturally accounts for measurement errors in the calibration data as well as for input and parameter uncertainty. BME is therefore perfectly suitable to assess model quality under uncertainty. We will explain in detail and with schematic illustrations what BME measures, i.e. how complexity is defined in the Bayesian setting and how this complexity is balanced with goodness of fit. We will further discuss how BME compares to other model evaluation metrics that address accuracy and precision such as the predictive logscore or other model selection criteria such as the AIC, BIC or KIC. Although computationally more expensive than other metrics or criteria, BME represents an appealing alternative because it provides a global measure of model quality. Even if not applicable to each and every case, we aim
Inventory model using bayesian dynamic linear model for demand forecasting
Directory of Open Access Journals (Sweden)
Marisol Valencia-Cárdenas
2014-12-01
Full Text Available An important factor of manufacturing process is the inventory management of terminated product. Constantly, industry is looking for better alternatives to establish an adequate plan of production and stored quantities, with optimal cost, getting quantities in a time horizon, which permits to define resources and logistics with anticipation, needed to distribute products on time. Total absence of historical data, required by many statistical models to forecast, demands the search for other kind of accurate techniques. This work presents an alternative that not only permits to forecast, in an adjusted way, but also, to provide optimal quantities to produce and store with an optimal cost, using Bayesian statistics. The proposal is illustrated with real data. Palabras clave: estadística bayesiana, optimización, modelo de inventarios, modelo lineal dinámico bayesiano. Keywords: Bayesian statistics, opti
CARBayes: An R Package for Bayesian Spatial Modeling with Conditional Autoregressive Priors
Directory of Open Access Journals (Sweden)
Duncan Lee
2013-11-01
Full Text Available Conditional autoregressive models are commonly used to represent spatial autocorrelation in data relating to a set of non-overlapping areal units, which arise in a wide variety of applications including agriculture, education, epidemiology and image analysis. Such models are typically specified in a hierarchical Bayesian framework, with inference based on Markov chain Monte Carlo (MCMC simulation. The most widely used software to fit such models is WinBUGS or OpenBUGS, but in this paper we introduce the R package CARBayes. The main advantage of CARBayes compared with the BUGS software is its ease of use, because: (1 the spatial adjacency information is easy to specify as a binary neighbourhood matrix; and (2 given the neighbourhood matrix the models can be implemented by a single function call in R. This paper outlines the general class of Bayesian hierarchical models that can be implemented in the CARBayes software, describes their implementation via MCMC simulation techniques, and illustrates their use with two worked examples in the fields of house price analysis and disease mapping.
Choi, Kyuwan
2014-06-01
In this study, a real-time cortical activity monitoring system was constructed, which could estimate cortical activities every 125 milliseconds over 2,240 vertexes from 64 channel electroencephalography signals through the Hierarchical Bayesian estimation that uses functional magnetic resonance imaging data as its prior information. Recently, functional magnetic resonance imaging has mostly been used in the neurofeedback field because it allows for high spatial resolution. However, in functional magnetic resonance imaging, the time for the neurofeedback information to reach the patient is delayed several seconds because of its poor temporal resolution. Therefore, a number of problems need to be solved to effectively implement feedback training paradigms in patients. To address this issue, this study used a new cortical activity monitoring system that improved both spatial and temporal resolution by using both functional magnetic resonance imaging data and electroencephalography signals in conjunction with one another. This system is advantageous as it can improve applications in the fields of real-time diagnosis, neurofeedback, and the brain-machine interface.
Directory of Open Access Journals (Sweden)
Ali Reza Soltanian
2016-08-01
Full Text Available Background Adolescence is one of the most important periods in the course of human evolution and the prevalence of mental disorders among adolescence in different regions of Iran, especially in southern Iran. Objectives This study was conducted to determine the prevalence of mental disorders among high school students in Bushehr province, south of Iran. Methods In this cross-sectional study, 286 high school students were recruited by a multi-stage random sampling in Bushehr province in 2015. A general health questionnaire (GHQ-28 was used to assess mental disorders. The small area method, under the hierarchical Bayesian approach, was used to determine the prevalence of mental disorders and data analysis. Results From 286 questionnaires only 182 were completely filed and evaluated (the response rate was 70.5%. Of the students, 58.79% and 41.21% were male and female, respectively. Of all students, the prevalence of mental disorders in Bushehr, Dayyer, Deylam, Kangan, Dashtestan, Tangestan, Genaveh, and Dashty were 0.48, 0.42, 0.45, 0.52, 0.41, 0.47, 0.42, and 0.43, respectively. Conclusions Based on this study, the prevalence of mental disorders among adolescents was increasing in Bushehr Province counties. The lack of a national policy in this way is a serious obstacle to mental health and wellbeing access.
Hierarchical Neural Regression Models for Customer Churn Prediction
Directory of Open Access Journals (Sweden)
Golshan Mohammadi
2013-01-01
Full Text Available As customers are the main assets of each industry, customer churn prediction is becoming a major task for companies to remain in competition with competitors. In the literature, the better applicability and efficiency of hierarchical data mining techniques has been reported. This paper considers three hierarchical models by combining four different data mining techniques for churn prediction, which are backpropagation artificial neural networks (ANN, self-organizing maps (SOM, alpha-cut fuzzy c-means (α-FCM, and Cox proportional hazards regression model. The hierarchical models are ANN + ANN + Cox, SOM + ANN + Cox, and α-FCM + ANN + Cox. In particular, the first component of the models aims to cluster data in two churner and nonchurner groups and also filter out unrepresentative data or outliers. Then, the clustered data as the outputs are used to assign customers to churner and nonchurner groups by the second technique. Finally, the correctly classified data are used to create Cox proportional hazards model. To evaluate the performance of the hierarchical models, an Iranian mobile dataset is considered. The experimental results show that the hierarchical models outperform the single Cox regression baseline model in terms of prediction accuracy, Types I and II errors, RMSE, and MAD metrics. In addition, the α-FCM + ANN + Cox model significantly performs better than the two other hierarchical models.
A Bayesian alternative for multi-objective ecohydrological model specification
Tang, Yating; Marshall, Lucy; Sharma, Ashish; Ajami, Hoori
2018-01-01
Recent studies have identified the importance of vegetation processes in terrestrial hydrologic systems. Process-based ecohydrological models combine hydrological, physical, biochemical and ecological processes of the catchments, and as such are generally more complex and parametric than conceptual hydrological models. Thus, appropriate calibration objectives and model uncertainty analysis are essential for ecohydrological modeling. In recent years, Bayesian inference has become one of the most popular tools for quantifying the uncertainties in hydrological modeling with the development of Markov chain Monte Carlo (MCMC) techniques. The Bayesian approach offers an appealing alternative to traditional multi-objective hydrologic model calibrations by defining proper prior distributions that can be considered analogous to the ad-hoc weighting often prescribed in multi-objective calibration. Our study aims to develop appropriate prior distributions and likelihood functions that minimize the model uncertainties and bias within a Bayesian ecohydrological modeling framework based on a traditional Pareto-based model calibration technique. In our study, a Pareto-based multi-objective optimization and a formal Bayesian framework are implemented in a conceptual ecohydrological model that combines a hydrological model (HYMOD) and a modified Bucket Grassland Model (BGM). Simulations focused on one objective (streamflow/LAI) and multiple objectives (streamflow and LAI) with different emphasis defined via the prior distribution of the model error parameters. Results show more reliable outputs for both predicted streamflow and LAI using Bayesian multi-objective calibration with specified prior distributions for error parameters based on results from the Pareto front in the ecohydrological modeling. The methodology implemented here provides insight into the usefulness of multiobjective Bayesian calibration for ecohydrologic systems and the importance of appropriate prior
Bayesian Estimation of the Logistic Positive Exponent IRT Model
Bolfarine, Heleno; Bazan, Jorge Luis
2010-01-01
A Bayesian inference approach using Markov Chain Monte Carlo (MCMC) is developed for the logistic positive exponent (LPE) model proposed by Samejima and for a new skewed Logistic Item Response Theory (IRT) model, named Reflection LPE model. Both models lead to asymmetric item characteristic curves (ICC) and can be appropriate because a symmetric…
Metrics for evaluating performance and uncertainty of Bayesian network models
Bruce G. Marcot
2012-01-01
This paper presents a selected set of existing and new metrics for gauging Bayesian network model performance and uncertainty. Selected existing and new metrics are discussed for conducting model sensitivity analysis (variance reduction, entropy reduction, case file simulation); evaluating scenarios (influence analysis); depicting model complexity (numbers of model...
Using consensus bayesian network to model the reactive oxygen species regulatory pathway.
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Liangdong Hu
Full Text Available Bayesian network is one of the most successful graph models for representing the reactive oxygen species regulatory pathway. With the increasing number of microarray measurements, it is possible to construct the bayesian network from microarray data directly. Although large numbers of bayesian network learning algorithms have been developed, when applying them to learn bayesian networks from microarray data, the accuracies are low due to that the databases they used to learn bayesian networks contain too few microarray data. In this paper, we propose a consensus bayesian network which is constructed by combining bayesian networks from relevant literatures and bayesian networks learned from microarray data. It would have a higher accuracy than the bayesian networks learned from one database. In the experiment, we validated the bayesian network combination algorithm on several classic machine learning databases and used the consensus bayesian network to model the Escherichia coli's ROS pathway.
Using consensus bayesian network to model the reactive oxygen species regulatory pathway.
Hu, Liangdong; Wang, Limin
2013-01-01
Bayesian network is one of the most successful graph models for representing the reactive oxygen species regulatory pathway. With the increasing number of microarray measurements, it is possible to construct the bayesian network from microarray data directly. Although large numbers of bayesian network learning algorithms have been developed, when applying them to learn bayesian networks from microarray data, the accuracies are low due to that the databases they used to learn bayesian networks contain too few microarray data. In this paper, we propose a consensus bayesian network which is constructed by combining bayesian networks from relevant literatures and bayesian networks learned from microarray data. It would have a higher accuracy than the bayesian networks learned from one database. In the experiment, we validated the bayesian network combination algorithm on several classic machine learning databases and used the consensus bayesian network to model the Escherichia coli's ROS pathway.
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....
Directory of Open Access Journals (Sweden)
Canty Angelo
2007-09-01
Full Text Available Abstract Background This study compares the Bayesian and frequentist (non-Bayesian approaches in the modelling of the association between the risk of preterm birth and maternal proximity to hazardous waste and pollution from the Sydney Tar Pond site in Nova Scotia, Canada. Methods The data includes 1604 observed cases of preterm birth out of a total population of 17559 at risk of preterm birth from 144 enumeration districts in the Cape Breton Regional Municipality. Other covariates include the distance from the Tar Pond; the rate of unemployment to population; the proportion of persons who are separated, divorced or widowed; the proportion of persons who have no high school diploma; the proportion of persons living alone; the proportion of single parent families and average income. Bayesian hierarchical Poisson regression, quasi-likelihood Poisson regression and weighted linear regression models were fitted to the data. Results The results of the analyses were compared together with their limitations. Conclusion The results of the weighted linear regression and the quasi-likelihood Poisson regression agrees with the result from the Bayesian hierarchical modelling which incorporates the spatial effects.
Towards a hierarchical optimization modeling framework for ...
Background:Bilevel optimization has been recognized as a 2-player Stackelberg game where players are represented as leaders and followers and each pursue their own set of objectives. Hierarchical optimization problems, which are a generalization of bilevel, are especially difficult because the optimization is nested, meaning that the objectives of one level depend on solutions to the other levels. We introduce a hierarchical optimization framework for spatially targeting multiobjective green infrastructure (GI) incentive policies under uncertainties related to policy budget, compliance, and GI effectiveness. We demonstrate the utility of the framework using a hypothetical urban watershed, where the levels are characterized by multiple levels of policy makers (e.g., local, regional, national) and policy followers (e.g., landowners, communities), and objectives include minimization of policy cost, implementation cost, and risk; reduction of combined sewer overflow (CSO) events; and improvement in environmental benefits such as reduced nutrient run-off and water availability. Conclusions: While computationally expensive, this hierarchical optimization framework explicitly simulates the interaction between multiple levels of policy makers (e.g., local, regional, national) and policy followers (e.g., landowners, communities) and is especially useful for constructing and evaluating environmental and ecological policy. Using the framework with a hypothetical urba
Bayesian inference model for fatigue life of laminated composites
DEFF Research Database (Denmark)
Dimitrov, Nikolay Krasimirov; Kiureghian, Armen Der; Berggreen, Christian
2016-01-01
A probabilistic model for estimating the fatigue life of laminated composite plates is developed. The model is based on lamina-level input data, making it possible to predict fatigue properties for a wide range of laminate configurations. Model parameters are estimated by Bayesian inference...
An Active Lattice Model in a Bayesian Framework
DEFF Research Database (Denmark)
Carstensen, Jens Michael
1996-01-01
A Markov Random Field is used as a structural model of a deformable rectangular lattice. When used as a template prior in a Bayesian framework this model is powerful for making inferences about lattice structures in images. The model assigns maximum probability to the perfect regular lattice by p...
An intercausal cancellation model for Bayesian-network engineering
Woudenberg, Steven P D; Van Der Gaag, Linda C.; Rademaker, Carin M A
2015-01-01
When constructing Bayesian networks with domain experts, network engineers often use the noisy-OR model, and causal interaction models more generally, to alleviate the burden of probability elicitation: the use of such a model serves to reduce the number of probabilities to be elicited on the one
A Bayesian Infinite Hidden Markov Vector Autoregressive Model
D. Nibbering (Didier); R. Paap (Richard); M. van der Wel (Michel)
2016-01-01
textabstractWe propose a Bayesian infinite hidden Markov model to estimate time-varying parameters in a vector autoregressive model. The Markov structure allows for heterogeneity over time while accounting for state-persistence. By modelling the transition distribution as a Dirichlet process mixture
Common quandaries and their practical solutions in Bayesian network modeling
Bruce G. Marcot
2017-01-01
Use and popularity of Bayesian network (BN) modeling has greatly expanded in recent years, but many common problems remain. Here, I summarize key problems in BN model construction and interpretation,along with suggested practical solutions. Problems in BN model construction include parameterizing probability values, variable definition, complex network structures,...
Bayesian Network Models for Local Dependence among Observable Outcome Variables
Almond, Russell G.; Mulder, Joris; Hemat, Lisa A.; Yan, Duanli
2009-01-01
Bayesian network models offer a large degree of flexibility for modeling dependence among observables (item outcome variables) from the same task, which may be dependent. This article explores four design patterns for modeling locally dependent observations: (a) no context--ignores dependence among observables; (b) compensatory context--introduces…
Bayesian inference of chemical kinetic models from proposed reactions
Galagali, Nikhil
2015-02-01
© 2014 Elsevier Ltd. Bayesian inference provides a natural framework for combining experimental data with prior knowledge to develop chemical kinetic models and quantify the associated uncertainties, not only in parameter values but also in model structure. Most existing applications of Bayesian model selection methods to chemical kinetics have been limited to comparisons among a small set of models, however. The significant computational cost of evaluating posterior model probabilities renders traditional Bayesian methods infeasible when the model space becomes large. We present a new framework for tractable Bayesian model inference and uncertainty quantification using a large number of systematically generated model hypotheses. The approach involves imposing point-mass mixture priors over rate constants and exploring the resulting posterior distribution using an adaptive Markov chain Monte Carlo method. The posterior samples are used to identify plausible models, to quantify rate constant uncertainties, and to extract key diagnostic information about model structure-such as the reactions and operating pathways most strongly supported by the data. We provide numerical demonstrations of the proposed framework by inferring kinetic models for catalytic steam and dry reforming of methane using available experimental data.
Energy Technology Data Exchange (ETDEWEB)
Wang, Li; Gac, Nicolas; Mohammad-Djafari, Ali [Laboratoire des Signaux et Systèmes 3, Rue Joliot-Curie 91192 Gif sur Yvette (France)
2015-01-13
In order to improve quality of 3D X-ray tomography reconstruction for Non Destructive Testing (NDT), we investigate in this paper hierarchical Bayesian methods. In NDT, useful prior information on the volume like the limited number of materials or the presence of homogeneous area can be included in the iterative reconstruction algorithms. In hierarchical Bayesian methods, not only the volume is estimated thanks to the prior model of the volume but also the hyper parameters of this prior. This additional complexity in the reconstruction methods when applied to large volumes (from 512{sup 3} to 8192{sup 3} voxels) results in an increasing computational cost. To reduce it, the hierarchical Bayesian methods investigated in this paper lead to an algorithm acceleration by Variational Bayesian Approximation (VBA) [1] and hardware acceleration thanks to projection and back-projection operators paralleled on many core processors like GPU [2]. In this paper, we will consider a Student-t prior on the gradient of the image implemented in a hierarchical way [3, 4, 1]. Operators H (forward or projection) and H{sup t} (adjoint or back-projection) implanted in multi-GPU [2] have been used in this study. Different methods will be evalued on synthetic volume 'Shepp and Logan' in terms of quality and time of reconstruction. We used several simple regularizations of order 1 and order 2. Other prior models also exists [5]. Sometimes for a discrete image, we can do the segmentation and reconstruction at the same time, then the reconstruction can be done with less projections.
Bayesian Subset Modeling for High-Dimensional Generalized Linear Models
Liang, Faming
2013-06-01
This article presents a new prior setting for high-dimensional generalized linear models, which leads to a Bayesian subset regression (BSR) with the maximum a posteriori model approximately equivalent to the minimum extended Bayesian information criterion model. The consistency of the resulting posterior is established under mild conditions. Further, a variable screening procedure is proposed based on the marginal inclusion probability, which shares the same properties of sure screening and consistency with the existing sure independence screening (SIS) and iterative sure independence screening (ISIS) procedures. However, since the proposed procedure makes use of joint information from all predictors, it generally outperforms SIS and ISIS in real applications. This article also makes extensive comparisons of BSR with the popular penalized likelihood methods, including Lasso, elastic net, SIS, and ISIS. The numerical results indicate that BSR can generally outperform the penalized likelihood methods. The models selected by BSR tend to be sparser and, more importantly, of higher prediction ability. In addition, the performance of the penalized likelihood methods tends to deteriorate as the number of predictors increases, while this is not significant for BSR. Supplementary materials for this article are available online. © 2013 American Statistical Association.
Hierarchical model analysis of the Atlantic Flyway Breeding Waterfowl Survey
Sauer, John R.; Zimmerman, Guthrie S.; Klimstra, Jon D.; Link, William A.
2014-01-01
We used log-linear hierarchical models to analyze data from the Atlantic Flyway Breeding Waterfowl Survey. The survey has been conducted by state biologists each year since 1989 in the northeastern United States from Virginia north to New Hampshire and Vermont. Although yearly population estimates from the survey are used by the United States Fish and Wildlife Service for estimating regional waterfowl population status for mallards (Anas platyrhynchos), black ducks (Anas rubripes), wood ducks (Aix sponsa), and Canada geese (Branta canadensis), they are not routinely adjusted to control for time of day effects and other survey design issues. The hierarchical model analysis permits estimation of year effects and population change while accommodating the repeated sampling of plots and controlling for time of day effects in counting. We compared population estimates from the current stratified random sample analysis to population estimates from hierarchical models with alternative model structures that describe year to year changes as random year effects, a trend with random year effects, or year effects modeled as 1-year differences. Patterns of population change from the hierarchical model results generally were similar to the patterns described by stratified random sample estimates, but significant visibility differences occurred between twilight to midday counts in all species. Controlling for the effects of time of day resulted in larger population estimates for all species in the hierarchical model analysis relative to the stratified random sample analysis. The hierarchical models also provided a convenient means of estimating population trend as derived statistics from the analysis. We detected significant declines in mallard and American black ducks and significant increases in wood ducks and Canada geese, a trend that had not been significant for 3 of these 4 species in the prior analysis. We recommend using hierarchical models for analysis of the Atlantic
Productioon uncertainties modelling by Bayesian inference using Gibbs sampling
Directory of Open Access Journals (Sweden)
Azizi, Amir
2015-11-01
Full Text Available Analysis by modelling production throughput is an efficient way to provide information for production decision-making. Observation and investigation based on a real-life tile production line revealed that the five main uncertain variables are demand rate, breakdown time, scrap rate, setup time, and lead time. The volatile nature of these random variables was observed over a specific period of 104 weeks. The processes were sequential and multi-stage. These five uncertain variables of production were modelled to reflect the performance of overall production by applying Bayesian inference using Gibbs sampling. The application of Bayesian inference for handling production uncertainties showed a robust model with 2.5 per cent mean absolute percentage error. It is recommended to consider the five main uncertain variables that are introduced in this study for production decision-making. The study proposes the use of Bayesian inference for superior accuracy in production decision-making.
A mixture copula Bayesian network model for multimodal genomic data
Directory of Open Access Journals (Sweden)
Qingyang Zhang
2017-04-01
Full Text Available Gaussian Bayesian networks have become a widely used framework to estimate directed associations between joint Gaussian variables, where the network structure encodes the decomposition of multivariate normal density into local terms. However, the resulting estimates can be inaccurate when the normality assumption is moderately or severely violated, making it unsuitable for dealing with recent genomic data such as the Cancer Genome Atlas data. In the present paper, we propose a mixture copula Bayesian network model which provides great flexibility in modeling non-Gaussian and multimodal data for causal inference. The parameters in mixture copula functions can be efficiently estimated by a routine expectation–maximization algorithm. A heuristic search algorithm based on Bayesian information criterion is developed to estimate the network structure, and prediction can be further improved by the best-scoring network out of multiple predictions from random initial values. Our method outperforms Gaussian Bayesian networks and regular copula Bayesian networks in terms of modeling flexibility and prediction accuracy, as demonstrated using a cell signaling data set. We apply the proposed methods to the Cancer Genome Atlas data to study the genetic and epigenetic pathways that underlie serous ovarian cancer.
A mixture copula Bayesian network model for multimodal genomic data.
Zhang, Qingyang; Shi, Xuan
2017-01-01
Gaussian Bayesian networks have become a widely used framework to estimate directed associations between joint Gaussian variables, where the network structure encodes the decomposition of multivariate normal density into local terms. However, the resulting estimates can be inaccurate when the normality assumption is moderately or severely violated, making it unsuitable for dealing with recent genomic data such as the Cancer Genome Atlas data. In the present paper, we propose a mixture copula Bayesian network model which provides great flexibility in modeling non-Gaussian and multimodal data for causal inference. The parameters in mixture copula functions can be efficiently estimated by a routine expectation-maximization algorithm. A heuristic search algorithm based on Bayesian information criterion is developed to estimate the network structure, and prediction can be further improved by the best-scoring network out of multiple predictions from random initial values. Our method outperforms Gaussian Bayesian networks and regular copula Bayesian networks in terms of modeling flexibility and prediction accuracy, as demonstrated using a cell signaling data set. We apply the proposed methods to the Cancer Genome Atlas data to study the genetic and epigenetic pathways that underlie serous ovarian cancer.
Item Analysis by the Hierarchical Generalized Linear Model.
Kamata, Akihito
2001-01-01
Presents the hierarchical generalized linear model (HGLM) as an explicit two-level formulation of a multilevel item response model. Shows that the HGLM is equivalent to the Rasch model, and that a characteristic of the HGLM is that person ability can be expressed as a latent regression model with person-characteristic variables. Shows that the…
Accurate phenotyping: Reconciling approaches through Bayesian model averaging.
Directory of Open Access Journals (Sweden)
Carla Chia-Ming Chen
Full Text Available Genetic research into complex diseases is frequently hindered by a lack of clear biomarkers for phenotype ascertainment. Phenotypes for such diseases are often identified on the basis of clinically defined criteria; however such criteria may not be suitable for understanding the genetic composition of the diseases. Various statistical approaches have been proposed for phenotype definition; however our previous studies have shown that differences in phenotypes estimated using different approaches have substantial impact on subsequent analyses. Instead of obtaining results based upon a single model, we propose a new method, using Bayesian model averaging to overcome problems associated with phenotype definition. Although Bayesian model averaging has been used in other fields of research, this is the first study that uses Bayesian model averaging to reconcile phenotypes obtained using multiple models. We illustrate the new method by applying it to simulated genetic and phenotypic data for Kofendred personality disorder-an imaginary disease with several sub-types. Two separate statistical methods were used to identify clusters of individuals with distinct phenotypes: latent class analysis and grade of membership. Bayesian model averaging was then used to combine the two clusterings for the purpose of subsequent linkage analyses. We found that causative genetic loci for the disease produced higher LOD scores using model averaging than under either individual model separately. We attribute this improvement to consolidation of the cores of phenotype clusters identified using each individual method.
On the Choice of Prior in Bayesian Model Averaging
Einmahl, J.H.J.; Magnus, J.R.; Kumar, K.
2011-01-01
Bayesian model averaging attempts to combine parameter estimation and model uncertainty in one coherent framework. The choice of prior is then critical. Within an explicit framework of ignorance we define a ‘suitable’ prior as one which leads to a continuous and suitable analog to the pretest
Bayesian log-periodic model for financial crashes
Rodríguez-Caballero, Carlos Vladimir; Knapik, Oskar
2014-10-01
This paper introduces a Bayesian approach in econophysics literature about financial bubbles in order to estimate the most probable time for a financial crash to occur. To this end, we propose using noninformative prior distributions to obtain posterior distributions. Since these distributions cannot be performed analytically, we develop a Markov Chain Monte Carlo algorithm to draw from posterior distributions. We consider three Bayesian models that involve normal and Student's t-distributions in the disturbances and an AR(1)-GARCH(1,1) structure only within the first case. In the empirical part of the study, we analyze a well-known example of financial bubble - the S&P 500 1987 crash - to show the usefulness of the three methods under consideration and crashes of Merval-94, Bovespa-97, IPCMX-94, Hang Seng-97 using the simplest method. The novelty of this research is that the Bayesian models provide 95% credible intervals for the estimated crash time.
A hierarchical linear model for tree height prediction.
Vicente J. Monleon
2003-01-01
Measuring tree height is a time-consuming process. Often, tree diameter is measured and height is estimated from a published regression model. Trees used to develop these models are clustered into stands, but this structure is ignored and independence is assumed. In this study, hierarchical linear models that account explicitly for the clustered structure of the data...
Model-based Bayesian inference for ROC data analysis
Lei, Tianhu; Bae, K. Ty
2013-03-01
This paper presents a study of model-based Bayesian inference to Receiver Operating Characteristics (ROC) data. The model is a simple version of general non-linear regression model. Different from Dorfman model, it uses a probit link function with a covariate variable having zero-one two values to express binormal distributions in a single formula. Model also includes a scale parameter. Bayesian inference is implemented by Markov Chain Monte Carlo (MCMC) method carried out by Bayesian analysis Using Gibbs Sampling (BUGS). Contrast to the classical statistical theory, Bayesian approach considers model parameters as random variables characterized by prior distributions. With substantial amount of simulated samples generated by sampling algorithm, posterior distributions of parameters as well as parameters themselves can be accurately estimated. MCMC-based BUGS adopts Adaptive Rejection Sampling (ARS) protocol which requires the probability density function (pdf) which samples are drawing from be log concave with respect to the targeted parameters. Our study corrects a common misconception and proves that pdf of this regression model is log concave with respect to its scale parameter. Therefore, ARS's requirement is satisfied and a Gaussian prior which is conjugate and possesses many analytic and computational advantages is assigned to the scale parameter. A cohort of 20 simulated data sets and 20 simulations from each data set are used in our study. Output analysis and convergence diagnostics for MCMC method are assessed by CODA package. Models and methods by using continuous Gaussian prior and discrete categorical prior are compared. Intensive simulations and performance measures are given to illustrate our practice in the framework of model-based Bayesian inference using MCMC method.
Hierarchical Bayesian calibration of tidal orbit decay rates among hot Jupiters
Cameron, Andrew Collier; Jardine, Moira
2018-02-01
Transiting hot Jupiters occupy a wedge-shaped region in the mass ratio-orbital separation diagram. Its upper boundary is eroded by tidal spiral-in of massive, close-in planets and is sensitive to the stellar tidal dissipation parameter Q_s^' }. We develop a simple generative model of the orbital separation distribution of the known population of transiting hot Jupiters, subject to tidal orbital decay, XUV-driven evaporation and observational selection bias. From the joint likelihood of the observed orbital separations of hot Jupiters discovered in ground-based wide-field transit surveys, measured with respect to the hyperparameters of the underlying population model, we recover narrow posterior probability distributions for Q_s^' } in two different tidal forcing frequency regimes. We validate the method using mock samples of transiting planets with known tidal parameters. We find that Q_s^' } and its temperature dependence are retrieved reliably over five orders of magnitude in Q_s^' }. A large sample of hot Jupiters from small-aperture ground-based surveys yields log _{10} Q_s^' }=(8.26± 0.14) for 223 systems in the equilibrium-tide regime. We detect no significant dependence of Q_s^' } on stellar effective temperature. A further 19 systems in the dynamical-tide regime yield log _{10} Q_s^' }=7.3± 0.4, indicating stronger coupling. Detection probabilities for transiting planets at a given orbital separation scale inversely with the increase in their tidal migration rates since birth. The resulting bias towards younger systems explains why the surface gravities of hot Jupiters correlate with their host stars' chromospheric emission fluxes. We predict departures from a linear transit-timing ephemeris of less than 4 seconds for WASP-18 over a 20-year baseline.
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
Ross, Cody T; Winterhalder, Bruce
2016-01-01
We conduct a revaluation of the Thornhill and Fincher research project on parasites using finely-resolved geographic data on parasite prevalence, individual-level sociocultural data, and multilevel Bayesian modeling. In contrast to the evolutionary psychological mechanisms linking parasites to human behavior and cultural characteristics proposed by Thornhill and Fincher, we offer an alternative hypothesis that structural racism and differential access to sanitation systems drive both variation in parasite prevalence and differential behaviors and cultural characteristics. We adopt a Bayesian framework to estimate parasite prevalence rates in 51 districts in eight Latin American countries using the disease status of 170,220 individuals tested for infection with the intestinal roundworm Ascaris lumbricoides (Hürlimann et al., []: PLoS Negl Trop Dis 5:e1404). We then use district-level estimates of parasite prevalence and individual-level social data from 5,558 individuals in the same 51 districts (Latinobarómetro, 2008) to assess claims of causal associations between parasite prevalence and sociocultural characteristics. We find, contrary to Thornhill and Fincher, that parasite prevalence is positively associated with preferences for democracy, negatively associated with preferences for collectivism, and not associated with violent crime rates or gender inequality. A positive association between parasite prevalence and religiosity, as in Fincher and Thornhill (: Behav Brain Sci 35:61-79), and a negative association between parasite prevalence and achieved education, as predicted by Eppig et al. (: Proc R S B: Biol Sci 277:3801-3808), become negative and unreliable when reasonable controls are included in the model. We find support for all predictions derived from our hypothesis linking structural racism to both parasite prevalence and cultural outcomes. We conclude that best practices in biocultural modeling require examining more than one hypothesis, retaining
Modelling hierarchical and modular complex networks: division and independence
Kim, D.-H.; Rodgers, G. J.; Kahng, B.; Kim, D.
2005-06-01
We introduce a growing network model which generates both modular and hierarchical structure in a self-organized way. To this end, we modify the Barabási-Albert model into the one evolving under the principles of division and independence as well as growth and preferential attachment (PA). A newly added vertex chooses one of the modules composed of existing vertices, and attaches edges to vertices belonging to that module following the PA rule. When the module size reaches a proper size, the module is divided into two, and a new module is created. The karate club network studied by Zachary is a simple version of the current model. We find that the model can reproduce both modular and hierarchical properties, characterized by the hierarchical clustering function of a vertex with degree k, C(k), being in good agreement with empirical measurements for real-world networks.
Shih, Ann T.; Ancel, Ersin; Jones, Sharon M.
2012-01-01
The concern for reducing aviation safety risk is rising as the National Airspace System in the United States transforms to the Next Generation Air Transportation System (NextGen). The NASA Aviation Safety Program is committed to developing an effective aviation safety technology portfolio to meet the challenges of this transformation and to mitigate relevant safety risks. The paper focuses on the reasoning of selecting Object-Oriented Bayesian Networks (OOBN) as the technique and commercial software for the accident modeling and portfolio assessment. To illustrate the benefits of OOBN in a large and complex aviation accident model, the in-flight Loss-of-Control Accident Framework (LOCAF) constructed as an influence diagram is presented. An OOBN approach not only simplifies construction and maintenance of complex causal networks for the modelers, but also offers a well-organized hierarchical network that is easier for decision makers to exploit the model examining the effectiveness of risk mitigation strategies through technology insertions.
Spatial and spatio-temporal bayesian models with R - INLA
Blangiardo, Marta
2015-01-01
Dedication iiiPreface ix1 Introduction 11.1 Why spatial and spatio-temporal statistics? 11.2 Why do we use Bayesian methods for modelling spatial and spatio-temporal structures? 21.3 Why INLA? 31.4 Datasets 32 Introduction to 212.1 The language 212.2 objects 222.3 Data and session management 342.4 Packages 352.5 Programming in 362.6 Basic statistical analysis with 393 Introduction to Bayesian Methods 533.1 Bayesian Philosophy 533.2 Basic Probability Elements 573.3 Bayes Theorem 623.4 Prior and Posterior Distributions 643.5 Working with the Posterior Distribution 663.6 Choosing the Prior Distr
DEFF Research Database (Denmark)
Quinonero, Joaquin; Girard, Agathe; Larsen, Jan
2003-01-01
The object of Bayesian modelling is predictive distribution, which, in a forecasting scenario, enables evaluation of forecasted values and their uncertainties. We focus on reliably estimating the predictive mean and variance of forecasted values using Bayesian kernel based models...
Bayesian modeling of measurement error in predictor variables
Fox, Gerardus J.A.; Glas, Cornelis A.W.
2003-01-01
It is shown that measurement error in predictor variables can be modeled using item response theory (IRT). The predictor variables, that may be defined at any level of an hierarchical regression model, are treated as latent variables. The normal ogive model is used to describe the relation between
Bayesian log-periodic model for financial crashes
DEFF Research Database (Denmark)
Rodríguez-Caballero, Carlos Vladimir; Knapik, Oskar
2014-01-01
cannot be performed analytically, we develop a Markov Chain Monte Carlo algorithm to draw from posterior distributions. We consider three Bayesian models that involve normal and Student’s t-distributions in the disturbances and an AR(1)-GARCH(1,1) structure only within the first case. In the empirical...
Efficient Bayesian Estimation and Combination of GARCH-Type Models
D. David (David); L.F. Hoogerheide (Lennart)
2010-01-01
textabstractThis paper proposes an up-to-date review of estimation strategies available for the Bayesian inference of GARCH-type models. The emphasis is put on a novel efficient procedure named AdMitIS. The methodology automatically constructs a mixture of Student-t distributions as an approximation
On Bayesian Modelling of Fat Tails and Skewness
Fernández, C.; Steel, M.F.J.
1996-01-01
We consider a Bayesian analysis of linear regression models that can account for skewed error distributions with fat tails.The latter two features are often observed characteristics of empirical data sets, and we will formally incorporate them in the inferential process.A general procedure for
Bayesian Modelling of fMRI Time Series
DEFF Research Database (Denmark)
Højen-Sørensen, Pedro; Hansen, Lars Kai; Rasmussen, Carl Edward
2000-01-01
We present a Hidden Markov Model (HMM) for inferring the hidden psychological state (or neural activity) during single trial fMRI activation experiments with blocked task paradigms. Inference is based on Bayesian methodology, using a combination of analytical and a variety of Markov Chain Monte...
Bayesian model discrimination for glucose-insulin homeostasis
DEFF Research Database (Denmark)
Andersen, Kim Emil; Brooks, Stephen P.; Højbjerre, Malene
In this paper we analyse a set of experimental data on a number of healthy and diabetic patients and discuss a variety of models for describing the physiological processes involved in glucose absorption and insulin secretion within the human body. We adopt a Bayesian approach which facilitates th...
Shortlist B: A Bayesian model of continuous speech recognition
Norris, D.; McQueen, J.M.
2008-01-01
A Bayesian model of continuous speech recognition is presented. It is based on Shortlist (D. Norris, 1994; D. Norris, J. M. McQueen, A. Cutler, & S. Butterfield, 1997) and shares many of its key assumptions: parallel competitive evaluation of multiple lexical hypotheses, phonologically abstract
Shortlist B: A Bayesian Model of Continuous Speech Recognition
Norris, Dennis; McQueen, James M.
2008-01-01
A Bayesian model of continuous speech recognition is presented. It is based on Shortlist (D. Norris, 1994; D. Norris, J. M. McQueen, A. Cutler, & S. Butterfield, 1997) and shares many of its key assumptions: parallel competitive evaluation of multiple lexical hypotheses, phonologically abstract prelexical and lexical representations, a feedforward…
Model-based hierarchical reinforcement learning and human action control.
Botvinick, Matthew; Weinstein, Ari
2014-11-05
Recent work has reawakened interest in goal-directed or 'model-based' choice, where decisions are based on prospective evaluation of potential action outcomes. Concurrently, there has been growing attention to the role of hierarchy in decision-making and action control. We focus here on the intersection between these two areas of interest, considering the topic of hierarchical model-based control. To characterize this form of action control, we draw on the computational framework of hierarchical reinforcement learning, using this to interpret recent empirical findings. The resulting picture reveals how hierarchical model-based mechanisms might play a special and pivotal role in human decision-making, dramatically extending the scope and complexity of human behaviour.
Applied Bayesian hierarchical methods
National Research Council Canada - National Science Library
Congdon, P
2010-01-01
... . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.2 Posterior Inference from Bayes Formula . . . . . . . . . . . . 1.3 Markov Chain Monte Carlo Sampling in Relation to Monte Carlo Methods: Obtaining Posterior...
Bayesian Dimensionality Assessment for the Multidimensional Nominal Response Model
Directory of Open Access Journals (Sweden)
Javier Revuelta
2017-06-01
Full Text Available This article introduces Bayesian estimation and evaluation procedures for the multidimensional nominal response model. The utility of this model is to perform a nominal factor analysis of items that consist of a finite number of unordered response categories. The key aspect of the model, in comparison with traditional factorial model, is that there is a slope for each response category on the latent dimensions, instead of having slopes associated to the items. The extended parameterization of the multidimensional nominal response model requires large samples for estimation. When sample size is of a moderate or small size, some of these parameters may be weakly empirically identifiable and the estimation algorithm may run into difficulties. We propose a Bayesian MCMC inferential algorithm to estimate the parameters and the number of dimensions underlying the multidimensional nominal response model. Two Bayesian approaches to model evaluation were compared: discrepancy statistics (DIC, WAICC, and LOO that provide an indication of the relative merit of different models, and the standardized generalized discrepancy measure that requires resampling data and is computationally more involved. A simulation study was conducted to compare these two approaches, and the results show that the standardized generalized discrepancy measure can be used to reliably estimate the dimensionality of the model whereas the discrepancy statistics are questionable. The paper also includes an example with real data in the context of learning styles, in which the model is used to conduct an exploratory factor analysis of nominal data.
Data Assimilation using an Ensemble of Models: A hierarchical approach
Rayner, Peter
2017-01-01
One characteristic of biogeochemical models is uncertainty about their formulation. Data assimilation should take this uncertainty into account. A common approach is to use an ensemble of models. We must assign probabilities not only to the parameters of the models but the models themselves. The method of hierarchical modelling allows us to calculate these probabilities. This paper describes the approach, develops the algebra for the most common case then applies it to the TRANSCO...
A Hierarchal Risk Assessment Model Using the Evidential Reasoning Rule
Directory of Open Access Journals (Sweden)
Xiaoxiao Ji
2017-02-01
Full Text Available This paper aims to develop a hierarchical risk assessment model using the newly-developed evidential reasoning (ER rule, which constitutes a generic conjunctive probabilistic reasoning process. In this paper, we first provide a brief introduction to the basics of the ER rule and emphasize the strengths for representing and aggregating uncertain information from multiple experts and sources. Further, we discuss the key steps of developing the hierarchical risk assessment framework systematically, including (1 formulation of risk assessment hierarchy; (2 representation of both qualitative and quantitative information; (3 elicitation of attribute weights and information reliabilities; (4 aggregation of assessment information using the ER rule and (5 quantification and ranking of risks using utility-based transformation. The proposed hierarchical risk assessment framework can potentially be implemented to various complex and uncertain systems. A case study on the fire/explosion risk assessment of marine vessels demonstrates the applicability of the proposed risk assessment model.
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
In this paper, we present a Bayesian channel estimation algorithm for multicarrier receivers based on pilot symbol observations. The inherent sparse nature of wireless multipath channels is exploited by modeling the prior distribution of multipath components' gains with a hierarchical...
Experiments in Error Propagation within Hierarchal Combat Models
2015-09-01
Bayesian Information Criterion CNO Chief of Naval Operations DOE Design of Experiments DOD Department of Defense MANA Map Aware Non-uniform Automata ...ground up” approach. First, it develops a mission-level model for one on one submarine combat in Map Aware Non-uniform Automata (MANA) simulation, an... Automata (MANA), an agent based simulation that can model the different postures of submarines. It feeds the results from MANA into stochastic
MULTILEVEL RECURRENT MODEL FOR HIERARCHICAL CONTROL OF COMPLEX REGIONAL SECURITY
Directory of Open Access Journals (Sweden)
Andrey V. Masloboev
2014-11-01
Full Text Available Subject of research. The research goal and scope are development of methods and software for mathematical and computer modeling of the regional security information support systems as multilevel hierarchical systems. Such systems are characterized by loosely formalization, multiple-aspect of descendent system processes and their interconnectivity, high level dynamics and uncertainty. The research methodology is based on functional-target approach and principles of multilevel hierarchical system theory. The work considers analysis and structural-algorithmic synthesis problem-solving of the multilevel computer-aided systems intended for management and decision-making information support in the field of regional security. Main results. A hierarchical control multilevel model of regional socio-economic system complex security has been developed. The model is based on functional-target approach and provides both formal statement and solving, and practical implementation of the automated information system structure and control algorithms synthesis problems of regional security management optimal in terms of specified criteria. An approach for intralevel and interlevel coordination problem-solving in the multilevel hierarchical systems has been proposed on the basis of model application. The coordination is provided at the expense of interconnection requirements satisfaction between the functioning quality indexes (objective functions, which are optimized by the different elements of multilevel systems. That gives the possibility for sufficient coherence reaching of the local decisions, being made on the different control levels, under decentralized decision-making and external environment high dynamics. Recurrent model application provides security control mathematical models formation of regional socioeconomic systems, functioning under uncertainty. Practical relevance. The model implementation makes it possible to automate synthesis realization of
Bayesian mixed models and the phylogeny of pitvipers (Viperidae: Serpentes).
Castoe, Todd A; Parkinson, Christopher L
2006-04-01
The subfamily Crotalinae (pitvipers) contains over 190 species of venomous snakes distributed in both the Old and New World. We incorporated an extensive sampling of taxa (including 28 of 29 genera), and sequences of four mitochondrial gene fragments (2.3kb) per individual, to estimate the phylogeny of pitvipers based on maximum parsimony and Bayesian phylogenetic methods. Our Bayesian analyses incorporated complex mixed models of nucleotide evolution that allocated independent models to various partitions of the dataset within combined analyses. We compared results of unpartitioned versus partitioned Bayesian analyses to investigate how much unpartitioned (versus partitioned) models were forced to compromise estimates of model parameters, and whether complex models substantially alter phylogenetic conclusions to the extent that they appear to extract more phylogenetic signal than simple models. Our results indicate that complex models do extract more phylogenetic signal from the data. We also address how differences in phylogenetic results (e.g., bipartition posterior probabilities) obtained from simple versus complex models may be interpreted in terms of relative credibility. Our estimates of pitviper phylogeny suggest that nearly all recently proposed generic reallocations appear valid, although certain Old and New World genera (Ovophis, Trimeresurus, and Bothrops) remain poly- or paraphyletic and require further taxonomic revision. While a majority of nodes were resolved, we could not confidently estimate the basal relationships among New World genera and which lineage of Old World species is most closely related to this New World group.
Bayesian models for comparative analysis integrating phylogenetic uncertainty
Directory of Open Access Journals (Sweden)
Villemereuil Pierre de
2012-06-01
Full Text Available Abstract Background Uncertainty in comparative analyses can come from at least two sources: a phylogenetic uncertainty in the tree topology or branch lengths, and b uncertainty due to intraspecific variation in trait values, either due to measurement error or natural individual variation. Most phylogenetic comparative methods do not account for such uncertainties. Not accounting for these sources of uncertainty leads to false perceptions of precision (confidence intervals will be too narrow and inflated significance in hypothesis testing (e.g. p-values will be too small. Although there is some application-specific software for fitting Bayesian models accounting for phylogenetic error, more general and flexible software is desirable. Methods We developed models to directly incorporate phylogenetic uncertainty into a range of analyses that biologists commonly perform, using a Bayesian framework and Markov Chain Monte Carlo analyses. Results We demonstrate applications in linear regression, quantification of phylogenetic signal, and measurement error models. Phylogenetic uncertainty was incorporated by applying a prior distribution for the phylogeny, where this distribution consisted of the posterior tree sets from Bayesian phylogenetic tree estimation programs. The models were analysed using simulated data sets, and applied to a real data set on plant traits, from rainforest plant species in Northern Australia. Analyses were performed using the free and open source software OpenBUGS and JAGS. Conclusions Incorporating phylogenetic uncertainty through an empirical prior distribution of trees leads to more precise estimation of regression model parameters than using a single consensus tree and enables a more realistic estimation of confidence intervals. In addition, models incorporating measurement errors and/or individual variation, in one or both variables, are easily formulated in the Bayesian framework. We show that BUGS is a useful, flexible
"On the construction of hierarchic models"
Out, D.-J.; Out, D.J.; van Rikxoort, R.P.; Bakker, R.R.; Bakker, R.R.
1994-01-01
One of the main problems in the field of model-based diagnosis of technical systems today is finding the most useful model or models of the system being diagnosed. Often, a model showing the physical components and the connections between them is all that is available. As systems grow larger and
Bayesian non parametric modelling of Higgs pair production
Directory of Open Access Journals (Sweden)
Scarpa Bruno
2017-01-01
Full Text Available Statistical classification models are commonly used to separate a signal from a background. In this talk we face the problem of isolating the signal of Higgs pair production using the decay channel in which each boson decays into a pair of b-quarks. Typically in this context non parametric methods are used, such as Random Forests or different types of boosting tools. We remain in the same non-parametric framework, but we propose to face the problem following a Bayesian approach. A Dirichlet process is used as prior for the random effects in a logit model which is fitted by leveraging the Polya-Gamma data augmentation. Refinements of the model include the insertion in the simple model of P-splines to relate explanatory variables with the response and the use of Bayesian trees (BART to describe the atoms in the Dirichlet process.
Bayesian non parametric modelling of Higgs pair production
Scarpa, Bruno; Dorigo, Tommaso
2017-03-01
Statistical classification models are commonly used to separate a signal from a background. In this talk we face the problem of isolating the signal of Higgs pair production using the decay channel in which each boson decays into a pair of b-quarks. Typically in this context non parametric methods are used, such as Random Forests or different types of boosting tools. We remain in the same non-parametric framework, but we propose to face the problem following a Bayesian approach. A Dirichlet process is used as prior for the random effects in a logit model which is fitted by leveraging the Polya-Gamma data augmentation. Refinements of the model include the insertion in the simple model of P-splines to relate explanatory variables with the response and the use of Bayesian trees (BART) to describe the atoms in the Dirichlet process.
Bayesian calibration of groundwater models with input data uncertainty
Xu, Tianfang; Valocchi, Albert J.; Ye, Ming; Liang, Feng; Lin, Yu-Feng
2017-04-01
Effective water resources management typically relies on numerical models to analyze groundwater flow and solute transport processes. Groundwater models are often subject to input data uncertainty, as some inputs (such as recharge and well pumping rates) are estimated and subject to uncertainty. Current practices of groundwater model calibration often overlook uncertainties in input data; this can lead to biased parameter estimates and compromised predictions. Through a synthetic case study of surface-ground water interaction under changing pumping conditions and land use, we investigate the impacts of uncertain pumping and recharge rates on model calibration and uncertainty analysis. We then present a Bayesian framework of model calibration to handle uncertain input of groundwater models. The framework implements a marginalizing step to account for input data uncertainty when evaluating likelihood. It was found that not accounting for input uncertainty may lead to biased, overconfident parameter estimates because parameters could be over-adjusted to compensate for possible input data errors. Parameter compensation can have deleterious impacts when the calibrated model is used to make forecast under a scenario that is different from calibration conditions. By marginalizing input data uncertainty, the Bayesian calibration approach effectively alleviates parameter compensation and gives more accurate predictions in the synthetic case study. The marginalizing Bayesian method also decomposes prediction uncertainty into uncertainties contributed by parameters, input data, and measurements. The results underscore the need to account for input uncertainty to better inform postmodeling decision making.
CSIR Research Space (South Africa)
Johnson, S
2010-02-01
Full Text Available metapopulations was the focus of a Bayesian Network (BN) modelling workshop in South Africa. Using a new heuristics, Iterative Bayesian Network Development Cycle (IBNDC), described in this paper, several networks were formulated to distinguish between the unique...
Update on Bayesian Blocks: Segmented Models for Sequential Data
Scargle, Jeff
2017-01-01
The Bayesian Block algorithm, in wide use in astronomy and other areas, has been improved in several ways. The model for block shape has been generalized to include other than constant signal rate - e.g., linear, exponential, or other parametric models. In addition the computational efficiency has been improved, so that instead of O(N**2) the basic algorithm is O(N) in most cases. Other improvements in the theory and application of segmented representations will be described.
Analysis of Error Propagation Within Hierarchical Air Combat Models
2016-06-01
NAVAL POSTGRADUATE SCHOOL MONTEREY, CALIFORNIA THESIS Approved for public release; distribution is unlimited ANALYSIS OF ERROR ...COVERED Master’s thesis 4. TITLE AND SUBTITLE ANALYSIS OF ERROR PROPAGATION WITHIN HIERARCHICAL AIR COMBAT MODELS 5. FUNDING NUMBERS 6...variance analysis , sampling methods, metamodeling, error propagation, Lanchester equations, agent- based simulation, design of experiments
Improving waterfowl population estimates using hierarchical models: A new approach
Barker, Nicole; Cumming, Steve; Darveau, Marcel
2013-01-01
Recommended citation: Barker, N. K. S., S. G. Cumming, and M. Darveau. 2013. Improving waterfowl population estimates using hierarchical models: A new approach. Poster, Ecology and Conservation of North American Waterfowl. Memphis, TN, USA. Retrieved from figshare: http://dx.doi.org/10.6084/m9.figshare.658776.
Hierarchical modelling for the environmental sciences statistical methods and applications
Clark, James S
2006-01-01
New statistical tools are changing the way in which scientists analyze and interpret data and models. Hierarchical Bayes and Markov Chain Monte Carlo methods for analysis provide a consistent framework for inference and prediction where information is heterogeneous and uncertain, processes are complicated, and responses depend on scale. Nowhere are these methods more promising than in the environmental sciences.
Perceptual multistability predicted by search model for Bayesian decisions.
Sundareswara, Rashmi; Schrater, Paul R
2008-05-23
Perceptual multistability refers to the phenomenon of spontaneous perceptual switching between two or more likely interpretations of an image. Although frequently explained by processes of adaptation or hysteresis, we show that perceptual switching can arise as a natural byproduct of perceptual decision making based on probabilistic (Bayesian) inference, which interprets images by combining probabilistic models of image formation with knowledge of scene regularities. Empirically, we investigated the effect of introducing scene regularities on Necker cube bistability by flanking the Necker cube with fields of unambiguous cubes that are oriented to coincide with one of the Necker cube percepts. We show that background cubes increase the time spent in percepts most similar to the background. To characterize changes in the temporal dynamics of the perceptual alternations beyond percept durations, we introduce Markov Renewal Processes (MRPs). MRPs provide a general mathematical framework for describing probabilistic switching behavior in finite state processes. Additionally, we introduce a simple theoretical model consistent with Bayesian models of vision that involves searching for good interpretations of an image by sampling a posterior distribution coupled with a decay process that favors recent to old interpretations. The model has the same quantitative characteristics as our human data and variation in model parameters can capture between-subject variation. Because the model produces the same kind of stochastic process found in human perceptual behavior, we conclude that multistability may represent an unavoidable by-product of normal perceptual (Bayesian) decision making with ambiguous images.
Exploring Bayesian model selection methods for effective field theory expansions
Schaffner, Taylor; Yamauchi, Yukari; Furnstahl, Richard
2017-09-01
A fundamental understanding of the microscopic properties and interactions of nuclei has long evaded physicists due to the complex nature of quantum chromodynamics (QCD). One approach to modeling nuclear interactions is known as chiral effective field theory (EFT). Today, the method's greatest limitation lies in the approximation of interaction potentials and their corresponding uncertainties. Computing EFT expansion coefficients, known as Low-Energy Constants (LECs), from experimental data reduces to a problem of statistics and fitting. In the conventional approach, the fitting is done using frequentist methods that fail to evaluate the quality of the model itself (e.g., how many orders to use) in addition to its fit to the data. By utilizing Bayesian statistical methods for model selection, the model's quality can be taken into account, providing a more controlled and robust EFT expansion. My research involves probing different Bayesian model checking techniques to determine the most effective means for use with estimating the values of LECs. In particular, we are using model problems to explore the Bayesian calculation of an EFT expansion's evidence and an approximation to this value known as the WAIC (Widely Applicable Information Criterion). This work was supported in part by the National Science Foundation under Grant No. PHY-1306250.
Modeling urban air pollution with optimized hierarchical fuzzy inference system.
Tashayo, Behnam; Alimohammadi, Abbas
2016-10-01
Environmental exposure assessments (EEA) and epidemiological studies require urban air pollution models with appropriate spatial and temporal resolutions. Uncertain available data and inflexible models can limit air pollution modeling techniques, particularly in under developing countries. This paper develops a hierarchical fuzzy inference system (HFIS) to model air pollution under different land use, transportation, and meteorological conditions. To improve performance, the system treats the issue as a large-scale and high-dimensional problem and develops the proposed model using a three-step approach. In the first step, a geospatial information system (GIS) and probabilistic methods are used to preprocess the data. In the second step, a hierarchical structure is generated based on the problem. In the third step, the accuracy and complexity of the model are simultaneously optimized with a multiple objective particle swarm optimization (MOPSO) algorithm. We examine the capabilities of the proposed model for predicting daily and annual mean PM2.5 and NO2 and compare the accuracy of the results with representative models from existing literature. The benefits provided by the model features, including probabilistic preprocessing, multi-objective optimization, and hierarchical structure, are precisely evaluated by comparing five different consecutive models in terms of accuracy and complexity criteria. Fivefold cross validation is used to assess the performance of the generated models. The respective average RMSEs and coefficients of determination (R (2)) for the test datasets using proposed model are as follows: daily PM2.5 = (8.13, 0.78), annual mean PM2.5 = (4.96, 0.80), daily NO2 = (5.63, 0.79), and annual mean NO2 = (2.89, 0.83). The obtained results demonstrate that the developed hierarchical fuzzy inference system can be utilized for modeling air pollution in EEA and epidemiological studies.
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...
Hierarchical Coloured Petrinet Based Healthcare Infrastructure Interdependency Model
Nivedita, N.; S. Durbha
2014-01-01
To ensure a resilient Healthcare Critical Infrastructure, understanding the vulnerabilities and analysing the interdependency on other critical infrastructures is important. To model this critical infrastructure and its dependencies, Hierarchal Coloured petri net modelling approach for simulating the vulnerability of Healthcare Critical infrastructure in a disaster situation is studied.. The model enables to analyse and understand various state changes, which occur when there is a di...
Bayesian analysis of botanical epidemics using stochastic compartmental models.
Gibson, G J; Kleczkowski, A; Gilligan, C A
2004-08-17
A stochastic model for an epidemic, incorporating susceptible, latent, and infectious states, is developed. The model represents primary and secondary infection rates and a time-varying host susceptibility with applications to a wide range of epidemiological systems. A Markov chain Monte Carlo algorithm is presented that allows the model to be fitted to experimental observations within a Bayesian framework. The approach allows the uncertainty in unobserved aspects of the process to be represented in the parameter posterior densities. The methods are applied to experimental observations of damping-off of radish (Raphanus sativus) caused by the fungal pathogen Rhizoctonia solani, in the presence and absence of the antagonistic fungus Trichoderma viride, a biological control agent that has previously been shown to affect the rate of primary infection by using a maximum-likelihood estimate for a simpler model with no allowance for a latent period. Using the Bayesian analysis, we are able to estimate the latent period from population data, even when there is uncertainty in discriminating infectious from latently infected individuals in data collection. We also show that the inference that T. viride can control primary, but not secondary, infection is robust to inclusion of the latent period in the model, although the absolute values of the parameters change. Some refinements and potential difficulties with the Bayesian approach in this context, when prior information on parameters is lacking, are discussed along with broader applications of the methods to a wide range of epidemiological systems.
Ghosh, Sujit K
2010-01-01
Bayesian methods are rapidly becoming popular tools for making statistical inference in various fields of science including biology, engineering, finance, and genetics. One of the key aspects of Bayesian inferential method is its logical foundation that provides a coherent framework to utilize not only empirical but also scientific information available to a researcher. Prior knowledge arising from scientific background, expert judgment, or previously collected data is used to build a prior distribution which is then combined with current data via the likelihood function to characterize the current state of knowledge using the so-called posterior distribution. Bayesian methods allow the use of models of complex physical phenomena that were previously too difficult to estimate (e.g., using asymptotic approximations). Bayesian methods offer a means of more fully understanding issues that are central to many practical problems by allowing researchers to build integrated models based on hierarchical conditional distributions that can be estimated even with limited amounts of data. Furthermore, advances in numerical integration methods, particularly those based on Monte Carlo methods, have made it possible to compute the optimal Bayes estimators. However, there is a reasonably wide gap between the background of the empirically trained scientists and the full weight of Bayesian statistical inference. Hence, one of the goals of this chapter is to bridge the gap by offering elementary to advanced concepts that emphasize linkages between standard approaches and full probability modeling via Bayesian methods.
Bayesian Two Stage Design Under Model Uncertainty
Neff, Angela R.
1997-01-01
procedures can be used to efficiently generate data for an assumed model. The model assumptions include the model form, the set of regressors and the error distribution. The nature of the response often provides information about the model form and the error distribution. It is more difficult to know, apriori, the specific set of regressors which will best explain the relationship between the response and a set of design (control) variables. Misspecific...
Kypraios, Theodore; Neal, Peter; Prangle, Dennis
2017-05-01
Likelihood-based inference for disease outbreak data can be very challenging due to the inherent dependence of the data and the fact that they are usually incomplete. In this paper we review recent Approximate Bayesian Computation (ABC) methods for the analysis of such data by fitting to them stochastic epidemic models without having to calculate the likelihood of the observed data. We consider both non-temporal and temporal-data and illustrate the methods with a number of examples featuring different models and datasets. In addition, we present extensions to existing algorithms which are easy to implement and provide an improvement to the existing methodology. Finally, R code to implement the algorithms presented in the paper is available on https://github.com/kypraios/epiABC. Copyright © 2016 Elsevier Inc. All rights reserved.
Bayesian estimation of the network autocorrelation model
Dittrich, D.; Leenders, R.T.A.J.; Mulder, J.
2017-01-01
The network autocorrelation model has been extensively used by researchers interested modeling social influence effects in social networks. The most common inferential method in the model is classical maximum likelihood estimation. This approach, however, has known problems such as negative bias of
Bayesian Inference of High-Dimensional Dynamical Ocean Models
Lin, J.; Lermusiaux, P. F. J.; Lolla, S. V. T.; Gupta, A.; Haley, P. J., Jr.
2015-12-01
This presentation addresses a holistic set of challenges in high-dimension ocean Bayesian nonlinear estimation: i) predict the probability distribution functions (pdfs) of large nonlinear dynamical systems using stochastic partial differential equations (PDEs); ii) assimilate data using Bayes' law with these pdfs; iii) predict the future data that optimally reduce uncertainties; and (iv) rank the known and learn the new model formulations themselves. Overall, we allow the joint inference of the state, equations, geometry, boundary conditions and initial conditions of dynamical models. Examples are provided for time-dependent fluid and ocean flows, including cavity, double-gyre and Strait flows with jets and eddies. The Bayesian model inference, based on limited observations, is illustrated first by the estimation of obstacle shapes and positions in fluid flows. Next, the Bayesian inference of biogeochemical reaction equations and of their states and parameters is presented, illustrating how PDE-based machine learning can rigorously guide the selection and discovery of complex ecosystem models. Finally, the inference of multiscale bottom gravity current dynamics is illustrated, motivated in part by classic overflows and dense water formation sites and their relevance to climate monitoring and dynamics. This is joint work with our MSEAS group at MIT.
Non-parametric Bayesian graph models reveal community structure in resting state fMRI.
Andersen, Kasper Winther; Madsen, Kristoffer H; Siebner, Hartwig Roman; Schmidt, Mikkel N; Mørup, Morten; Hansen, Lars Kai
2014-10-15
Modeling of resting state functional magnetic resonance imaging (rs-fMRI) data using network models is of increasing interest. It is often desirable to group nodes into clusters to interpret the communication patterns between nodes. In this study we consider three different nonparametric Bayesian models for node clustering in complex networks. In particular, we test their ability to predict unseen data and their ability to reproduce clustering across datasets. The three generative models considered are the Infinite Relational Model (IRM), Bayesian Community Detection (BCD), and the Infinite Diagonal Model (IDM). The models define probabilities of generating links within and between clusters and the difference between the models lies in the restrictions they impose upon the between-cluster link probabilities. IRM is the most flexible model with no restrictions on the probabilities of links between clusters. BCD restricts the between-cluster link probabilities to be strictly lower than within-cluster link probabilities to conform to the community structure typically seen in social networks. IDM only models a single between-cluster link probability, which can be interpreted as a background noise probability. These probabilistic models are compared against three other approaches for node clustering, namely Infomap, Louvain modularity, and hierarchical clustering. Using 3 different datasets comprising healthy volunteers' rs-fMRI we found that the BCD model was in general the most predictive and reproducible model. This suggests that rs-fMRI data exhibits community structure and furthermore points to the significance of modeling heterogeneous between-cluster link probabilities. Copyright © 2014 Elsevier Inc. All rights reserved.
Operational modal analysis modeling, Bayesian inference, uncertainty laws
Au, Siu-Kui
2017-01-01
This book presents operational modal analysis (OMA), employing a coherent and comprehensive Bayesian framework for modal identification and covering stochastic modeling, theoretical formulations, computational algorithms, and practical applications. Mathematical similarities and philosophical differences between Bayesian and classical statistical approaches to system identification are discussed, allowing their mathematical tools to be shared and their results correctly interpreted. Many chapters can be used as lecture notes for the general topic they cover beyond the OMA context. After an introductory chapter (1), Chapters 2–7 present the general theory of stochastic modeling and analysis of ambient vibrations. Readers are first introduced to the spectral analysis of deterministic time series (2) and structural dynamics (3), which do not require the use of probability concepts. The concepts and techniques in these chapters are subsequently extended to a probabilistic context in Chapter 4 (on stochastic pro...
A localization model to localize multiple sources using Bayesian inference
Dunham, Joshua Rolv
Accurate localization of a sound source in a room setting is important in both psychoacoustics and architectural acoustics. Binaural models have been proposed to explain how the brain processes and utilizes the interaural time differences (ITDs) and interaural level differences (ILDs) of sound waves arriving at the ears of a listener in determining source location. Recent work shows that applying Bayesian methods to this problem is proving fruitful. In this thesis, pink noise samples are convolved with head-related transfer functions (HRTFs) and compared to combinations of one and two anechoic speech signals convolved with different HRTFs or binaural room impulse responses (BRIRs) to simulate room positions. Through exhaustive calculation of Bayesian posterior probabilities and using a maximal likelihood approach, model selection will determine the number of sources present, and parameter estimation will result in azimuthal direction of the source(s).
BayesX: Analyzing Bayesian Structural Additive Regression Models
Directory of Open Access Journals (Sweden)
Andreas Brezger
2005-09-01
Full Text Available There has been much recent interest in Bayesian inference for generalized additive and related models. The increasing popularity of Bayesian methods for these and other model classes is mainly caused by the introduction of Markov chain Monte Carlo (MCMC simulation techniques which allow realistic modeling of complex problems. This paper describes the capabilities of the free software package BayesX for estimating regression models with structured additive predictor based on MCMC inference. The program extends the capabilities of existing software for semiparametric regression included in S-PLUS, SAS, R or Stata. Many model classes well known from the literature are special cases of the models supported by BayesX. Examples are generalized additive (mixed models, dynamic models, varying coefficient models, geoadditive models, geographically weighted regression and models for space-time regression. BayesX supports the most common distributions for the response variable. For univariate responses these are Gaussian, Binomial, Poisson, Gamma, negative Binomial, zero inflated Poisson and zero inflated negative binomial. For multicategorical responses, both multinomial logit and probit models for unordered categories of the response as well as cumulative threshold models for ordered categories can be estimated. Moreover, BayesX allows the estimation of complex continuous time survival and hazard rate models.
Nonparametric Bayesian models through probit stick-breaking processes.
Rodríguez, Abel; Dunson, David B
2011-03-01
We describe a novel class of Bayesian nonparametric priors based on stick-breaking constructions where the weights of the process are constructed as probit transformations of normal random variables. We show that these priors are extremely flexible, allowing us to generate a great variety of models while preserving computational simplicity. Particular emphasis is placed on the construction of rich temporal and spatial processes, which are applied to two problems in finance and ecology.
A Bayesian Combination Forecasting Model for Retail Supply Chain Coordination
Wang, W.J.; Xu, Q.
2014-01-01
Retailing plays an important part in modern economic development, and supply chain coordination is the research focus in retail operations management. This paper reviews the collaborative forecasting process within the framework of the collaborative planning, forecasting and replenishment of retail supply chain. A Bayesian combination forecasting model is proposed to integrate multiple forecasting resources and coordinate forecasting processes among partners in the retail supply chain. Based ...
Shortlist B: A Bayesian model of continuous speech recognition
Norris, D.; McQueen, J.
2008-01-01
A Bayesian model of continuous speech recognition is presented. It is based on Shortlist ( D. Norris, 1994; D. Norris, J. M. McQueen, A. Cutler, & S. Butterfield, 1997) and shares many of its key assumptions: parallel competitive evaluation of multiple lexical hypotheses, phonologically abstract prelexical and lexical representations, a feedforward architecture with no online feedback, and a lexical segmentation algorithm based on the viability of chunks of the input as possible words. Shortl...
Toribo, S.G.; Gray, B.R.; Liang, S.
2011-01-01
The N-mixture model proposed by Royle in 2004 may be used to approximate the abundance and detection probability of animal species in a given region. In 2006, Royle and Dorazio discussed the advantages of using a Bayesian approach in modelling animal abundance and occurrence using a hierarchical N-mixture model. N-mixture models assume replication on sampling sites, an assumption that may be violated when the site is not closed to changes in abundance during the survey period or when nominal replicates are defined spatially. In this paper, we studied the robustness of a Bayesian approach to fitting the N-mixture model for pseudo-replicated count data. Our simulation results showed that the Bayesian estimates for abundance and detection probability are slightly biased when the actual detection probability is small and are sensitive to the presence of extra variability within local sites.
Hierarchical Modelling of Flood Risk for Engineering Decision Analysis
DEFF Research Database (Denmark)
Custer, Rocco
to changing flood risk. In the presence of flood protection structures, flood development depends on the state of all protection structures in the system. As such, hazard is a function not only of rainfall and river discharge, but also of protection structures’ fragility. A methodology for flood risk analysis...... and decision analysis for hierarchical flood protection systems is proposed, which allows for joint consideration of hazard models and fragility models of protection structures. In the implementation of the flood risk analysis methodology several challenges are identified, two of which are addressed...... systems, as well as the implementation of the flood risk analysis methodology and the vulnerability modelling approach are illustrated with an example application. In summary, the present thesis provides a characterisation of hierarchical flood protection systems as well as several methodologies to model...
Petascale Hierarchical Modeling VIA Parallel Execution
Energy Technology Data Exchange (ETDEWEB)
Gelman, Andrew [Principal Investigator
2014-04-14
The research allows more effective model building. By allowing researchers to fit complex models to large datasets in a scalable manner, our algorithms and software enable more effective scientific research. In the new area of “big data,” it is often necessary to fit “big models” to adjust for systematic differences between sample and population. For this task, scalable and efficient model-fitting tools are needed, and these have been achieved with our new Hamiltonian Monte Carlo algorithm, the no-U-turn sampler, and our new C++ program, Stan. In layman’s terms, our research enables researchers to create improved mathematical modes for large and complex systems.
A Bayesian Nonparametric Meta-Analysis Model
Karabatsos, George; Talbott, Elizabeth; Walker, Stephen G.
2015-01-01
In a meta-analysis, it is important to specify a model that adequately describes the effect-size distribution of the underlying population of studies. The conventional normal fixed-effect and normal random-effects models assume a normal effect-size population distribution, conditionally on parameters and covariates. For estimating the mean overall…
A hierarchical model for ordinal matrix factorization
DEFF Research Database (Denmark)
Paquet, Ulrich; Thomson, Blaise; Winther, Ole
2012-01-01
their ratings for other movies. The Netflix data set is used for evaluation, which consists of around 100 million ratings. Using root mean-squared error (RMSE) as an evaluation metric, results show that the suggested model outperforms alternative factorization techniques. Results also show how Gibbs sampling...
An endogenous policy model of hierarchical government
Mazza, I.; van Winden, F.
2008-01-01
Endogenous policy models usually neglect that government policies are frequently the result of decisions taken at different tiers by different agents, each enjoying some degree of autonomy. In this paper, policies are the outcome of the choices made by two agents within a hierarchy. A legislator
A Hierarchical Visualization Analysis Model of Power Big Data
Li, Yongjie; Wang, Zheng; Hao, Yang
2018-01-01
Based on the conception of integrating VR scene and power big data analysis, a hierarchical visualization analysis model of power big data is proposed, in which levels are designed, targeting at different abstract modules like transaction, engine, computation, control and store. The regularly departed modules of power data storing, data mining and analysis, data visualization are integrated into one platform by this model. It provides a visual analysis solution for the power big data.
A simple Bayesian mixture model with a hybrid procedure for genome-wide association studies
Wei, Yu-Chung; Wen, Shu-Hui; Chen, Pei-Chun; Wang, Chih-Hao; Hsiao, Chuhsing K
2010-01-01
Genome-wide association studies often face the undesirable result of either failing to detect any influential markers at all because of a stringent level for testing error corrections or encountering difficulty in quantifying the importance of markers by their P-values. Advocates of estimation procedures prefer to estimate the proportion of association rather than test significance to avoid overinterpretation. Here, we adopt a Bayesian hierarchical mixture model to estimate directly the proportion of influential markers, and then proceed to a selection procedure based on the Bayes factor (BF). This mixture model is able to accommodate different sources of dependence in the data through only a few parameters. Specifically, we focus on a standardized risk measure of unit variance so that fewer parameters are involved in inference. The expected value of this measure follows a mixture distribution with a mixing probability of association, and it is robust to minor allele frequencies. Furthermore, to select promising markers, we use the magnitude of the BF to represent the strength of evidence in support of the association between markers and disease. We demonstrate this procedure both with simulations and with SNP data from studies on rheumatoid arthritis, coronary artery disease, and Crohn's disease obtained from the Wellcome Trust Case–Control Consortium. This Bayesian procedure outperforms other existing methods in terms of accuracy, power, and computational efficiency. The R code that implements this method is available at http://homepage.ntu.edu.tw/~ckhsiao/Bmix/Bmix.htm. PMID:20407469
Distributed Bayesian Piecewise Sparse Linear Models
Asahara, Masato; Fujimaki, Ryohei
2017-01-01
The importance of interpretability of machine learning models has been increasing due to emerging enterprise predictive analytics, threat of data privacy, accountability of artificial intelligence in society, and so on. Piecewise linear models have been actively studied to achieve both accuracy and interpretability. They often produce competitive accuracy against state-of-the-art non-linear methods. In addition, their representations (i.e., rule-based segmentation plus sparse linear formula) ...
A hierarchical modeling framework for multiple observer transect surveys.
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Paul B Conn
Full Text Available Ecologists often use multiple observer transect surveys to census animal populations. In addition to animal counts, these surveys produce sequences of detections and non-detections for each observer. When combined with additional data (i.e. covariates such as distance from the transect line, these sequences provide the additional information to estimate absolute abundance when detectability on the transect line is less than one. Although existing analysis approaches for such data have proven extremely useful, they have some limitations. For instance, it is difficult to extrapolate from observed areas to unobserved areas unless a rigorous sampling design is adhered to; it is also difficult to share information across spatial and temporal domains or to accommodate habitat-abundance relationships. In this paper, we introduce a hierarchical modeling framework for multiple observer line transects that removes these limitations. In particular, abundance intensities can be modeled as a function of habitat covariates, making it easier to extrapolate to unsampled areas. Our approach relies on a complete data representation of the state space, where unobserved animals and their covariates are modeled using a reversible jump Markov chain Monte Carlo algorithm. Observer detections are modeled via a bivariate normal distribution on the probit scale, with dependence induced by a distance-dependent correlation parameter. We illustrate performance of our approach with simulated data and on a known population of golf tees. In both cases, we show that our hierarchical modeling approach yields accurate inference about abundance and related parameters. In addition, we obtain accurate inference about population-level covariates (e.g. group size. We recommend that ecologists consider using hierarchical models when analyzing multiple-observer transect data, especially when it is difficult to rigorously follow pre-specified sampling designs. We provide a new R package
Mohebbi, Mohammadreza; Wolfe, Rory; Forbes, Andrew
2014-01-09
This paper applies the generalised linear model for modelling geographical variation to esophageal cancer incidence data in the Caspian region of Iran. The data have a complex and hierarchical structure that makes them suitable for hierarchical analysis using Bayesian techniques, but with care required to deal with problems arising from counts of events observed in small geographical areas when overdispersion and residual spatial autocorrelation are present. These considerations lead to nine regression models derived from using three probability distributions for count data: Poisson, generalised Poisson and negative binomial, and three different autocorrelation structures. We employ the framework of Bayesian variable selection and a Gibbs sampling based technique to identify significant cancer risk factors. The framework deals with situations where the number of possible models based on different combinations of candidate explanatory variables is large enough such that calculation of posterior probabilities for all models is difficult or infeasible. The evidence from applying the modelling methodology suggests that modelling strategies based on the use of generalised Poisson and negative binomial with spatial autocorrelation work well and provide a robust basis for inference.
Directory of Open Access Journals (Sweden)
Mohammadreza Mohebbi
2014-01-01
Full Text Available This paper applies the generalised linear model for modelling geographical variation to esophageal cancer incidence data in the Caspian region of Iran. The data have a complex and hierarchical structure that makes them suitable for hierarchical analysis using Bayesian techniques, but with care required to deal with problems arising from counts of events observed in small geographical areas when overdispersion and residual spatial autocorrelation are present. These considerations lead to nine regression models derived from using three probability distributions for count data: Poisson, generalised Poisson and negative binomial, and three different autocorrelation structures. We employ the framework of Bayesian variable selection and a Gibbs sampling based technique to identify significant cancer risk factors. The framework deals with situations where the number of possible models based on different combinations of candidate explanatory variables is large enough such that calculation of posterior probabilities for all models is difficult or infeasible. The evidence from applying the modelling methodology suggests that modelling strategies based on the use of generalised Poisson and negative binomial with spatial autocorrelation work well and provide a robust basis for inference.
Mohebbi, Mohammadreza; Wolfe, Rory; Forbes, Andrew
2014-01-01
This paper applies the generalised linear model for modelling geographical variation to esophageal cancer incidence data in the Caspian region of Iran. The data have a complex and hierarchical structure that makes them suitable for hierarchical analysis using Bayesian techniques, but with care required to deal with problems arising from counts of events observed in small geographical areas when overdispersion and residual spatial autocorrelation are present. These considerations lead to nine regression models derived from using three probability distributions for count data: Poisson, generalised Poisson and negative binomial, and three different autocorrelation structures. We employ the framework of Bayesian variable selection and a Gibbs sampling based technique to identify significant cancer risk factors. The framework deals with situations where the number of possible models based on different combinations of candidate explanatory variables is large enough such that calculation of posterior probabilities for all models is difficult or infeasible. The evidence from applying the modelling methodology suggests that modelling strategies based on the use of generalised Poisson and negative binomial with spatial autocorrelation work well and provide a robust basis for inference. PMID:24413702
Directory of Open Access Journals (Sweden)
Fikse Freddy
2010-03-01
Full Text Available Abstract Background The sensitivity to microenvironmental changes varies among animals and may be under genetic control. It is essential to take this element into account when aiming at breeding robust farm animals. Here, linear mixed models with genetic effects in the residual variance part of the model can be used. Such models have previously been fitted using EM and MCMC algorithms. Results We propose the use of double hierarchical generalized linear models (DHGLM, where the squared residuals are assumed to be gamma distributed and the residual variance is fitted using a generalized linear model. The algorithm iterates between two sets of mixed model equations, one on the level of observations and one on the level of variances. The method was validated using simulations and also by re-analyzing a data set on pig litter size that was previously analyzed using a Bayesian approach. The pig litter size data contained 10,060 records from 4,149 sows. The DHGLM was implemented using the ASReml software and the algorithm converged within three minutes on a Linux server. The estimates were similar to those previously obtained using Bayesian methodology, especially the variance components in the residual variance part of the model. Conclusions We have shown that variance components in the residual variance part of a linear mixed model can be estimated using a DHGLM approach. The method enables analyses of animal models with large numbers of observations. An important future development of the DHGLM methodology is to include the genetic correlation between the random effects in the mean and residual variance parts of the model as a parameter of the DHGLM.
Bayesian geostatistical modeling of leishmaniasis incidence in Brazil.
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Dimitrios-Alexios Karagiannis-Voules
Full Text Available BACKGROUND: Leishmaniasis is endemic in 98 countries with an estimated 350 million people at risk and approximately 2 million cases annually. Brazil is one of the most severely affected countries. METHODOLOGY: We applied Bayesian geostatistical negative binomial models to analyze reported incidence data of cutaneous and visceral leishmaniasis in Brazil covering a 10-year period (2001-2010. Particular emphasis was placed on spatial and temporal patterns. The models were fitted using integrated nested Laplace approximations to perform fast approximate Bayesian inference. Bayesian variable selection was employed to determine the most important climatic, environmental, and socioeconomic predictors of cutaneous and visceral leishmaniasis. PRINCIPAL FINDINGS: For both types of leishmaniasis, precipitation and socioeconomic proxies were identified as important risk factors. The predicted number of cases in 2010 were 30,189 (standard deviation [SD]: 7,676 for cutaneous leishmaniasis and 4,889 (SD: 288 for visceral leishmaniasis. Our risk maps predicted the highest numbers of infected people in the states of Minas Gerais and Pará for visceral and cutaneous leishmaniasis, respectively. CONCLUSIONS/SIGNIFICANCE: Our spatially explicit, high-resolution incidence maps identified priority areas where leishmaniasis control efforts should be targeted with the ultimate goal to reduce disease incidence.
Bayesian Model for Optimization Adaptive E-Learning Process
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F. J. Tapia
2008-06-01
Full Text Available In this paper, a Bayesian-Network-based model isproposed to optimize the Global Adaptive e-LearningProcess (GAeLP. This model determines the type ofpersonalization required for a learner according to his orher real needs, in which we have considered both objectsand objectives of personalization. Furthermore, cause-andeffectrelations among these objects and objectives with thelearning phases, the learner, and the Intelligent TutorialSystem (ITS are accomplished. These cause-and-effectrelations were coded into a Bayesian Network (BN, suchthat it involves the entire GAeLP. Four fundamental phasesthat have a direct effect in the learner’s learning process areconsidered: Learner’s previous knowledge Phase, Learner’sProgress Knowledge Phase, Learner’s /Teacher’s Aims andGoals Phase, and Navigation Preferences and ExperiencesPhase. The efficacy of the Bayesian networks is proventhrough the first phase, in which learners of differentknowledge area were select. The main results in this workare: causal relations among objects and objectives ofpersonalization, knowledge phases, learner and electronicsystem. Personalization profiles set and their probabilities inthe first phase were obtained to diagnose the type ofpersonalization of the learner.
Sparse Bayesian modeling with adaptive kernel learning.
Tzikas, Dimitris G; Likas, Aristidis C; Galatsanos, Nikolaos P
2009-06-01
Sparse kernel methods are very efficient in solving regression and classification problems. The sparsity and performance of these methods depend on selecting an appropriate kernel function, which is typically achieved using a cross-validation procedure. In this paper, we propose an incremental method for supervised learning, which is similar to the relevance vector machine (RVM) but also learns the parameters of the kernels during model training. Specifically, we learn different parameter values for each kernel, resulting in a very flexible model. In order to avoid overfitting, we use a sparsity enforcing prior that controls the effective number of parameters of the model. We present experimental results on artificial data to demonstrate the advantages of the proposed method and we provide a comparison with the typical RVM on several commonly used regression and classification data sets.
Hierarchical Model Predictive Control for Resource Distribution
DEFF Research Database (Denmark)
Bendtsen, Jan Dimon; Trangbæk, K; Stoustrup, Jakob
2010-01-01
This paper deals with hierarchichal model predictive control (MPC) of distributed systems. A three level hierachical approach is proposed, consisting of a high level MPC controller, a second level of so-called aggregators, controlled by an online MPC-like algorithm, and a lower level of autonomous...... units. The approach is inspired by smart-grid electric power production and consumption systems, where the flexibility of a large number of power producing and/or power consuming units can be exploited in a smart-grid solution. The objective is to accommodate the load variation on the grid, arising...... facilitates plug-and-play addition of subsystems without redesign of any controllers. The method is supported by a number of simulations featuring a three-level smart-grid power control system for a small isolated power grid....
Hierarchical spatial models for predicting pygmy rabbit distribution and relative abundance
Wilson, T.L.; Odei, J.B.; Hooten, M.B.; Edwards, T.C.
2010-01-01
Conservationists routinely use species distribution models to plan conservation, restoration and development actions, while ecologists use them to infer process from pattern. These models tend to work well for common or easily observable species, but are of limited utility for rare and cryptic species. This may be because honest accounting of known observation bias and spatial autocorrelation are rarely included, thereby limiting statistical inference of resulting distribution maps. We specified and implemented a spatially explicit Bayesian hierarchical model for a cryptic mammal species (pygmy rabbit Brachylagus idahoensis). Our approach used two levels of indirect sign that are naturally hierarchical (burrows and faecal pellets) to build a model that allows for inference on regression coefficients as well as spatially explicit model parameters. We also produced maps of rabbit distribution (occupied burrows) and relative abundance (number of burrows expected to be occupied by pygmy rabbits). The model demonstrated statistically rigorous spatial prediction by including spatial autocorrelation and measurement uncertainty. We demonstrated flexibility of our modelling framework by depicting probabilistic distribution predictions using different assumptions of pygmy rabbit habitat requirements. Spatial representations of the variance of posterior predictive distributions were obtained to evaluate heterogeneity in model fit across the spatial domain. Leave-one-out cross-validation was conducted to evaluate the overall model fit. Synthesis and applications. Our method draws on the strengths of previous work, thereby bridging and extending two active areas of ecological research: species distribution models and multi-state occupancy modelling. Our framework can be extended to encompass both larger extents and other species for which direct estimation of abundance is difficult. ?? 2010 The Authors. Journal compilation ?? 2010 British Ecological Society.
A personalised thermal comfort model using a Bayesian network
Auffenberg, Frederik; Stein, Sebastian; Rogers, Alex
2015-01-01
In this paper, we address the challenge of predicting optimal comfort temperatures of individual users of a smart heating system. At present, such systems use simple models of user comfort when deciding on a set point temperature. These models generally fail to adapt to an individual user’s preferences, resulting in poor estimates of a user’s preferred temperature. To address this issue, we propose a personalised thermal comfort model that uses a Bayesian network to learn and adapt to a user’...
A Bayesian Network View on Nested Effects Models
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Fröhlich Holger
2009-01-01
Full Text Available Nested effects models (NEMs are a class of probabilistic models that were designed to reconstruct a hidden signalling structure from a large set of observable effects caused by active interventions into the signalling pathway. We give a more flexible formulation of NEMs in the language of Bayesian networks. Our framework constitutes a natural generalization of the original NEM model, since it explicitly states the assumptions that are tacitly underlying the original version. Our approach gives rise to new learning methods for NEMs, which have been implemented in the /Bioconductor package nem. We validate these methods in a simulation study and apply them to a synthetic lethality dataset in yeast.
Bayesian inference and model comparison for metallic fatigue data
Babuška, Ivo
2016-02-23
In this work, we present a statistical treatment of stress-life (S-N) data drawn from a collection of records of fatigue experiments that were performed on 75S-T6 aluminum alloys. Our main objective is to predict the fatigue life of materials by providing a systematic approach to model calibration, model selection and model ranking with reference to S-N data. To this purpose, we consider fatigue-limit models and random fatigue-limit models that are specially designed to allow the treatment of the run-outs (right-censored data). We first fit the models to the data by maximum likelihood methods and estimate the quantiles of the life distribution of the alloy specimen. To assess the robustness of the estimation of the quantile functions, we obtain bootstrap confidence bands by stratified resampling with respect to the cycle ratio. We then compare and rank the models by classical measures of fit based on information criteria. We also consider a Bayesian approach that provides, under the prior distribution of the model parameters selected by the user, their simulation-based posterior distributions. We implement and apply Bayesian model comparison methods, such as Bayes factor ranking and predictive information criteria based on cross-validation techniques under various a priori scenarios.
DPpackage: Bayesian Semi- and Nonparametric Modeling in R
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Alejandro Jara
2011-04-01
Full Text Available Data analysis sometimes requires the relaxation of parametric assumptions in order to gain modeling flexibility and robustness against mis-specification of the probability model. In the Bayesian context, this is accomplished by placing a prior distribution on a function space, such as the space of all probability distributions or the space of all regression functions. Unfortunately, posterior distributions ranging over function spaces are highly complex and hence sampling methods play a key role. This paper provides an introduction to a simple, yet comprehensive, set of programs for the implementation of some Bayesian nonparametric and semiparametric models in R, DPpackage. Currently, DPpackage includes models for marginal and conditional density estimation, receiver operating characteristic curve analysis, interval-censored data, binary regression data, item response data, longitudinal and clustered data using generalized linear mixed models, and regression data using generalized additive models. The package also contains functions to compute pseudo-Bayes factors for model comparison and for eliciting the precision parameter of the Dirichlet process prior, and a general purpose Metropolis sampling algorithm. To maximize computational efficiency, the actual sampling for each model is carried out using compiled C, C++ or Fortran code.
Hierarchical stochastic model of terrain subsidence during tunnel excavation
Janda, Tomáš; Šejnoha, Jiří; Šejnoha, Michal
2017-09-01
In this contribution the Bayesian statistical method is applied to assess the expected probability distribution of the terrain subsidence in the course of tunnel excavation. The approach utilizes a number of simplifying assumptions regarding the system kinematics to arrive at a very simple model with just a few degrees of freedom. This deterministic model together with the intrinsic uncertainties of its parameters and measurement inaccuracies are used to formulate the stochastic model which defines a distribution of the predicted values of terrain subsidence. Assuming the measured data to be fixed, the stochastic model thus defines the likelihood function of the model parameters which is directly used for updating their prior distribution. This way the model parameters can be incrementally updated with each excavation step and the prediction of the model refined.
Hierarchical models and the analysis of bird survey information
Sauer, J.R.; Link, W.A.
2003-01-01
Management of birds often requires analysis of collections of estimates. We describe a hierarchical modeling approach to the analysis of these data, in which parameters associated with the individual species estimates are treated as random variables, and probability statements are made about the species parameters conditioned on the data. A Markov-Chain Monte Carlo (MCMC) procedure is used to fit the hierarchical model. This approach is computer intensive, and is based upon simulation. MCMC allows for estimation both of parameters and of derived statistics. To illustrate the application of this method, we use the case in which we are interested in attributes of a collection of estimates of population change. Using data for 28 species of grassland-breeding birds from the North American Breeding Bird Survey, we estimate the number of species with increasing populations, provide precision-adjusted rankings of species trends, and describe a measure of population stability as the probability that the trend for a species is within a certain interval. Hierarchical models can be applied to a variety of bird survey applications, and we are investigating their use in estimation of population change from survey data.
Bayesian analysis of physiologically based toxicokinetic and toxicodynamic models.
Hack, C Eric
2006-04-17
Physiologically based toxicokinetic (PBTK) and toxicodynamic (TD) models of bromate in animals and humans would improve our ability to accurately estimate the toxic doses in humans based on available animal studies. These mathematical models are often highly parameterized and must be calibrated in order for the model predictions of internal dose to adequately fit the experimentally measured doses. Highly parameterized models are difficult to calibrate and it is difficult to obtain accurate estimates of uncertainty or variability in model parameters with commonly used frequentist calibration methods, such as maximum likelihood estimation (MLE) or least squared error approaches. The Bayesian approach called Markov chain Monte Carlo (MCMC) analysis can be used to successfully calibrate these complex models. Prior knowledge about the biological system and associated model parameters is easily incorporated in this approach in the form of prior parameter distributions, and the distributions are refined or updated using experimental data to generate posterior distributions of parameter estimates. The goal of this paper is to give the non-mathematician a brief description of the Bayesian approach and Markov chain Monte Carlo analysis, how this technique is used in risk assessment, and the issues associated with this approach.
A Bayesian Combination Forecasting Model for Retail Supply Chain Coordination
Directory of Open Access Journals (Sweden)
W.J. Wang
2014-04-01
Full Text Available Retailing plays an important part in modern economic development, and supply chain coordination is the research focus in retail operations management. This paper reviews the collaborative forecasting process within the framework of the collaborative planning, forecasting and replenishment of retail supply chain. A Bayesian combination forecasting model is proposed to integrate multiple forecasting resources and coordinate forecasting processes among partners in the retail supply chain. Based on simulation results for retail sales, the effectiveness of this combination forecasting model is demonstrated for coordinating the collaborative forecasting processes, resulting in an improvement of demand forecasting accuracy in the retail supply chain.
A Bayesian Generative Model for Surface Template Estimation
Directory of Open Access Journals (Sweden)
Jun Ma
2010-01-01
Full Text Available 3D surfaces are important geometric models for many objects of interest in image analysis and Computational Anatomy. In this paper, we describe a Bayesian inference scheme for estimating a template surface from a set of observed surface data. In order to achieve this, we use the geodesic shooting approach to construct a statistical model for the generation and the observations of random surfaces. We develop a mode approximation EM algorithm to infer the maximum a posteriori estimation of initial momentum μ, which determines the template surface. Experimental results of caudate, thalamus, and hippocampus data are presented.
Genealogical Working Distributions for Bayesian Model Testing with Phylogenetic Uncertainty.
Baele, Guy; Lemey, Philippe; Suchard, Marc A
2016-03-01
Marginal likelihood estimates to compare models using Bayes factors frequently accompany Bayesian phylogenetic inference. Approaches to estimate marginal likelihoods have garnered increased attention over the past decade. In particular, the introduction of path sampling (PS) and stepping-stone sampling (SS) into Bayesian phylogenetics has tremendously improved the accuracy of model selection. These sampling techniques are now used to evaluate complex evolutionary and population genetic models on empirical data sets, but considerable computational demands hamper their widespread adoption. Further, when very diffuse, but proper priors are specified for model parameters, numerical issues complicate the exploration of the priors, a necessary step in marginal likelihood estimation using PS or SS. To avoid such instabilities, generalized SS (GSS) has recently been proposed, introducing the concept of "working distributions" to facilitate--or shorten--the integration process that underlies marginal likelihood estimation. However, the need to fix the tree topology currently limits GSS in a coalescent-based framework. Here, we extend GSS by relaxing the fixed underlying tree topology assumption. To this purpose, we introduce a "working" distribution on the space of genealogies, which enables estimating marginal likelihoods while accommodating phylogenetic uncertainty. We propose two different "working" distributions that help GSS to outperform PS and SS in terms of accuracy when comparing demographic and evolutionary models applied to synthetic data and real-world examples. Further, we show that the use of very diffuse priors can lead to a considerable overestimation in marginal likelihood when using PS and SS, while still retrieving the correct marginal likelihood using both GSS approaches. The methods used in this article are available in BEAST, a powerful user-friendly software package to perform Bayesian evolutionary analyses. © The Author(s) 2015. Published by Oxford
A new approach for modeling generalization gradients: a case for hierarchical models
Vanbrabant, Koen; Boddez, Yannick; Verduyn, Philippe; Mestdagh, Merijn; Hermans, Dirk; Raes, Filip
2015-01-01
A case is made for the use of hierarchical models in the analysis of generalization gradients. Hierarchical models overcome several restrictions that are imposed by repeated measures analysis-of-variance (rANOVA), the default statistical method in current generalization research. More specifically, hierarchical models allow to include continuous independent variables and overcomes problematic assumptions such as sphericity. We focus on how generalization research can benefit from this added flexibility. In a simulation study we demonstrate the dominance of hierarchical models over rANOVA. In addition, we show the lack of efficiency of the Mauchly's sphericity test in sample sizes typical for generalization research, and confirm how violations of sphericity increase the probability of type I errors. A worked example of a hierarchical model is provided, with a specific emphasis on the interpretation of parameters relevant for generalization research. PMID:26074834
Geometrical destabilization, premature end of inflation and Bayesian model selection
Renaux-Petel, Sébastien; Turzyński, Krzysztof; Vennin, Vincent
2017-11-01
By means of Bayesian techniques, we study how a premature ending of inflation, motivated by geometrical destabilization, affects the observational evidences of typical inflationary models. Large-field models are worsened, and inflection point potentials are drastically improved for a specific range of the field-space curvature characterizing the geometrical destabilization. For other models we observe shifts in the preferred values of the model parameters. For quartic hilltop models for instance, contrary to the standard case, we find preference for theoretically natural sub-Planckian hill widths. Eventually, the Bayesian ranking of models becomes substantially reordered with a premature end of inflation. Such a phenomenon also modifies the constraints on the reheating expansion history, which has to be properly accounted for since it determines the position of the observational window with respect to the end of inflation. Our results demonstrate how the interpretation of cosmological data in terms of fundamental physics is considerably modified in the presence of premature end of inflation mechanisms.
A Bayesian subgroup analysis using collections of ANOVA models.
Liu, Jinzhong; Sivaganesan, Siva; Laud, Purushottam W; Müller, Peter
2017-07-01
We develop a Bayesian approach to subgroup analysis using ANOVA models with multiple covariates, extending an earlier work. We assume a two-arm clinical trial with normally distributed response variable. We also assume that the covariates for subgroup finding are categorical and are a priori specified, and parsimonious easy-to-interpret subgroups are preferable. We represent the subgroups of interest by a collection of models and use a model selection approach to finding subgroups with heterogeneous effects. We develop suitable priors for the model space and use an objective Bayesian approach that yields multiplicity adjusted posterior probabilities for the models. We use a structured algorithm based on the posterior probabilities of the models to determine which subgroup effects to report. Frequentist operating characteristics of the approach are evaluated using simulation. While our approach is applicable in more general cases, we mainly focus on the 2 × 2 case of two covariates each at two levels for ease of presentation. The approach is illustrated using a real data example. © 2017 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim.
Energy Technology Data Exchange (ETDEWEB)
Zhang, Guannan [ORNL; Webster, Clayton G [ORNL; Gunzburger, Max D [ORNL
2012-09-01
Although Bayesian analysis has become vital to the quantification of prediction uncertainty in groundwater modeling, its application has been hindered due to the computational cost associated with numerous model executions needed for exploring the posterior probability density function (PPDF) of model parameters. This is particularly the case when the PPDF is estimated using Markov Chain Monte Carlo (MCMC) sampling. In this study, we develop a new approach that improves computational efficiency of Bayesian inference by constructing a surrogate system based on an adaptive sparse-grid high-order stochastic collocation (aSG-hSC) method. Unlike previous works using first-order hierarchical basis, we utilize a compactly supported higher-order hierar- chical basis to construct the surrogate system, resulting in a significant reduction in the number of computational simulations required. In addition, we use hierarchical surplus as an error indi- cator to determine adaptive sparse grids. This allows local refinement in the uncertain domain and/or anisotropic detection with respect to the random model parameters, which further improves computational efficiency. Finally, we incorporate a global optimization technique and propose an iterative algorithm for building the surrogate system for the PPDF with multiple significant modes. Once the surrogate system is determined, the PPDF can be evaluated by sampling the surrogate system directly with very little computational cost. The developed method is evaluated first using a simple analytical density function with multiple modes and then using two synthetic groundwater reactive transport models. The groundwater models represent different levels of complexity; the first example involves coupled linear reactions and the second example simulates nonlinear ura- nium surface complexation. The results show that the aSG-hSC is an effective and efficient tool for Bayesian inference in groundwater modeling in comparison with conventional
Forecasting natural gas consumption in China by Bayesian Model Averaging
Directory of Open Access Journals (Sweden)
Wei Zhang
2015-11-01
Full Text Available With rapid growth of natural gas consumption in China, it is in urgent need of more accurate and reliable models to make a reasonable forecast. Considering the limitations of the single model and the model uncertainty, this paper presents a combinative method to forecast natural gas consumption by Bayesian Model Averaging (BMA. It can effectively handle the uncertainty associated with model structure and parameters, and thus improves the forecasting accuracy. This paper chooses six variables for forecasting the natural gas consumption, including GDP, urban population, energy consumption structure, industrial structure, energy efficiency and exports of goods and services. The results show that comparing to Gray prediction model, Linear regression model and Artificial neural networks, the BMA method provides a flexible tool to forecast natural gas consumption that will have a rapid growth in the future. This study can provide insightful information on natural gas consumption in the future.
Bayesian model averaging of naive Bayes for clustering.
Santafé, Guzmán; Lozano, Jose A; Larrañaga, Pedro
2006-10-01
This paper considers a Bayesian model-averaging (MA) approach to learn an unsupervised naive Bayes classification model. By using the expectation model-averaging (EMA) algorithm, which is proposed in this paper, a unique naive Bayes model that approximates an MA over selective naive Bayes structures is obtained. This algorithm allows to obtain the parameters for the approximate MA clustering model in the same time complexity needed to learn the maximum-likelihood model with the expectation-maximization algorithm. On the other hand, the proposed method can also be regarded as an approach to an unsupervised feature subset selection due to the fact that the model obtained by the EMA algorithm incorporates information on how dependent every predictive variable is on the cluster variable.
Hierarchical Heteroclinics in Dynamical Model of Cognitive Processes: Chunking
Afraimovich, Valentin S.; Young, Todd R.; Rabinovich, Mikhail I.
Combining the results of brain imaging and nonlinear dynamics provides a new hierarchical vision of brain network functionality that is helpful in understanding the relationship of the network to different mental tasks. Using these ideas it is possible to build adequate models for the description and prediction of different cognitive activities in which the number of variables is usually small enough for analysis. The dynamical images of different mental processes depend on their temporal organization and, as a rule, cannot be just simple attractors since cognition is characterized by transient dynamics. The mathematical image for a robust transient is a stable heteroclinic channel consisting of a chain of saddles connected by unstable separatrices. We focus here on hierarchical chunking dynamics that can represent several cognitive activities. Chunking is the dynamical phenomenon that means dividing a long information chain into shorter items. Chunking is known to be important in many processes of perception, learning, memory and cognition. We prove that in the phase space of the model that describes chunking there exists a new mathematical object — heteroclinic sequence of heteroclinic cycles — using the technique of slow-fast approximations. This new object serves as a skeleton of motions reflecting sequential features of hierarchical chunking dynamics and is an adequate image of the chunking processing.
Directory of Open Access Journals (Sweden)
Hashem Salarzadeh Jenatabadi
2016-11-01
Full Text Available There are many factors which could influence the sustainability of airlines. The main purpose of this study is to introduce a framework for a financial sustainability index and model it based on structural equation modeling (SEM with maximum likelihood and Bayesian predictors. The introduced framework includes economic performance, operational performance, cost performance, and financial performance. Based on both Bayesian SEM (Bayesian-SEM and Classical SEM (Classical-SEM, it was found that economic performance with both operational performance and cost performance are significantly related to the financial performance index. The four mathematical indices employed are root mean square error, coefficient of determination, mean absolute error, and mean absolute percentage error to compare the efficiency of Bayesian-SEM and Classical-SEM in predicting the airline financial performance. The outputs confirmed that the framework with Bayesian prediction delivered a good fit with the data, although the framework predicted with a Classical-SEM approach did not prepare a well-fitting model. The reasons for this discrepancy between Classical and Bayesian predictions, as well as the potential advantages and caveats with the application of Bayesian approach in airline sustainability studies, are debated.
Quantum-Like Bayesian Networks for Modeling Decision Making
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Catarina eMoreira
2016-01-01
Full Text Available In this work, we explore an alternative quantum structure to perform quantum probabilistic inferences to accommodate the paradoxical findings of the Sure Thing Principle. We propose a Quantum-Like Bayesian Network, which consists in replacing classical probabilities by quantum probability amplitudes. However, since this approach suffers from the problem of exponential growth of quantum parameters, we also propose a similarity heuristic that automatically fits quantum parameters through vector similarities. This makes the proposed model general and predictive in contrast to the current state of the art models, which cannot be generalized for more complex decision scenarios and that only provide an explanatory nature for the observed paradoxes. In the end, the model that we propose consists in a nonparametric method for estimating inference effects from a statistical point of view. It is a statistical model that is simpler than the previous quantum dynamic and quantum-like models proposed in the literature. We tested the proposed network with several empirical data from the literature, mainly from the Prisoner's Dilemma game and the Two Stage Gambling game. The results obtained show that the proposed quantum Bayesian Network is a general method that can accommodate violations of the laws of classical probability theory and make accurate predictions regarding human decision-making in these scenarios.
Bayesian Modeling of Biomolecular Assemblies with Cryo-EM Maps.
Habeck, Michael
2017-01-01
A growing array of experimental techniques allows us to characterize the three-dimensional structure of large biological assemblies at increasingly higher resolution. In addition to X-ray crystallography and nuclear magnetic resonance in solution, new structure determination methods such cryo-electron microscopy (cryo-EM), crosslinking/mass spectrometry and solid-state NMR have emerged. Often it is not sufficient to use a single experimental method, but complementary data need to be collected by using multiple techniques. The integration of all datasets can only be achieved by computational means. This article describes Inferential structure determination, a Bayesian approach to integrative modeling of biomolecular complexes with hybrid structural data. I will introduce probabilistic models for cryo-EM maps and outline Markov chain Monte Carlo algorithms for sampling model structures from the posterior distribution. I will focus on rigid and flexible modeling with cryo-EM data and discuss some of the computational challenges of Bayesian inference in the context of biomolecular modeling.
From qualitative reasoning models to Bayesian-based learner modeling
Milošević, U.; Bredeweg, B.; de Kleer, J.; Forbus, K.D.
2010-01-01
Assessing the knowledge of a student is a fundamental part of intelligent learning environments. We present a Bayesian network based approach to dealing with uncertainty when estimating a learner’s state of knowledge in the context of Qualitative Reasoning (QR). A proposal for a global architecture
Experimental validation of a Bayesian model of visual acuity.
LENUS (Irish Health Repository)
Dalimier, Eugénie
2009-01-01
Based on standard procedures used in optometry clinics, we compare measurements of visual acuity for 10 subjects (11 eyes tested) in the presence of natural ocular aberrations and different degrees of induced defocus, with the predictions given by a Bayesian model customized with aberrometric data of the eye. The absolute predictions of the model, without any adjustment, show good agreement with the experimental data, in terms of correlation and absolute error. The efficiency of the model is discussed in comparison with image quality metrics and other customized visual process models. An analysis of the importance and customization of each stage of the model is also given; it stresses the potential high predictive power from precise modeling of ocular and neural transfer functions.
Bayesian Model Comparison With the g-Prior
DEFF Research Database (Denmark)
Nielsen, Jesper Kjær; Christensen, Mads Græsbøll; Cemgil, Ali Taylan
2014-01-01
Model comparison and selection is an important problem in many model-based signal processing applications. Often, very simple information criteria such as the Akaike information criterion or the Bayesian information criterion are used despite their shortcomings. Compared to these methods, Djuric......, and develop new model selection rules for a regression model containing both linear and non-linear parameters. Moreover, we use this framework to give a new interpretation of the popular information criteria and relate their performance to the signal-to-noise ratio of the data. By use of simulations, we also...... demonstrate that our proposed model comparison and selection rules outperform the traditional information criteria both in terms of detecting the true model and in terms of predicting unobserved data. The simulation code is available online....
Bayesian Predictive Inference of a Proportion Under a Twofold Small-Area Model
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Nandram Balgobin
2016-03-01
Full Text Available We extend the twofold small-area model of Stukel and Rao (1997; 1999 to accommodate binary data. An example is the Third International Mathematics and Science Study (TIMSS, in which pass-fail data for mathematics of students from US schools (clusters are available at the third grade by regions and communities (small areas. We compare the finite population proportions of these small areas. We present a hierarchical Bayesian model in which the firststage binary responses have independent Bernoulli distributions, and each subsequent stage is modeled using a beta distribution, which is parameterized by its mean and a correlation coefficient. This twofold small-area model has an intracluster correlation at the first stage and an intercluster correlation at the second stage. The final-stage mean and all correlations are assumed to be noninformative independent random variables. We show how to infer the finite population proportion of each area. We have applied our models to synthetic TIMSS data to show that the twofold model is preferred over a onefold small-area model that ignores the clustering within areas. We further compare these models using a simulation study, which shows that the intracluster correlation is particularly important.
Bayesian statistic methods and theri application in probabilistic simulation models
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Sergio Iannazzo
2007-03-01
Full Text Available Bayesian statistic methods are facing a rapidly growing level of interest and acceptance in the field of health economics. The reasons of this success are probably to be found on the theoretical fundaments of the discipline that make these techniques more appealing to decision analysis. To this point should be added the modern IT progress that has developed different flexible and powerful statistical software framework. Among them probably one of the most noticeably is the BUGS language project and its standalone application for MS Windows WinBUGS. Scope of this paper is to introduce the subject and to show some interesting applications of WinBUGS in developing complex economical models based on Markov chains. The advantages of this approach reside on the elegance of the code produced and in its capability to easily develop probabilistic simulations. Moreover an example of the integration of bayesian inference models in a Markov model is shown. This last feature let the analyst conduce statistical analyses on the available sources of evidence and exploit them directly as inputs in the economic model.
Crimmins, Shawn M.; Walleser, Liza R.; Hertel, Dan R.; McKann, Patrick C.; Rohweder, Jason J.; Thogmartin, Wayne E.
2016-01-01
There is growing need to develop models of spatial patterns in animal abundance, yet comparatively few examples of such models exist. This is especially true in situations where the abundance of one species may inhibit that of another, such as the intensively-farmed landscape of the Prairie Pothole Region (PPR) of the central United States, where waterfowl production is largely constrained by mesocarnivore nest predation. We used a hierarchical Bayesian approach to relate the distribution of various land-cover types to the relative abundances of four mesocarnivores in the PPR: coyote Canis latrans, raccoon Procyon lotor, red fox Vulpes vulpes, and striped skunk Mephitis mephitis. We developed models for each species at multiple spatial resolutions (41.4 km2, 10.4 km2, and 2.6 km2) to address different ecological and management-related questions. Model results for each species were similar irrespective of resolution. We found that the amount of row-crop agriculture was nearly ubiquitous in our best models, exhibiting a positive relationship with relative abundance for each species. The amount of native grassland land-cover was positively associated with coyote and raccoon relative abundance, but generally absent from models for red fox and skunk. Red fox and skunk were positively associated with each other, suggesting potential niche overlap. We found no evidence that coyote abundance limited that of other mesocarnivore species, as might be expected under a hypothesis of mesopredator release. The relationships between relative abundance and land-cover types were similar across spatial resolutions. Our results indicated that mesocarnivores in the PPR are most likely to occur in portions of the landscape with large amounts of agricultural land-cover. Further, our results indicated that track-survey data can be used in a hierarchical framework to gain inferences regarding spatial patterns in animal relative abundance.
Unsupervised Modeling of Objects and Their Hierarchical Contextual Interactions
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Tsuhan Chen
2009-01-01
Full Text Available A successful representation of objects in literature is as a collection of patches, or parts, with a certain appearance and position. The relative locations of the different parts of an object are constrained by the geometry of the object. Going beyond a single object, consider a collection of images of a particular scene category containing multiple (recurring objects. The parts belonging to different objects are not constrained by such a geometry. However, the objects themselves, arguably due to their semantic relationships, demonstrate a pattern in their relative locations. Hence, analyzing the interactions among the parts across the collection of images can allow for extraction of the foreground objects, and analyzing the interactions among these objects can allow for a semantically meaningful grouping of these objects, which characterizes the entire scene. These groupings are typically hierarchical. We introduce hierarchical semantics of objects (hSO that captures this hierarchical grouping. We propose an approach for the unsupervised learning of the hSO from a collection of images of a particular scene. We also demonstrate the use of the hSO in providing context for enhanced object localization in the presence of significant occlusions, and show its superior performance over a fully connected graphical model for the same task.
Wu, Haiyan
2013-01-01
General diagnostic models (GDMs) and Bayesian networks are mathematical frameworks that cover a wide variety of psychometric models. Both extend latent class models, and while GDMs also extend item response theory (IRT) models, Bayesian networks can be parameterized using discretized IRT. The purpose of this study is to examine similarities and…
A hierarchical model for estimating density in camera-trap studies
Royle, J. Andrew; Nichols, James D.; Karanth, K.Ullas; Gopalaswamy, Arjun M.
2009-01-01
Estimating animal density using capture–recapture data from arrays of detection devices such as camera traps has been problematic due to the movement of individuals and heterogeneity in capture probability among them induced by differential exposure to trapping.We develop a spatial capture–recapture model for estimating density from camera-trapping data which contains explicit models for the spatial point process governing the distribution of individuals and their exposure to and detection by traps.We adopt a Bayesian approach to analysis of the hierarchical model using the technique of data augmentation.The model is applied to photographic capture–recapture data on tigers Panthera tigris in Nagarahole reserve, India. Using this model, we estimate the density of tigers to be 14·3 animals per 100 km2 during 2004.Synthesis and applications. Our modelling framework largely overcomes several weaknesses in conventional approaches to the estimation of animal density from trap arrays. It effectively deals with key problems such as individual heterogeneity in capture probabilities, movement of traps, presence of potential ‘holes’ in the array and ad hoc estimation of sample area. The formulation, thus, greatly enhances flexibility in the conduct of field surveys as well as in the analysis of data, from studies that may involve physical, photographic or DNA-based ‘captures’ of individual animals.
Bayesian Learning of a Language Model from Continuous Speech
Neubig, Graham; Mimura, Masato; Mori, Shinsuke; Kawahara, Tatsuya
We propose a novel scheme to learn a language model (LM) for automatic speech recognition (ASR) directly from continuous speech. In the proposed method, we first generate phoneme lattices using an acoustic model with no linguistic constraints, then perform training over these phoneme lattices, simultaneously learning both lexical units and an LM. As a statistical framework for this learning problem, we use non-parametric Bayesian statistics, which make it possible to balance the learned model's complexity (such as the size of the learned vocabulary) and expressive power, and provide a principled learning algorithm through the use of Gibbs sampling. Implementation is performed using weighted finite state transducers (WFSTs), which allow for the simple handling of lattice input. Experimental results on natural, adult-directed speech demonstrate that LMs built using only continuous speech are able to significantly reduce ASR phoneme error rates. The proposed technique of joint Bayesian learning of lexical units and an LM over lattices is shown to significantly contribute to this improvement.
Bayesian inference for generalized linear models for spiking neurons
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Sebastian Gerwinn
2010-05-01
Full Text Available Generalized Linear Models (GLMs are commonly used statistical methods for modelling the relationship between neural population activity and presented stimuli. When the dimension of the parameter space is large, strong regularization has to be used in order to fit GLMs to datasets of realistic size without overfitting. By imposing properly chosen priors over parameters, Bayesian inference provides an effective and principled approach for achieving regularization. Here we show how the posterior distribution over model parameters of GLMs can be approximated by a Gaussian using the Expectation Propagation algorithm. In this way, we obtain an estimate of the posterior mean and posterior covariance, allowing us to calculate Bayesian confidence intervals that characterize the uncertainty about the optimal solution. From the posterior we also obtain a different point estimate, namely the posterior mean as opposed to the commonly used maximum a posteriori estimate. We systematically compare the different inference techniques on simulated as well as on multi-electrode recordings of retinal ganglion cells, and explore the effects of the chosen prior and the performance measure used. We find that good performance can be achieved by choosing an Laplace prior together with the posterior mean estimate.
Enhancing debris flow modeling parameters integrating Bayesian networks
Graf, C.; Stoffel, M.; Grêt-Regamey, A.
2009-04-01
Applied debris-flow modeling requires suitably constraint input parameter sets. Depending on the used model, there is a series of parameters to define before running the model. Normally, the data base describing the event, the initiation conditions, the flow behavior, the deposition process and mainly the potential range of possible debris flow events in a certain torrent is limited. There are only some scarce places in the world, where we fortunately can find valuable data sets describing event history of debris flow channels delivering information on spatial and temporal distribution of former flow paths and deposition zones. Tree-ring records in combination with detailed geomorphic mapping for instance provide such data sets over a long time span. Considering the significant loss potential associated with debris-flow disasters, it is crucial that decisions made in regard to hazard mitigation are based on a consistent assessment of the risks. This in turn necessitates a proper assessment of the uncertainties involved in the modeling of the debris-flow frequencies and intensities, the possible run out extent, as well as the estimations of the damage potential. In this study, we link a Bayesian network to a Geographic Information System in order to assess debris-flow risk. We identify the major sources of uncertainty and show the potential of Bayesian inference techniques to improve the debris-flow model. We model the flow paths and deposition zones of a highly active debris-flow channel in the Swiss Alps using the numerical 2-D model RAMMS. Because uncertainties in run-out areas cause large changes in risk estimations, we use the data of flow path and deposition zone information of reconstructed debris-flow events derived from dendrogeomorphological analysis covering more than 400 years to update the input parameters of the RAMMS model. The probabilistic model, which consistently incorporates this available information, can serve as a basis for spatial risk
Recursive Bayesian recurrent neural networks for time-series modeling.
Mirikitani, Derrick T; Nikolaev, Nikolay
2010-02-01
This paper develops a probabilistic approach to recursive second-order training of recurrent neural networks (RNNs) for improved time-series modeling. A general recursive Bayesian Levenberg-Marquardt algorithm is derived to sequentially update the weights and the covariance (Hessian) matrix. The main strengths of the approach are a principled handling of the regularization hyperparameters that leads to better generalization, and stable numerical performance. The framework involves the adaptation of a noise hyperparameter and local weight prior hyperparameters, which represent the noise in the data and the uncertainties in the model parameters. Experimental investigations using artificial and real-world data sets show that RNNs equipped with the proposed approach outperform standard real-time recurrent learning and extended Kalman training algorithms for recurrent networks, as well as other contemporary nonlinear neural models, on time-series modeling.
Markov chain Monte Carlo simulation for Bayesian Hidden Markov Models
Chan, Lay Guat; Ibrahim, Adriana Irawati Nur Binti
2016-10-01
A hidden Markov model (HMM) is a mixture model which has a Markov chain with finite states as its mixing distribution. HMMs have been applied to a variety of fields, such as speech and face recognitions. The main purpose of this study is to investigate the Bayesian approach to HMMs. Using this approach, we can simulate from the parameters' posterior distribution using some Markov chain Monte Carlo (MCMC) sampling methods. HMMs seem to be useful, but there are some limitations. Therefore, by using the Mixture of Dirichlet processes Hidden Markov Model (MDPHMM) based on Yau et. al (2011), we hope to overcome these limitations. We shall conduct a simulation study using MCMC methods to investigate the performance of this model.
A bayesian integrative model for genetical genomics with spatially informed variable selection.
Cassese, Alberto; Guindani, Michele; Vannucci, Marina
2014-01-01
We consider a Bayesian hierarchical model for the integration of gene expression levels with comparative genomic hybridization (CGH) array measurements collected on the same subjects. The approach defines a measurement error model that relates the gene expression levels to latent copy number states. In turn, the latent states are related to the observed surrogate CGH measurements via a hidden Markov model. The model further incorporates variable selection with a spatial prior based on a probit link that exploits dependencies across adjacent DNA segments. Posterior inference is carried out via Markov chain Monte Carlo stochastic search techniques. We study the performance of the model in simulations and show better results than those achieved with recently proposed alternative priors. We also show an application to data from a genomic study on lung squamous cell carcinoma, where we identify potential candidates of associations between copy number variants and the transcriptional activity of target genes. Gene ontology (GO) analyses of our findings reveal enrichments in genes that code for proteins involved in cancer. Our model also identifies a number of potential candidate biomarkers for further experimental validation.
Marshall, L. A.; Sharma, A.; Nott, D.
2005-12-01
Rigidity in a modelling framework has been known to result in considerable bias in cases where the system behaviour is closely linked to the catchment antecedent conditions. An alternative to accommodate such variations in the system makeup is to enable the model to be flexible enough to evolve as antecedent conditions change. We present a framework that incorporates such flexibility by expressing the model through the combination of a number of different model structures. Each structure is adopted at a given time with a probability that depends on the current hydrologic state of the catchment. This framework is known as a Hierarchical Mixture of Experts (HME). When applied in a hydrological context, the HME approach has two major functions. It can act as a powerful predictive tool where simulation is extended beyond the calibration period. It also offers a basis for model development and building based on interpretation of the final model architecture in calibration. The probabilistic nature of HME means that it is ideally specified using Bayesian inference. The Bayesian approach also formalises the incorporation of uncertainty in the model specification. The interpretability of the overall HME framework is largely influenced by the individual model structures. One model which can be applied in the HME context is the popular Topmodel. Topmodel is a modelling tool that allows the simulation of distributed catchment response to rainfall. Many different versions of the basic model structure exist as the underlying concepts are challenged by different catchment studies. One modification often made is to the description of the baseflow recession. This study will investigate the predictive capability of Topmodel when the model is specified using both a Bayesian and HME approach. The specification of the distribution of model errors is investigated by definition of several different probability distributions. The HME approach is applied in a framework that compares two
Bayesian Dose-Response Modeling in Sparse Data
Kim, Steven B.
This book discusses Bayesian dose-response modeling in small samples applied to two different settings. The first setting is early phase clinical trials, and the second setting is toxicology studies in cancer risk assessment. In early phase clinical trials, experimental units are humans who are actual patients. Prior to a clinical trial, opinions from multiple subject area experts are generally more informative than the opinion of a single expert, but we may face a dilemma when they have disagreeing prior opinions. In this regard, we consider compromising the disagreement and compare two different approaches for making a decision. In addition to combining multiple opinions, we also address balancing two levels of ethics in early phase clinical trials. The first level is individual-level ethics which reflects the perspective of trial participants. The second level is population-level ethics which reflects the perspective of future patients. We extensively compare two existing statistical methods which focus on each perspective and propose a new method which balances the two conflicting perspectives. In toxicology studies, experimental units are living animals. Here we focus on a potential non-monotonic dose-response relationship which is known as hormesis. Briefly, hormesis is a phenomenon which can be characterized by a beneficial effect at low doses and a harmful effect at high doses. In cancer risk assessments, the estimation of a parameter, which is known as a benchmark dose, can be highly sensitive to a class of assumptions, monotonicity or hormesis. In this regard, we propose a robust approach which considers both monotonicity and hormesis as a possibility. In addition, We discuss statistical hypothesis testing for hormesis and consider various experimental designs for detecting hormesis based on Bayesian decision theory. Past experiments have not been optimally designed for testing for hormesis, and some Bayesian optimal designs may not be optimal under a
Bayesian network as a modelling tool for risk management in agriculture
DEFF Research Database (Denmark)
Rasmussen, Svend; Madsen, Anders L.; Lund, Mogens
. In this paper we use Bayesian networks as an integrated modelling approach for representing uncertainty and analysing risk management in agriculture. It is shown how historical farm account data may be efficiently used to estimate conditional probabilities, which are the core elements in Bayesian network models....... We further show how the Bayesian network model RiBay is used for stochastic simulation of farm income, and we demonstrate how RiBay can be used to simulate risk management at the farm level. It is concluded that the key strength of a Bayesian network is the transparency of assumptions...
Hierarchical models for estimating density from DNA mark-recapture studies.
Gardner, Beth; Royle, J Andrew; Wegan, Michael T
2009-04-01
Genetic sampling is increasingly used as a tool by wildlife biologists and managers to estimate abundance and density of species. Typically, DNA is used to identify individuals captured in an array of traps (e.g., baited hair snares) from which individual encounter histories are derived. Standard methods for estimating the size of a closed population can be applied to such data. However, due to the movement of individuals on and off the trapping array during sampling, the area over which individuals are exposed to trapping is unknown, and so obtaining unbiased estimates of density has proved difficult. We propose a hierarchical spatial capture-recapture model which contains explicit models for the spatial point process governing the distribution of individuals and their exposure to (via movement) and detection by traps. Detection probability is modeled as a function of each individual's distance to the trap. We applied this model to a black bear (Ursus americanus) study conducted in 2006 using a hair-snare trap array in the Adirondack region of New York, USA. We estimated the density of bears to be 0.159 bears/km2, which is lower than the estimated density (0.410 bears/km2) based on standard closed population techniques. A Bayesian analysis of the model is fully implemented in the software program WinBUGS.
A hierarchical neuronal model for generation and online recognition of birdsongs.
Directory of Open Access Journals (Sweden)
Izzet B Yildiz
2011-12-01
Full Text Available The neuronal system underlying learning, generation and recognition of song in birds is one of the best-studied systems in the neurosciences. Here, we use these experimental findings to derive a neurobiologically plausible, dynamic, hierarchical model of birdsong generation and transform it into a functional model of birdsong recognition. The generation model consists of neuronal rate models and includes critical anatomical components like the premotor song-control nucleus HVC (proper name, the premotor nucleus RA (robust nucleus of the arcopallium, and a model of the syringeal and respiratory organs. We use Bayesian inference of this dynamical system to derive a possible mechanism for how birds can efficiently and robustly recognize the songs of their conspecifics in an online fashion. Our results indicate that the specific way birdsong is generated enables a listening bird to robustly and rapidly perceive embedded information at multiple time scales of a song. The resulting mechanism can be useful for investigating the functional roles of auditory recognition areas and providing predictions for future birdsong experiments.
Bayesian Age-Period-Cohort Model of Lung Cancer Mortality
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Bhikhari P. Tharu
2015-09-01
Full Text Available Background The objective of this study was to analyze the time trend for lung cancer mortality in the population of the USA by 5 years based on most recent available data namely to 2010. The knowledge of the mortality rates in the temporal trends is necessary to understand cancer burden.Methods Bayesian Age-Period-Cohort model was fitted using Poisson regression with histogram smoothing prior to decompose mortality rates based on age at death, period at death, and birth-cohort.Results Mortality rates from lung cancer increased more rapidly from age 52 years. It ended up to 325 deaths annually for 82 years on average. The mortality of younger cohorts was lower than older cohorts. The risk of lung cancer was lowered from period 1993 to recent periods.Conclusions The fitted Bayesian Age-Period-Cohort model with histogram smoothing prior is capable of explaining mortality rate of lung cancer. The reduction in carcinogens in cigarettes and increase in smoking cessation from around 1960 might led to decreasing trend of lung cancer mortality after calendar period 1993.
Optimal inference with suboptimal models: addiction and active Bayesian inference.
Schwartenbeck, Philipp; FitzGerald, Thomas H B; Mathys, Christoph; Dolan, Ray; Wurst, Friedrich; Kronbichler, Martin; Friston, Karl
2015-02-01
When casting behaviour as active (Bayesian) inference, optimal inference is defined with respect to an agent's beliefs - based on its generative model of the world. This contrasts with normative accounts of choice behaviour, in which optimal actions are considered in relation to the true structure of the environment - as opposed to the agent's beliefs about worldly states (or the task). This distinction shifts an understanding of suboptimal or pathological behaviour away from aberrant inference as such, to understanding the prior beliefs of a subject that cause them to behave less 'optimally' than our prior beliefs suggest they should behave. Put simply, suboptimal or pathological behaviour does not speak against understanding behaviour in terms of (Bayes optimal) inference, but rather calls for a more refined understanding of the subject's generative model upon which their (optimal) Bayesian inference is based. Here, we discuss this fundamental distinction and its implications for understanding optimality, bounded rationality and pathological (choice) behaviour. We illustrate our argument using addictive choice behaviour in a recently described 'limited offer' task. Our simulations of pathological choices and addictive behaviour also generate some clear hypotheses, which we hope to pursue in ongoing empirical work. Copyright © 2014 The Authors. Published by Elsevier Ltd.. All rights reserved.
Sparse linear models: Variational approximate inference and Bayesian experimental design
Energy Technology Data Exchange (ETDEWEB)
Seeger, Matthias W [Saarland University and Max Planck Institute for Informatics, Campus E1.4, 66123 Saarbruecken (Germany)
2009-12-01
A wide range of problems such as signal reconstruction, denoising, source separation, feature selection, and graphical model search are addressed today by posterior maximization for linear models with sparsity-favouring prior distributions. The Bayesian posterior contains useful information far beyond its mode, which can be used to drive methods for sampling optimization (active learning), feature relevance ranking, or hyperparameter estimation, if only this representation of uncertainty can be approximated in a tractable manner. In this paper, we review recent results for variational sparse inference, and show that they share underlying computational primitives. We discuss how sampling optimization can be implemented as sequential Bayesian experimental design. While there has been tremendous recent activity to develop sparse estimation, little attendance has been given to sparse approximate inference. In this paper, we argue that many problems in practice, such as compressive sensing for real-world image reconstruction, are served much better by proper uncertainty approximations than by ever more aggressive sparse estimation algorithms. Moreover, since some variational inference methods have been given strong convex optimization characterizations recently, theoretical analysis may become possible, promising new insights into nonlinear experimental design.
Hierarchical Swarm Model: A New Approach to Optimization
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Hanning Chen
2010-01-01
Full Text Available This paper presents a novel optimization model called hierarchical swarm optimization (HSO, which simulates the natural hierarchical complex system from where more complex intelligence can emerge for complex problems solving. This proposed model is intended to suggest ways that the performance of HSO-based algorithms on complex optimization problems can be significantly improved. This performance improvement is obtained by constructing the HSO hierarchies, which means that an agent in a higher level swarm can be composed of swarms of other agents from lower level and different swarms of different levels evolve on different spatiotemporal scale. A novel optimization algorithm (named PS2O, based on the HSO model, is instantiated and tested to illustrate the ideas of HSO model clearly. Experiments were conducted on a set of 17 benchmark optimization problems including both continuous and discrete cases. The results demonstrate remarkable performance of the PS2O algorithm on all chosen benchmark functions when compared to several successful swarm intelligence and evolutionary algorithms.
Linguistic steganography on Twitter: hierarchical language modeling with manual interaction
Wilson, Alex; Blunsom, Phil; Ker, Andrew D.
2014-02-01
This work proposes a natural language stegosystem for Twitter, modifying tweets as they are written to hide 4 bits of payload per tweet, which is a greater payload than previous systems have achieved. The system, CoverTweet, includes novel components, as well as some already developed in the literature. We believe that the task of transforming covers during embedding is equivalent to unilingual machine translation (paraphrasing), and we use this equivalence to de ne a distortion measure based on statistical machine translation methods. The system incorporates this measure of distortion to rank possible tweet paraphrases, using a hierarchical language model; we use human interaction as a second distortion measure to pick the best. The hierarchical language model is designed to model the speci c language of the covers, which in this setting is the language of the Twitter user who is embedding. This is a change from previous work, where general-purpose language models have been used. We evaluate our system by testing the output against human judges, and show that humans are unable to distinguish stego tweets from cover tweets any better than random guessing.
Perceptual decision making: Drift-diffusion model is equivalent to a Bayesian model
Directory of Open Access Journals (Sweden)
Sebastian eBitzer
2014-02-01
Full Text Available Behavioural data obtained with perceptual decision making experiments are typically analysed with the drift-diffusion model. This parsimonious model accumulates noisy pieces of evidence towards a decision bound to explain the accuracy and reaction times of subjects. Recently, Bayesian models have been proposed to explain how the brain extracts information from noisy input as typically presented in perceptual decision making tasks. It has long been known that the drift-diffusion model is tightly linked with such functional Bayesian models but the precise relationship of the two mechanisms was never made explicit. Using a Bayesian model, we derived the equations which relate parameter values between these models. In practice we show that this equivalence is useful when fitting multi-subject data. We further show that the Bayesian model suggests different decision variables which all predict equal responses and discuss how these may be discriminated based on neural correlates of accumulated evidence. In addition, we discuss extensions to the Bayesian model which would be difficult to derive for the drift-diffusion model. We suggest that these and other extensions may be highly useful for deriving new experiments which test novel hypotheses.
Perceptual decision making: drift-diffusion model is equivalent to a Bayesian model.
Bitzer, Sebastian; Park, Hame; Blankenburg, Felix; Kiebel, Stefan J
2014-01-01
Behavioral data obtained with perceptual decision making experiments are typically analyzed with the drift-diffusion model. This parsimonious model accumulates noisy pieces of evidence toward a decision bound to explain the accuracy and reaction times of subjects. Recently, Bayesian models have been proposed to explain how the brain extracts information from noisy input as typically presented in perceptual decision making tasks. It has long been known that the drift-diffusion model is tightly linked with such functional Bayesian models but the precise relationship of the two mechanisms was never made explicit. Using a Bayesian model, we derived the equations which relate parameter values between these models. In practice we show that this equivalence is useful when fitting multi-subject data. We further show that the Bayesian model suggests different decision variables which all predict equal responses and discuss how these may be discriminated based on neural correlates of accumulated evidence. In addition, we discuss extensions to the Bayesian model which would be difficult to derive for the drift-diffusion model. We suggest that these and other extensions may be highly useful for deriving new experiments which test novel hypotheses.
Hierarchical Stochastic Simulation Algorithm for SBML Models of Genetic Circuits
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Leandro eWatanabe
2014-11-01
Full Text Available This paper describes a hierarchical stochastic simulation algorithm which has been implemented within iBioSim, a tool used to model, analyze, and visualize genetic circuits. Many biological analysis tools flatten out hierarchy before simulation, but there are many disadvantages associated with this approach. First, the memory required to represent the model can quickly expand in the process. Second, the flattening process is computationally expensive. Finally, when modeling a dynamic cellular population within iBioSim, inlining the hierarchy of the model is inefficient since models must grow dynamically over time. This paper discusses a new approach to handle hierarchy on the fly to make the tool faster and more memory-efficient. This approach yields significant performance improvements as compared to the former flat analysis method.
Performance and Prediction: Bayesian Modelling of Fallible Choice in Chess
Haworth, Guy; Regan, Ken; di Fatta, Giuseppe
Evaluating agents in decision-making applications requires assessing their skill and predicting their behaviour. Both are well developed in Poker-like situations, but less so in more complex game and model domains. This paper addresses both tasks by using Bayesian inference in a benchmark space of reference agents. The concepts are explained and demonstrated using the game of chess but the model applies generically to any domain with quantifiable options and fallible choice. Demonstration applications address questions frequently asked by the chess community regarding the stability of the rating scale, the comparison of players of different eras and/or leagues, and controversial incidents possibly involving fraud. The last include alleged under-performance, fabrication of tournament results, and clandestine use of computer advice during competition. Beyond the model world of games, the aim is to improve fallible human performance in complex, high-value tasks.
Bayesian inference for duplication-mutation with complementarity network models.
Jasra, Ajay; Persing, Adam; Beskos, Alexandros; Heine, Kari; De Iorio, Maria
2015-11-01
We observe an undirected graph G without multiple edges and self-loops, which is to represent a protein-protein interaction (PPI) network. We assume that G evolved under the duplication-mutation with complementarity (DMC) model from a seed graph, G0, and we also observe the binary forest Γ that represents the duplication history of G. A posterior density for the DMC model parameters is established, and we outline a sampling strategy by which one can perform Bayesian inference; that sampling strategy employs a particle marginal Metropolis-Hastings (PMMH) algorithm. We test our methodology on numerical examples to demonstrate a high accuracy and precision in the inference of the DMC model's mutation and homodimerization parameters.
Bayesian Inference for Duplication–Mutation with Complementarity Network Models
Persing, Adam; Beskos, Alexandros; Heine, Kari; De Iorio, Maria
2015-01-01
Abstract We observe an undirected graph G without multiple edges and self-loops, which is to represent a protein–protein interaction (PPI) network. We assume that G evolved under the duplication–mutation with complementarity (DMC) model from a seed graph, G0, and we also observe the binary forest Γ that represents the duplication history of G. A posterior density for the DMC model parameters is established, and we outline a sampling strategy by which one can perform Bayesian inference; that sampling strategy employs a particle marginal Metropolis–Hastings (PMMH) algorithm. We test our methodology on numerical examples to demonstrate a high accuracy and precision in the inference of the DMC model's mutation and homodimerization parameters. PMID:26355682
A Bayesian Network View on Nested Effects Models
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Achim Tresch
2009-01-01
Full Text Available Nested effects models (NEMs are a class of probabilistic models that were designed to reconstruct a hidden signalling structure from a large set of observable effects caused by active interventions into the signalling pathway. We give a more flexible formulation of NEMs in the language of Bayesian networks. Our framework constitutes a natural generalization of the original NEM model, since it explicitly states the assumptions that are tacitly underlying the original version. Our approach gives rise to new learning methods for NEMs, which have been implemented in the R/Bioconductor package nem. We validate these methods in a simulation study and apply them to a synthetic lethality dataset in yeast.
Development of a Bayesian Belief Network Runway Incursion Model
Green, Lawrence L.
2014-01-01
In a previous paper, a statistical analysis of runway incursion (RI) events was conducted to ascertain their relevance to the top ten Technical Challenges (TC) of the National Aeronautics and Space Administration (NASA) Aviation Safety Program (AvSP). The study revealed connections to perhaps several of the AvSP top ten TC. That data also identified several primary causes and contributing factors for RI events that served as the basis for developing a system-level Bayesian Belief Network (BBN) model for RI events. The system-level BBN model will allow NASA to generically model the causes of RI events and to assess the effectiveness of technology products being developed under NASA funding. These products are intended to reduce the frequency of RI events in particular, and to improve runway safety in general. The development, structure and assessment of that BBN for RI events by a Subject Matter Expert panel are documented in this paper.
Advances in Bayesian Model Based Clustering Using Particle Learning
Energy Technology Data Exchange (ETDEWEB)
Merl, D M
2009-11-19
Recent work by Carvalho, Johannes, Lopes and Polson and Carvalho, Lopes, Polson and Taddy introduced a sequential Monte Carlo (SMC) alternative to traditional iterative Monte Carlo strategies (e.g. MCMC and EM) for Bayesian inference for a large class of dynamic models. The basis of SMC techniques involves representing the underlying inference problem as one of state space estimation, thus giving way to inference via particle filtering. The key insight of Carvalho et al was to construct the sequence of filtering distributions so as to make use of the posterior predictive distribution of the observable, a distribution usually only accessible in certain Bayesian settings. Access to this distribution allows a reversal of the usual propagate and resample steps characteristic of many SMC methods, thereby alleviating to a large extent many problems associated with particle degeneration. Furthermore, Carvalho et al point out that for many conjugate models the posterior distribution of the static variables can be parametrized in terms of [recursively defined] sufficient statistics of the previously observed data. For models where such sufficient statistics exist, particle learning as it is being called, is especially well suited for the analysis of streaming data do to the relative invariance of its algorithmic complexity with the number of data observations. Through a particle learning approach, a statistical model can be fit to data as the data is arriving, allowing at any instant during the observation process direct quantification of uncertainty surrounding underlying model parameters. Here we describe the use of a particle learning approach for fitting a standard Bayesian semiparametric mixture model as described in Carvalho, Lopes, Polson and Taddy. In Section 2 we briefly review the previously presented particle learning algorithm for the case of a Dirichlet process mixture of multivariate normals. In Section 3 we describe several novel extensions to the original
Integrated Bayesian network framework for modeling complex ecological issues.
Johnson, Sandra; Mengersen, Kerrie
2012-07-01
The management of environmental problems is multifaceted, requiring varied and sometimes conflicting objectives and perspectives to be considered. Bayesian network (BN) modeling facilitates the integration of information from diverse sources and is well suited to tackling the management challenges of complex environmental problems. However, combining several perspectives in one model can lead to large, unwieldy BNs that are difficult to maintain and understand. Conversely, an oversimplified model may lead to an unrealistic representation of the environmental problem. Environmental managers require the current research and available knowledge about an environmental problem of interest to be consolidated in a meaningful way, thereby enabling the assessment of potential impacts and different courses of action. Previous investigations of the environmental problem of interest may have already resulted in the construction of several disparate ecological models. On the other hand, the opportunity may exist to initiate this modeling. In the first instance, the challenge is to integrate existing models and to merge the information and perspectives from these models. In the second instance, the challenge is to include different aspects of the environmental problem incorporating both the scientific and management requirements. Although the paths leading to the combined model may differ for these 2 situations, the common objective is to design an integrated model that captures the available information and research, yet is simple to maintain, expand, and refine. BN modeling is typically an iterative process, and we describe a heuristic method, the iterative Bayesian network development cycle (IBNDC), for the development of integrated BN models that are suitable for both situations outlined above. The IBNDC approach facilitates object-oriented BN (OOBN) modeling, arguably viewed as the next logical step in adaptive management modeling, and that embraces iterative development
Bayesian Geostatistical Modeling of Malaria Indicator Survey Data in Angola
Gosoniu, Laura; Veta, Andre Mia; Vounatsou, Penelope
2010-01-01
The 2006–2007 Angola Malaria Indicator Survey (AMIS) is the first nationally representative household survey in the country assessing coverage of the key malaria control interventions and measuring malaria-related burden among children under 5 years of age. In this paper, the Angolan MIS data were analyzed to produce the first smooth map of parasitaemia prevalence based on contemporary nationwide empirical data in the country. Bayesian geostatistical models were fitted to assess the effect of interventions after adjusting for environmental, climatic and socio-economic factors. Non-linear relationships between parasitaemia risk and environmental predictors were modeled by categorizing the covariates and by employing two non-parametric approaches, the B-splines and the P-splines. The results of the model validation showed that the categorical model was able to better capture the relationship between parasitaemia prevalence and the environmental factors. Model fit and prediction were handled within a Bayesian framework using Markov chain Monte Carlo (MCMC) simulations. Combining estimates of parasitaemia prevalence with the number of children under we obtained estimates of the number of infected children in the country. The population-adjusted prevalence ranges from in Namibe province to in Malanje province. The odds of parasitaemia in children living in a household with at least ITNs per person was by 41% lower (CI: 14%, 60%) than in those with fewer ITNs. The estimates of the number of parasitaemic children produced in this paper are important for planning and implementing malaria control interventions and for monitoring the impact of prevention and control activities. PMID:20351775
Modeling Land-Use Decision Behavior with Bayesian Belief Networks
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Inge Aalders
2008-06-01
Full Text Available The ability to incorporate and manage the different drivers of land-use change in a modeling process is one of the key challenges because they are complex and are both quantitative and qualitative in nature. This paper uses Bayesian belief networks (BBN to incorporate characteristics of land managers in the modeling process and to enhance our understanding of land-use change based on the limited and disparate sources of information. One of the two models based on spatial data represented land managers in the form of a quantitative variable, the area of individual holdings, whereas the other model included qualitative data from a survey of land managers. Random samples from the spatial data provided evidence of the relationship between the different variables, which I used to develop the BBN structure. The model was tested for four different posterior probability distributions, and results showed that the trained and learned models are better at predicting land use than the uniform and random models. The inference from the model demonstrated the constraints that biophysical characteristics impose on land managers; for older land managers without heirs, there is a higher probability of the land use being arable agriculture. The results show the benefits of incorporating a more complex notion of land managers in land-use models, and of using different empirical data sources in the modeling process. Future research should focus on incorporating more complex social processes into the modeling structure, as well as incorporating spatio-temporal dynamics in a BBN.
PDS-Modelling and Regional Bayesian Estimation of Extreme Rainfalls
DEFF Research Database (Denmark)
Madsen, Henrik; Rosbjerg, Dan; Harremoës, Poul
1994-01-01
rainfalls. The method is applied to two variables: the total precipitation depth and the maximum 10-minute rain intensity of individual storms. On the basis of the atsite modelling a regional analysis is carried out. It is shown that the previous assumption of spatial homogeneity of extreme rainfalls......Since 1979 a country-wide system of raingauges has been operated in Denmark in order to obtain a better basis for design and analysis of urban drainage systems. As an alternative to the traditional non-parametric approach the Partial Duration Series method is employed in the modelling of extreme....... The application of the Bayesian approach is derived in case of both exponential and generalized Pareto distributed exceedances. Finally, the aspect of including economic perspectives in the estimation of the design events is briefly discussed....
Spatial Bayesian latent factor regression modeling of coordinate-based meta-analysis data.
Montagna, Silvia; Wager, Tor; Barrett, Lisa Feldman; Johnson, Timothy D; Nichols, Thomas E
2017-05-12
Now over 20 years old, functional MRI (fMRI) has a large and growing literature that is best synthesised with meta-analytic tools. As most authors do not share image data, only the peak activation coordinates (foci) reported in the article are available for Coordinate-Based Meta-Analysis (CBMA). Neuroimaging meta-analysis is used to (i) identify areas of consistent activation; and (ii) build a predictive model of task type or cognitive process for new studies (reverse inference). To simultaneously address these aims, we propose a Bayesian point process hierarchical model for CBMA. We model the foci from each study as a doubly stochastic Poisson process, where the study-specific log intensity function is characterized as a linear combination of a high-dimensional basis set. A sparse representation of the intensities is guaranteed through latent factor modeling of the basis coefficients. Within our framework, it is also possible to account for the effect of study-level covariates (meta-regression), significantly expanding the capabilities of the current neuroimaging meta-analysis methods available. We apply our methodology to synthetic data and neuroimaging meta-analysis datasets. © 2017, The International Biometric Society.
Joint Modeling of Multiple Crimes: A Bayesian Spatial Approach
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Hongqiang Liu
2017-01-01
Full Text Available A multivariate Bayesian spatial modeling approach was used to jointly model the counts of two types of crime, i.e., burglary and non-motor vehicle theft, and explore the geographic pattern of crime risks and relevant risk factors. In contrast to the univariate model, which assumes independence across outcomes, the multivariate approach takes into account potential correlations between crimes. Six independent variables are included in the model as potential risk factors. In order to fully present this method, both the multivariate model and its univariate counterpart are examined. We fitted the two models to the data and assessed them using the deviance information criterion. A comparison of the results from the two models indicates that the multivariate model was superior to the univariate model. Our results show that population density and bar density are clearly associated with both burglary and non-motor vehicle theft risks and indicate a close relationship between these two types of crime. The posterior means and 2.5% percentile of type-specific crime risks estimated by the multivariate model were mapped to uncover the geographic patterns. The implications, limitations and future work of the study are discussed in the concluding section.
Modelling of population dynamics of red king crab using Bayesian approach
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Bakanev Sergey ...
2012-10-01
Modeling population dynamics based on the Bayesian approach enables to successfully resolve the above issues. The integration of the data from various studies into a unified model based on Bayesian parameter estimation method provides a much more detailed description of the processes occurring in the population.
Dynamic Bayesian Network Modeling of Game Based Diagnostic Assessments. CRESST Report 837
Levy, Roy
2014-01-01
Digital games offer an appealing environment for assessing student proficiencies, including skills and misconceptions in a diagnostic setting. This paper proposes a dynamic Bayesian network modeling approach for observations of student performance from an educational video game. A Bayesian approach to model construction, calibration, and use in…
Ising model with long range correlated disorder on hierarchical lattices
Andrade, Roberto F. S.; Cason, Daniel
2010-01-01
A next-neighbor Ising model with disordered but long range correlated coupling constants is investigated. The model is built on a hierarchical lattice and the correlation strength depends on a tuning parameter α . The results are obtained within a transfer-matrix framework, which allows for the evaluation of the properties of individual samples. Collective behavior is computed by averaging over a large number of independent realizations. The dependence of the thermodynamic and magnetic functions with respect to the temperature is investigated for each value of α . Phase diagrams in the (α,T) plane are constructed for two distinct versions of the model, indicating the existence of regions of paramagnetic and ordered phases. Critical values αc , below which the system always assumes the paramagnetic phase, are found for both versions.
Multi-mode clustering model for hierarchical wireless sensor networks
Hu, Xiangdong; Li, Yongfu; Xu, Huifen
2017-03-01
The topology management, i.e., clusters maintenance, of wireless sensor networks (WSNs) is still a challenge due to its numerous nodes, diverse application scenarios and limited resources as well as complex dynamics. To address this issue, a multi-mode clustering model (M2 CM) is proposed to maintain the clusters for hierarchical WSNs in this study. In particular, unlike the traditional time-trigger model based on the whole-network and periodic style, the M2 CM is proposed based on the local and event-trigger operations. In addition, an adaptive local maintenance algorithm is designed for the broken clusters in the WSNs using the spatial-temporal demand changes accordingly. Numerical experiments are performed using the NS2 network simulation platform. Results validate the effectiveness of the proposed model with respect to the network maintenance costs, node energy consumption and transmitted data as well as the network lifetime.
Lopez, Michael J; Schuckers, Michael
2017-05-01
Roughly 14% of regular season National Hockey League games since the 2005-06 season have been decided by a shoot-out, and the resulting allocation of points has impacted play-off races each season. But despite interest from fans, players and league officials, there is little in the way of published research on team or individual shoot-out performance. This manuscript attempts to fill that void. We present both generalised linear mixed model and Bayesian hierarchical model frameworks to model shoot-out outcomes, with results suggesting that there are (i) small but statistically significant talent gaps between shooters, (ii) marginal differences in performance among netminders and (iii) few, if any, predictors of player success after accounting for individual talent. We also provide a resampling strategy to highlight a selection bias with respect to shooter assignment, in which coaches choose their most skilled offensive players early in shoot-out rounds and are less likely to select players with poor past performances. Finally, given that per-shot data for shoot-outs do not currently exist in a single location for public use, we provide both our data and source code for other researchers interested in studying shoot-out outcomes.
A Bayesian Approach for Structural Learning with Hidden Markov Models
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Cen Li
2002-01-01
Full Text Available Hidden Markov Models(HMM have proved to be a successful modeling paradigm for dynamic and spatial processes in many domains, such as speech recognition, genomics, and general sequence alignment. Typically, in these applications, the model structures are predefined by domain experts. Therefore, the HMM learning problem focuses on the learning of the parameter values of the model to fit the given data sequences. However, when one considers other domains, such as, economics and physiology, model structure capturing the system dynamic behavior is not available. In order to successfully apply the HMM methodology in these domains, it is important that a mechanism is available for automatically deriving the model structure from the data. This paper presents a HMM learning procedure that simultaneously learns the model structure and the maximum likelihood parameter values of a HMM from data. The HMM model structures are derived based on the Bayesian model selection methodology. In addition, we introduce a new initialization procedure for HMM parameter value estimation based on the K-means clustering method. Experimental results with artificially generated data show the effectiveness of the approach.
Bayesian dynamic modeling of time series of dengue disease case counts.
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Daniel Adyro Martínez-Bello
2017-07-01
Full Text Available The aim of this study is to model the association between weekly time series of dengue case counts and meteorological variables, in a high-incidence city of Colombia, applying Bayesian hierarchical dynamic generalized linear models over the period January 2008 to August 2015. Additionally, we evaluate the model's short-term performance for predicting dengue cases. The methodology shows dynamic Poisson log link models including constant or time-varying coefficients for the meteorological variables. Calendar effects were modeled using constant or first- or second-order random walk time-varying coefficients. The meteorological variables were modeled using constant coefficients and first-order random walk time-varying coefficients. We applied Markov Chain Monte Carlo simulations for parameter estimation, and deviance information criterion statistic (DIC for model selection. We assessed the short-term predictive performance of the selected final model, at several time points within the study period using the mean absolute percentage error. The results showed the best model including first-order random walk time-varying coefficients for calendar trend and first-order random walk time-varying coefficients for the meteorological variables. Besides the computational challenges, interpreting the results implies a complete analysis of the time series of dengue with respect to the parameter estimates of the meteorological effects. We found small values of the mean absolute percentage errors at one or two weeks out-of-sample predictions for most prediction points, associated with low volatility periods in the dengue counts. We discuss the advantages and limitations of the dynamic Poisson models for studying the association between time series of dengue disease and meteorological variables. The key conclusion of the study is that dynamic Poisson models account for the dynamic nature of the variables involved in the modeling of time series of dengue disease
Bayesian network models for error detection in radiotherapy plans.
Kalet, Alan M; Gennari, John H; Ford, Eric C; Phillips, Mark H
2015-04-07
The purpose of this study is to design and develop a probabilistic network for detecting errors in radiotherapy plans for use at the time of initial plan verification. Our group has initiated a multi-pronged approach to reduce these errors. We report on our development of Bayesian models of radiotherapy plans. Bayesian networks consist of joint probability distributions that define the probability of one event, given some set of other known information. Using the networks, we find the probability of obtaining certain radiotherapy parameters, given a set of initial clinical information. A low probability in a propagated network then corresponds to potential errors to be flagged for investigation. To build our networks we first interviewed medical physicists and other domain experts to identify the relevant radiotherapy concepts and their associated interdependencies and to construct a network topology. Next, to populate the network's conditional probability tables, we used the Hugin Expert software to learn parameter distributions from a subset of de-identified data derived from a radiation oncology based clinical information database system. These data represent 4990 unique prescription cases over a 5 year period. Under test case scenarios with approximately 1.5% introduced error rates, network performance produced areas under the ROC curve of 0.88, 0.98, and 0.89 for the lung, brain and female breast cancer error detection networks, respectively. Comparison of the brain network to human experts performance (AUC of 0.90 ± 0.01) shows the Bayes network model performs better than domain experts under the same test conditions. Our results demonstrate the feasibility and effectiveness of comprehensive probabilistic models as part of decision support systems for improved detection of errors in initial radiotherapy plan verification procedures.
Bayesian network models for error detection in radiotherapy plans
Kalet, Alan M.; Gennari, John H.; Ford, Eric C.; Phillips, Mark H.
2015-04-01
The purpose of this study is to design and develop a probabilistic network for detecting errors in radiotherapy plans for use at the time of initial plan verification. Our group has initiated a multi-pronged approach to reduce these errors. We report on our development of Bayesian models of radiotherapy plans. Bayesian networks consist of joint probability distributions that define the probability of one event, given some set of other known information. Using the networks, we find the probability of obtaining certain radiotherapy parameters, given a set of initial clinical information. A low probability in a propagated network then corresponds to potential errors to be flagged for investigation. To build our networks we first interviewed medical physicists and other domain experts to identify the relevant radiotherapy concepts and their associated interdependencies and to construct a network topology. Next, to populate the network’s conditional probability tables, we used the Hugin Expert software to learn parameter distributions from a subset of de-identified data derived from a radiation oncology based clinical information database system. These data represent 4990 unique prescription cases over a 5 year period. Under test case scenarios with approximately 1.5% introduced error rates, network performance produced areas under the ROC curve of 0.88, 0.98, and 0.89 for the lung, brain and female breast cancer error detection networks, respectively. Comparison of the brain network to human experts performance (AUC of 0.90 ± 0.01) shows the Bayes network model performs better than domain experts under the same test conditions. Our results demonstrate the feasibility and effectiveness of comprehensive probabilistic models as part of decision support systems for improved detection of errors in initial radiotherapy plan verification procedures.
Holbrook, Andrew; Vandenberg-Rodes, Alexander; Fortin, Norbert; Shahbaba, Babak
2017-01-01
Neuroscientists are increasingly collecting multimodal data during experiments and observational studies. Different data modalities-such as EEG, fMRI, LFP, and spike trains-offer different views of the complex systems contributing to neural phenomena. Here, we focus on joint modeling of LFP and spike train data, and present a novel Bayesian method for neural decoding to infer behavioral and experimental conditions. This model performs supervised dual-dimensionality reduction: it learns low-dimensional representations of two different sources of information that not only explain variation in the input data itself, but also predict extra-neuronal outcomes. Despite being one probabilistic unit, the model consists of multiple modules: exponential PCA and wavelet PCA are used for dimensionality reduction in the spike train and LFP modules, respectively; these modules simultaneously interface with a Bayesian binary regression module. We demonstrate how this model may be used for prediction, parametric inference, and identification of influential predictors. In prediction, the hierarchical model outperforms other models trained on LFP alone, spike train alone, and combined LFP and spike train data. We compare two methods for modeling the loading matrix and find them to perform similarly. Finally, model parameters and their posterior distributions yield scientific insights.
Chen, Cong; Zhang, Guohui; Huang, Helai; Wang, Jiangfeng; Tarefder, Rafiqul A
2016-11-01
Rural non-interstate crashes induce a significant amount of severe injuries and fatalities. Examination of such injury patterns and the associated contributing factors is of practical importance. Taking into account the ordinal nature of injury severity levels and the hierarchical feature of crash data, this study employs a hierarchical ordered logit model to examine the significant factors in predicting driver injury severities in rural non-interstate crashes based on two-year New Mexico crash records. Bayesian inference is utilized in model estimation procedure and 95% Bayesian Credible Interval (BCI) is applied to testing variable significance. An ordinary ordered logit model omitting the between-crash variance effect is evaluated as well for model performance comparison. Results indicate that the model employed in this study outperforms ordinary ordered logit model in model fit and parameter estimation. Variables regarding crash features, environment conditions, and driver and vehicle characteristics are found to have significant influence on the predictions of driver injury severities in rural non-interstate crashes. Factors such as road segments far from intersection, wet road surface condition, collision with animals, heavy vehicle drivers, male drivers and driver seatbelt used tend to induce less severe driver injury outcomes than the factors such as multiple-vehicle crashes, severe vehicle damage in a crash, motorcyclists, females, senior drivers, driver with alcohol or drug impairment, and other major collision types. Research limitations regarding crash data and model assumptions are also discussed. Overall, this research provides reasonable results and insight in developing effective road safety measures for crash injury severity reduction and prevention. Copyright © 2016 Elsevier Ltd. All rights reserved.
A Bayesian Attractor Model for Perceptual Decision Making.
Bitzer, Sebastian; Bruineberg, Jelle; Kiebel, Stefan J
2015-08-01
Even for simple perceptual decisions, the mechanisms that the brain employs are still under debate. Although current consensus states that the brain accumulates evidence extracted from noisy sensory information, open questions remain about how this simple model relates to other perceptual phenomena such as flexibility in decisions, decision-dependent modulation of sensory gain, or confidence about a decision. We propose a novel approach of how perceptual decisions are made by combining two influential formalisms into a new model. Specifically, we embed an attractor model of decision making into a probabilistic framework that models decision making as Bayesian inference. We show that the new model can explain decision making behaviour by fitting it to experimental data. In addition, the new model combines for the first time three important features: First, the model can update decisions in response to switches in the underlying stimulus. Second, the probabilistic formulation accounts for top-down effects that may explain recent experimental findings of decision-related gain modulation of sensory neurons. Finally, the model computes an explicit measure of confidence which we relate to recent experimental evidence for confidence computations in perceptual decision tasks.
Bayesian inference and model comparison for metallic fatigue data
Babuska, Ivo
2016-01-06
In this work, we present a statistical treatment of stress-life (S-N) data drawn from a collection of records of fatigue experiments that were performed on 75S-T6 aluminum alloys. Our main objective is to predict the fatigue life of materials by providing a systematic approach to model calibration, model selection and model ranking with reference to S-N data. To this purpose, we consider fatigue-limit models and random fatigue-limit models that are specially designed to allow the treatment of the run-outs (right-censored data). We first fit the models to the data by maximum likelihood methods and estimate the quantiles of the life distribution of the alloy specimen. We then compare and rank the models by classical measures of fit based on information criteria. We also consider a Bayesian approach that provides, under the prior distribution of the model parameters selected by the user, their simulation-based posterior distributions.
Modeling evolutionary dynamics of epigenetic mutations in hierarchically organized tumors.
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Andrea Sottoriva
2011-05-01
Full Text Available The cancer stem cell (CSC concept is a highly debated topic in cancer research. While experimental evidence in favor of the cancer stem cell theory is apparently abundant, the results are often criticized as being difficult to interpret. An important reason for this is that most experimental data that support this model rely on transplantation studies. In this study we use a novel cellular Potts model to elucidate the dynamics of established malignancies that are driven by a small subset of CSCs. Our results demonstrate that epigenetic mutations that occur during mitosis display highly altered dynamics in CSC-driven malignancies compared to a classical, non-hierarchical model of growth. In particular, the heterogeneity observed in CSC-driven tumors is considerably higher. We speculate that this feature could be used in combination with epigenetic (methylation sequencing studies of human malignancies to prove or refute the CSC hypothesis in established tumors without the need for transplantation. Moreover our tumor growth simulations indicate that CSC-driven tumors display evolutionary features that can be considered beneficial during tumor progression. Besides an increased heterogeneity they also exhibit properties that allow the escape of clones from local fitness peaks. This leads to more aggressive phenotypes in the long run and makes the neoplasm more adaptable to stringent selective forces such as cancer treatment. Indeed when therapy is applied the clone landscape of the regrown tumor is more aggressive with respect to the primary tumor, whereas the classical model demonstrated similar patterns before and after therapy. Understanding these often counter-intuitive fundamental properties of (non-hierarchically organized malignancies is a crucial step in validating the CSC concept as well as providing insight into the therapeutical consequences of this model.
A Bayesian spatio-temporal geostatistical model with an auxiliary lattice for large datasets
Xu, Ganggang
2015-01-01
When spatio-temporal datasets are large, the computational burden can lead to failures in the implementation of traditional geostatistical tools. In this paper, we propose a computationally efficient Bayesian hierarchical spatio-temporal model in which the spatial dependence is approximated by a Gaussian Markov random field (GMRF) while the temporal correlation is described using a vector autoregressive model. By introducing an auxiliary lattice on the spatial region of interest, the proposed method is not only able to handle irregularly spaced observations in the spatial domain, but it is also able to bypass the missing data problem in a spatio-temporal process. Because the computational complexity of the proposed Markov chain Monte Carlo algorithm is of the order O(n) with n the total number of observations in space and time, our method can be used to handle very large spatio-temporal datasets with reasonable CPU times. The performance of the proposed model is illustrated using simulation studies and a dataset of precipitation data from the coterminous United States.
Predicting bison migration out of Yellowstone National Park using bayesian models.
Directory of Open Access Journals (Sweden)
Chris Geremia
Full Text Available Long distance migrations by ungulate species often surpass the boundaries of preservation areas where conflicts with various publics lead to management actions that can threaten populations. We chose the partially migratory bison (Bison bison population in Yellowstone National Park as an example of integrating science into management policies to better conserve migratory ungulates. Approximately 60% of these bison have been exposed to bovine brucellosis and thousands of migrants exiting the park boundary have been culled during the past two decades to reduce the risk of disease transmission to cattle. Data were assimilated using models representing competing hypotheses of bison migration during 1990-2009 in a hierarchal bayesian framework. Migration differed at the scale of herds, but a single unifying logistic model was useful for predicting migrations by both herds. Migration beyond the northern park boundary was affected by herd size, accumulated snow water equivalent, and aboveground dried biomass. Migration beyond the western park boundary was less influenced by these predictors and process model performance suggested an important control on recent migrations was excluded. Simulations of migrations over the next decade suggest that allowing increased numbers of bison beyond park boundaries during severe climate conditions may be the only means of avoiding episodic, large-scale reductions to the Yellowstone bison population in the foreseeable future. This research is an example of how long distance migration dynamics can be incorporated into improved management policies.
Predicting bison migration out of Yellowstone National Park using bayesian models.
Geremia, Chris; White, P J; Wallen, Rick L; Watson, Fred G R; Treanor, John J; Borkowski, John; Potter, Christopher S; Crabtree, Robert L
2011-02-14
Long distance migrations by ungulate species often surpass the boundaries of preservation areas where conflicts with various publics lead to management actions that can threaten populations. We chose the partially migratory bison (Bison bison) population in Yellowstone National Park as an example of integrating science into management policies to better conserve migratory ungulates. Approximately 60% of these bison have been exposed to bovine brucellosis and thousands of migrants exiting the park boundary have been culled during the past two decades to reduce the risk of disease transmission to cattle. Data were assimilated using models representing competing hypotheses of bison migration during 1990-2009 in a hierarchal bayesian framework. Migration differed at the scale of herds, but a single unifying logistic model was useful for predicting migrations by both herds. Migration beyond the northern park boundary was affected by herd size, accumulated snow water equivalent, and aboveground dried biomass. Migration beyond the western park boundary was less influenced by these predictors and process model performance suggested an important control on recent migrations was excluded. Simulations of migrations over the next decade suggest that allowing increased numbers of bison beyond park boundaries during severe climate conditions may be the only means of avoiding episodic, large-scale reductions to the Yellowstone bison population in the foreseeable future. This research is an example of how long distance migration dynamics can be incorporated into improved management policies.
A Bayesian modelling framework for tornado occurrences in North America.
Cheng, Vincent Y S; Arhonditsis, George B; Sills, David M L; Gough, William A; Auld, Heather
2015-03-25
Tornadoes represent one of nature's most hazardous phenomena that have been responsible for significant destruction and devastating fatalities. Here we present a Bayesian modelling approach for elucidating the spatiotemporal patterns of tornado activity in North America. Our analysis shows a significant increase in the Canadian Prairies and the Northern Great Plains during the summer, indicating a clear transition of tornado activity from the United States to Canada. The linkage between monthly-averaged atmospheric variables and likelihood of tornado events is characterized by distinct seasonality; the convective available potential energy is the predominant factor in the summer; vertical wind shear appears to have a strong signature primarily in the winter and secondarily in the summer; and storm relative environmental helicity is most influential in the spring. The present probabilistic mapping can be used to draw inference on the likelihood of tornado occurrence in any location in North America within a selected time period of the year.
iSEDfit: Bayesian spectral energy distribution modeling of galaxies
Moustakas, John
2017-08-01
iSEDfit uses Bayesian inference to extract the physical properties of galaxies from their observed broadband photometric spectral energy distribution (SED). In its default mode, the inputs to iSEDfit are the measured photometry (fluxes and corresponding inverse variances) and a measurement of the galaxy redshift. Alternatively, iSEDfit can be used to estimate photometric redshifts from the input photometry alone. After the priors have been specified, iSEDfit calculates the marginalized posterior probability distributions for the physical parameters of interest, including the stellar mass, star-formation rate, dust content, star formation history, and stellar metallicity. iSEDfit also optionally computes K-corrections and produces multiple "quality assurance" (QA) plots at each stage of the modeling procedure to aid in the interpretation of the prior parameter choices and subsequent fitting results. The software is distributed as part of the impro IDL suite.
Hierarchical decision modeling essays in honor of Dundar F. Kocaoglu
2016-01-01
This volume, developed in honor of Dr. Dundar F. Kocaoglu, aims to demonstrate the applications of the Hierarchical Decision Model (HDM) in different sectors and its capacity in decision analysis. It is comprised of essays from noted scholars, academics and researchers of engineering and technology management around the world. This book is organized into four parts: Technology Assessment, Strategic Planning, National Technology Planning and Decision Making Tools. Dr. Dundar F. Kocaoglu is one of the pioneers of multiple decision models using hierarchies, and creator of the HDM in decision analysis. HDM is a mission-oriented method for evaluation and/or selection among alternatives. A wide range of alternatives can be considered, including but not limited to, different technologies, projects, markets, jobs, products, cities to live in, houses to buy, apartments to rent, and schools to attend. Dr. Kocaoglu’s approach has been adopted for decision problems in many industrial sectors, including electronics rese...
Bridging groundwater models and decision support with a Bayesian network
Fienen, Michael N.; Masterson, John P.; Plant, Nathaniel G.; Gutierrez, Benjamin T.; Thieler, E. Robert
2013-01-01
Resource managers need to make decisions to plan for future environmental conditions, particularly sea level rise, in the face of substantial uncertainty. Many interacting processes factor in to the decisions they face. Advances in process models and the quantification of uncertainty have made models a valuable tool for this purpose. Long-simulation runtimes and, often, numerical instability make linking process models impractical in many cases. A method for emulating the important connections between model input and forecasts, while propagating uncertainty, has the potential to provide a bridge between complicated numerical process models and the efficiency and stability needed for decision making. We explore this using a Bayesian network (BN) to emulate a groundwater flow model. We expand on previous approaches to validating a BN by calculating forecasting skill using cross validation of a groundwater model of Assateague Island in Virginia and Maryland, USA. This BN emulation was shown to capture the important groundwater-flow characteristics and uncertainty of the groundwater system because of its connection to island morphology and sea level. Forecast power metrics associated with the validation of multiple alternative BN designs guided the selection of an optimal level of BN complexity. Assateague island is an ideal test case for exploring a forecasting tool based on current conditions because the unique hydrogeomorphological variability of the island includes a range of settings indicative of past, current, and future conditions. The resulting BN is a valuable tool for exploring the response of groundwater conditions to sea level rise in decision support.
Malesevic, Nebojsa; Markovic, Dimitrije; Kanitz, Gunter; Controzzi, Marco; Cipriani, Christian; Antfolk, Christian
2017-07-01
In this paper we present a novel method for predicting individual fingers movements from surface electromyography (EMG). The method is intended for real-time dexterous control of a multifunctional prosthetic hand device. The EMG data was recorded using 16 single-ended channels positioned on the forearm of healthy participants. Synchronously with the EMG recording, the subjects performed consecutive finger movements based on the visual cues. Our algorithm could be described in following steps: extracting mean average value (MAV) of the EMG to be used as the feature for classification, piece-wise linear modeling of EMG feature dynamics, implementation of hierarchical hidden Markov models (HHMM) to capture transitions between linear models, and implementation of Bayesian inference as the classifier. The performance of our classifier was evaluated against commonly used real-time classifiers. The results show that the current algorithm setup classifies EMG data similarly to the best among tested classifiers but with equal or less computational complexity.
Aguirre-Salado, Alejandro Ivan; Vaquera-Huerta, Humberto; Aguirre-Salado, Carlos Arturo; Reyes-Mora, Silvia; Olvera-Cervantes, Ana Delia; Lancho-Romero, Guillermo Arturo; Soubervielle-Montalvo, Carlos
2017-07-06
We implemented a spatial model for analysing PM 10 maxima across the Mexico City metropolitan area during the period 1995-2016. We assumed that these maxima follow a non-identical generalized extreme value (GEV) distribution and modeled the trend by introducing multivariate smoothing spline functions into the probability GEV distribution. A flexible, three-stage hierarchical Bayesian approach was developed to analyse the distribution of the PM 10 maxima in space and time. We evaluated the statistical model's performance by using a simulation study. The results showed strong evidence of a positive correlation between the PM 10 maxima and the longitude and latitude. The relationship between time and the PM 10 maxima was negative, indicating a decreasing trend over time. Finally, a high risk of PM 10 maxima presenting levels above 1000 μ g/m 3 (return period: 25 yr) was observed in the northwestern region of the study area.
Bayesian Network Webserver: a comprehensive tool for biological network modeling.
Ziebarth, Jesse D; Bhattacharya, Anindya; Cui, Yan
2013-11-01
The Bayesian Network Webserver (BNW) is a platform for comprehensive network modeling of systems genetics and other biological datasets. It allows users to quickly and seamlessly upload a dataset, learn the structure of the network model that best explains the data and use the model to understand relationships between network variables. Many datasets, including those used to create genetic network models, contain both discrete (e.g. genotype) and continuous (e.g. gene expression traits) variables, and BNW allows for modeling hybrid datasets. Users of BNW can incorporate prior knowledge during structure learning through an easy-to-use structural constraint interface. After structure learning, users are immediately presented with an interactive network model, which can be used to make testable hypotheses about network relationships. BNW, including a downloadable structure learning package, is available at http://compbio.uthsc.edu/BNW. (The BNW interface for adding structural constraints uses HTML5 features that are not supported by current version of Internet Explorer. We suggest using other browsers (e.g. Google Chrome or Mozilla Firefox) when accessing BNW). ycui2@uthsc.edu. Supplementary data are available at Bioinformatics online.
Taming Many-Parameter BSM Models with Bayesian Neural Networks
Kuchera, M. P.; Karbo, A.; Prosper, H. B.; Sanchez, A.; Taylor, J. Z.
2017-09-01
The search for physics Beyond the Standard Model (BSM) is a major focus of large-scale high energy physics experiments. One method is to look for specific deviations from the Standard Model that are predicted by BSM models. In cases where the model has a large number of free parameters, standard search methods become intractable due to computation time. This talk presents results using Bayesian Neural Networks, a supervised machine learning method, to enable the study of higher-dimensional models. The popular phenomenological Minimal Supersymmetric Standard Model was studied as an example of the feasibility and usefulness of this method. Graphics Processing Units (GPUs) are used to expedite the calculations. Cross-section predictions for 13 TeV proton collisions will be presented. My participation in the Conference Experience for Undergraduates (CEU) in 2004-2006 exposed me to the national and global significance of cutting-edge research. At the 2005 CEU, I presented work from the previous summer's SULI internship at Lawrence Berkeley Laboratory, where I learned to program while working on the Majorana Project. That work inspired me to follow a similar research path, which led me to my current work on computational methods applied to BSM physics.
Bayesian model ensembling using meta-trained recurrent neural networks
Ambrogioni, L.; Berezutskaya, Y.; Gü ç lü , U.; Borne, E.W.P. van den; Gü ç lü tü rk, Y.; Gerven, M.A.J. van; Maris, E.G.G.
2017-01-01
In this paper we demonstrate that a recurrent neural network meta-trained on an ensemble of arbitrary classification tasks can be used as an approximation of the Bayes optimal classifier. This result is obtained by relying on the framework of e-free approximate Bayesian inference, where the Bayesian
A Bayesian Reformulation of the Extended Drift-Diffusion Model in Perceptual Decision Making.
Fard, Pouyan R; Park, Hame; Warkentin, Andrej; Kiebel, Stefan J; Bitzer, Sebastian
2017-01-01
Perceptual decision making can be described as a process of accumulating evidence to a bound which has been formalized within drift-diffusion models (DDMs). Recently, an equivalent Bayesian model has been proposed. In contrast to standard DDMs, this Bayesian model directly links information in the stimulus to the decision process. Here, we extend this Bayesian model further and allow inter-trial variability of two parameters following the extended version of the DDM. We derive parameter distributions for the Bayesian model and show that they lead to predictions that are qualitatively equivalent to those made by the extended drift-diffusion model (eDDM). Further, we demonstrate the usefulness of the extended Bayesian model (eBM) for the analysis of concrete behavioral data. Specifically, using Bayesian model selection, we find evidence that including additional inter-trial parameter variability provides for a better model, when the model is constrained by trial-wise stimulus features. This result is remarkable because it was derived using just 200 trials per condition, which is typically thought to be insufficient for identifying variability parameters in DDMs. In sum, we present a Bayesian analysis, which provides for a novel and promising analysis of perceptual decision making experiments.
A Bayesian Reformulation of the Extended Drift-Diffusion Model in Perceptual Decision Making
Fard, Pouyan R.; Park, Hame; Warkentin, Andrej; Kiebel, Stefan J.; Bitzer, Sebastian
2017-01-01
Perceptual decision making can be described as a process of accumulating evidence to a bound which has been formalized within drift-diffusion models (DDMs). Recently, an equivalent Bayesian model has been proposed. In contrast to standard DDMs, this Bayesian model directly links information in the stimulus to the decision process. Here, we extend this Bayesian model further and allow inter-trial variability of two parameters following the extended version of the DDM. We derive parameter distributions for the Bayesian model and show that they lead to predictions that are qualitatively equivalent to those made by the extended drift-diffusion model (eDDM). Further, we demonstrate the usefulness of the extended Bayesian model (eBM) for the analysis of concrete behavioral data. Specifically, using Bayesian model selection, we find evidence that including additional inter-trial parameter variability provides for a better model, when the model is constrained by trial-wise stimulus features. This result is remarkable because it was derived using just 200 trials per condition, which is typically thought to be insufficient for identifying variability parameters in DDMs. In sum, we present a Bayesian analysis, which provides for a novel and promising analysis of perceptual decision making experiments. PMID:28553219
A Bayesian Reformulation of the Extended Drift-Diffusion Model in Perceptual Decision Making
Directory of Open Access Journals (Sweden)
Pouyan R. Fard
2017-05-01
Full Text Available Perceptual decision making can be described as a process of accumulating evidence to a bound which has been formalized within drift-diffusion models (DDMs. Recently, an equivalent Bayesian model has been proposed. In contrast to standard DDMs, this Bayesian model directly links information in the stimulus to the decision process. Here, we extend this Bayesian model further and allow inter-trial variability of two parameters following the extended version of the DDM. We derive parameter distributions for the Bayesian model and show that they lead to predictions that are qualitatively equivalent to those made by the extended drift-diffusion model (eDDM. Further, we demonstrate the usefulness of the extended Bayesian model (eBM for the analysis of concrete behavioral data. Specifically, using Bayesian model selection, we find evidence that including additional inter-trial parameter variability provides for a better model, when the model is constrained by trial-wise stimulus features. This result is remarkable because it was derived using just 200 trials per condition, which is typically thought to be insufficient for identifying variability parameters in DDMs. In sum, we present a Bayesian analysis, which provides for a novel and promising analysis of perceptual decision making experiments.
Bayesian modeling of consumer behavior in the presence of anonymous visits
Novak, Julie Esther
Tailoring content to consumers has become a hallmark of marketing and digital media, particularly as it has become easier to identify customers across usage or purchase occasions. However, across a wide variety of contexts, companies find that customers do not consistently identify themselves, leaving a substantial fraction of anonymous visits. We develop a Bayesian hierarchical model that allows us to probabilistically assign anonymous sessions to users. These probabilistic assignments take into account a customer's demographic information, frequency of visitation, activities taken when visiting, and times of arrival. We present two studies, one with synthetic and one with real data, where we demonstrate improved performance over two popular practices (nearest-neighbor matching and deleting the anonymous visits) due to increased efficiency and reduced bias driven by the non-ignorability of which types of events are more likely to be anonymous. Using our proposed model, we avoid potential bias in understanding the effect of a firm's marketing on its customers, improve inference about the total number of customers in the dataset, and provide more precise targeted marketing to both previously observed and unobserved customers.
Bayesian Modeling of MPSS Data: Gene Expression Analysis of Bovine Salmonella Infection
Dhavala, Soma S.
2010-09-01
Massively Parallel Signature Sequencing (MPSS) is a high-throughput, counting-based technology available for gene expression profiling. It produces output that is similar to Serial Analysis of Gene Expression and is ideal for building complex relational databases for gene expression. Our goal is to compare the in vivo global gene expression profiles of tissues infected with different strains of Salmonella obtained using the MPSS technology. In this article, we develop an exact ANOVA type model for this count data using a zero-inflatedPoisson distribution, different from existing methods that assume continuous densities. We adopt two Bayesian hierarchical models-one parametric and the other semiparametric with a Dirichlet process prior that has the ability to "borrow strength" across related signatures, where a signature is a specific arrangement of the nucleotides, usually 16-21 base pairs long. We utilize the discreteness of Dirichlet process prior to cluster signatures that exhibit similar differential expression profiles. Tests for differential expression are carried out using nonparametric approaches, while controlling the false discovery rate. We identify several differentially expressed genes that have important biological significance and conclude with a summary of the biological discoveries. This article has supplementary materials online. © 2010 American Statistical Association.
Toman, Blaza; Nelson, Michael A; Lippa, Katrice A
2016-01-01
Chemical purity assessment using quantitative 1H-nuclear magnetic resonance spectroscopy is a method based on ratio references of mass and signal intensity of the analyte species to that of chemical standards of known purity. As such, it is an example of a calculation using a known measurement equation with multiple inputs. Though multiple samples are often analyzed during purity evaluations in order to assess measurement repeatability, the uncertainty evaluation must also account for contributions from inputs to the measurement equation. Furthermore, there may be other uncertainty components inherent in the experimental design, such as independent implementation of multiple calibration standards. As such, the uncertainty evaluation is not purely bottom up (based on the measurement equation) or top down (based on the experimental design), but inherently contains elements of both. This hybrid form of uncertainty analysis is readily implemented with Bayesian statistical analysis. In this article we describe this type of analysis in detail and illustrate it using data from an evaluation of chemical purity and its uncertainty for a folic acid material.
Sebro, Negusse Yohannes; Goshu, Ayele Taye
2017-01-01
This study aims to explore Bayesian multilevel modeling to investigate variations of average academic achievement of grade eight school students. A sample of 636 students is randomly selected from 26 private and government schools by a two-stage stratified sampling design. Bayesian method is used to estimate the fixed and random effects. Input and…
Stock Index Returns' Density Prediction using GARCH Models: Frequentist or Bayesian Estimation?
L.F. Hoogerheide (Lennart); D. David (David); N. Corre (Nienke)
2011-01-01
textabstractUsing well-known GARCH models for density prediction of daily S&P 500 and Nikkei 225 index returns, a comparison is provided between frequentist and Bayesian estimation. No significant difference is found between the qualities of the forecasts of the whole density, whereas the Bayesian
West, Patti; Rutstein, Daisy Wise; Mislevy, Robert J.; Liu, Junhui; Choi, Younyoung; Levy, Roy; Crawford, Aaron; DiCerbo, Kristen E.; Chappel, Kristina; Behrens, John T.
2010-01-01
A major issue in the study of learning progressions (LPs) is linking student performance on assessment tasks to the progressions. This report describes the challenges faced in making this linkage using Bayesian networks to model LPs in the field of computer networking. The ideas are illustrated with exemplar Bayesian networks built on Cisco…
Model-based Bayesian signal extraction algorithm for peripheral nerves
Eggers, Thomas E.; Dweiri, Yazan M.; McCallum, Grant A.; Durand, Dominique M.
2017-10-01
Objective. Multi-channel cuff electrodes have recently been investigated for extracting fascicular-level motor commands from mixed neural recordings. Such signals could provide volitional, intuitive control over a robotic prosthesis for amputee patients. Recent work has demonstrated success in extracting these signals in acute and chronic preparations using spatial filtering techniques. These extracted signals, however, had low signal-to-noise ratios and thus limited their utility to binary classification. In this work a new algorithm is proposed which combines previous source localization approaches to create a model based method which operates in real time. Approach. To validate this algorithm, a saline benchtop setup was created to allow the precise placement of artificial sources within a cuff and interference sources outside the cuff. The artificial source was taken from five seconds of chronic neural activity to replicate realistic recordings. The proposed algorithm, hybrid Bayesian signal extraction (HBSE), is then compared to previous algorithms, beamforming and a Bayesian spatial filtering method, on this test data. An example chronic neural recording is also analyzed with all three algorithms. Main results. The proposed algorithm improved the signal to noise and signal to interference ratio of extracted test signals two to three fold, as well as increased the correlation coefficient between the original and recovered signals by 10–20%. These improvements translated to the chronic recording example and increased the calculated bit rate between the recovered signals and the recorded motor activity. Significance. HBSE significantly outperforms previous algorithms in extracting realistic neural signals, even in the presence of external noise sources. These results demonstrate the feasibility of extracting dynamic motor signals from a multi-fascicled intact nerve trunk, which in turn could extract motor command signals from an amputee for the end goal of
Ensemble bayesian model averaging using markov chain Monte Carlo sampling
Energy Technology Data Exchange (ETDEWEB)
Vrugt, Jasper A [Los Alamos National Laboratory; Diks, Cees G H [NON LANL; Clark, Martyn P [NON LANL
2008-01-01
Bayesian model averaging (BMA) has recently been proposed as a statistical method to calibrate forecast ensembles from numerical weather models. Successful implementation of BMA however, requires accurate estimates of the weights and variances of the individual competing models in the ensemble. In their seminal paper (Raftery etal. Mon Weather Rev 133: 1155-1174, 2(05)) has recommended the Expectation-Maximization (EM) algorithm for BMA model training, even though global convergence of this algorithm cannot be guaranteed. In this paper, we compare the performance of the EM algorithm and the recently developed Differential Evolution Adaptive Metropolis (DREAM) Markov Chain Monte Carlo (MCMC) algorithm for estimating the BMA weights and variances. Simulation experiments using 48-hour ensemble data of surface temperature and multi-model stream-flow forecasts show that both methods produce similar results, and that their performance is unaffected by the length of the training data set. However, MCMC simulation with DREAM is capable of efficiently handling a wide variety of BMA predictive distributions, and provides useful information about the uncertainty associated with the estimated BMA weights and variances.
Bayesian calibration of the Community Land Model using surrogates
Energy Technology Data Exchange (ETDEWEB)
Ray, Jaideep; Hou, Zhangshuan; Huang, Maoyi; Swiler, Laura Painton
2014-02-01
We present results from the Bayesian calibration of hydrological parameters of the Community Land Model (CLM), which is often used in climate simulations and Earth system models. A statistical inverse problem is formulated for three hydrological parameters, conditional on observations of latent heat surface fluxes over 48 months. Our calibration method uses polynomial and Gaussian process surrogates of the CLM, and solves the parameter estimation problem using a Markov chain Monte Carlo sampler. Posterior probability densities for the parameters are developed for two sites with different soil and vegetation covers. Our method also allows us to examine the structural error in CLM under two error models. We find that surrogate models can be created for CLM in most cases. The posterior distributions are more predictive than the default parameter values in CLM. Climatologically averaging the observations does not modify the parameters' distributions significantly. The structural error model reveals a correlation time-scale which can be used to identify the physical process that could be contributing to it. While the calibrated CLM has a higher predictive skill, the calibration is under-dispersive.
Bayesian Models for Streamflow and River Network Reconstruction using Tree Rings
Ravindranath, A.; Devineni, N.
2016-12-01
Water systems face non-stationary, dynamically shifting risks due to shifting societal conditions and systematic long-term variations in climate manifesting as quasi-periodic behavior on multi-decadal time scales. Water systems are thus vulnerable to long periods of wet or dry hydroclimatic conditions. Streamflow is a major component of water systems and a primary means by which water is transported to serve ecosystems' and human needs. Thus, our concern is in understanding streamflow variability. Climate variability and impacts on water resources are crucial factors affecting streamflow, and multi-scale variability increases risk to water sustainability and systems. Dam operations are necessary for collecting water brought by streamflow while maintaining downstream ecological health. Rules governing dam operations are based on streamflow records that are woefully short compared to periods of systematic variation present in the climatic factors driving streamflow variability and non-stationarity. We use hierarchical Bayesian regression methods in order to reconstruct paleo-streamflow records for dams within a basin using paleoclimate proxies (e.g. tree rings) to guide the reconstructions. The riverine flow network for the entire basin is subsequently modeled hierarchically using feeder stream and tributary flows. This is a starting point in analyzing streamflow variability and risks to water systems, and developing a scientifically-informed dynamic risk management framework for formulating dam operations and water policies to best hedge such risks. We will apply this work to the Missouri and Delaware River Basins (DRB). Preliminary results of streamflow reconstructions for eight dams in the upper DRB using standard Gaussian regression with regional tree ring chronologies give streamflow records that now span two to two and a half centuries, and modestly smoothed versions of these reconstructed flows indicate physically-justifiable trends in the time series.
Application Bayesian Model Averaging method for ensemble system for Poland
Guzikowski, Jakub; Czerwinska, Agnieszka
2014-05-01
The aim of the project is to evaluate methods for generating numerical ensemble weather prediction using a meteorological data from The Weather Research & Forecasting Model and calibrating this data by means of Bayesian Model Averaging (WRF BMA) approach. We are constructing height resolution short range ensemble forecasts using meteorological data (temperature) generated by nine WRF's models. WRF models have 35 vertical levels and 2.5 km x 2.5 km horizontal resolution. The main emphasis is that the used ensemble members has a different parameterization of the physical phenomena occurring in the boundary layer. To calibrate an ensemble forecast we use Bayesian Model Averaging (BMA) approach. The BMA predictive Probability Density Function (PDF) is a weighted average of predictive PDFs associated with each individual ensemble member, with weights that reflect the member's relative skill. For test we chose a case with heat wave and convective weather conditions in Poland area from 23th July to 1st August 2013. From 23th July to 29th July 2013 temperature oscillated below or above 30 Celsius degree in many meteorology stations and new temperature records were added. During this time the growth of the hospitalized patients with cardiovascular system problems was registered. On 29th July 2013 an advection of moist tropical air masses was recorded in the area of Poland causes strong convection event with mesoscale convection system (MCS). MCS caused local flooding, damage to the transport infrastructure, destroyed buildings, trees and injuries and direct threat of life. Comparison of the meteorological data from ensemble system with the data recorded on 74 weather stations localized in Poland is made. We prepare a set of the model - observations pairs. Then, the obtained data from single ensemble members and median from WRF BMA system are evaluated on the basis of the deterministic statistical error Root Mean Square Error (RMSE), Mean Absolute Error (MAE). To evaluation
A Hierarchical Model for Continuous Gesture Recognition Using Kinect
DEFF Research Database (Denmark)
Jensen, Søren Kejser; Moesgaard, Christoffer; Nielsen, Christoffer Samuel
2013-01-01
Human gesture recognition is an area, which has been studied thoroughly in recent years,and close to100% recognition rates in restricted environments have been achieved, often either with single separated gestures in the input stream, or with computationally intensive systems. The results...... are unfortunately not as striking, when it comes to a continuous stream of gestures. In this paper we introduce a hierarchical system for gesture recognition for use in a gaming setting, with a continuous stream of data. Layer 1 is based on Nearest Neighbor Search and layer 2 uses Hidden Markov Models. The system...... propose a way of attributing recognised gestures with a force attribute, for use in gaming. The recognition rate in layer 1 is 68.2%, with an even higher rate for simple gestures. Layer 2 reduces the noise and has aaverage recognition rate of 85.1%. When some simple constraints are added we reach...
Forecasting unconventional resource productivity - A spatial Bayesian model
Montgomery, J.; O'sullivan, F.
2015-12-01
Today's low prices mean that unconventional oil and gas development requires ever greater efficiency and better development decision-making. Inter and intra-field variability in well productivity, which is a major contemporary driver of uncertainty regarding resource size and its economics is driven by factors including geological conditions, well and completion design (which companies vary as they seek to optimize their performance), and uncertainty about the nature of fracture propagation. Geological conditions are often not be well understood early on in development campaigns, but nevertheless critical assessments and decisions must be made regarding the value of drilling an area and the placement of wells. In these situations, location provides a reasonable proxy for geology and the "rock quality." We propose a spatial Bayesian model for forecasting acreage quality, which improves decision-making by leveraging available production data and provides a framework for statistically studying the influence of different parameters on well productivity. Our approach consists of subdividing a field into sections and forming prior distributions for productivity in each section based on knowledge about the overall field. Production data from wells is used to update these estimates in a Bayesian fashion, improving model accuracy far more rapidly and with less sensitivity to outliers than a model that simply establishes an "average" productivity in each section. Additionally, forecasts using this model capture the importance of uncertainty—either due to a lack of information or for areas that demonstrate greater geological risk. We demonstrate the forecasting utility of this method using public data and also provide examples of how information from this model can be combined with knowledge about a field's geology or changes in technology to better quantify development risk. This approach represents an important shift in the way that production data is used to guide
Etienne, RS; Olff, H
Species abundances are undoubtedly the most widely available macroecological data, but can we use them to distinguish among several models of community structure? Here we present a Bayesian analysis of species-abundance data that yields a full joint probability distribution of each model's
Etienne, R.S.; Olff, H.
2005-01-01
Species abundances are undoubtedly the most widely available macroecological data, but can we use them to distinguish among several models of community structure? Here we present a Bayesian analysis of species-abundance data that yields a full joint probability distribution of each model's
Assessing fit in Bayesian models for spatial processes
Jun, M.
2014-09-16
© 2014 John Wiley & Sons, Ltd. Gaussian random fields are frequently used to model spatial and spatial-temporal data, particularly in geostatistical settings. As much of the attention of the statistics community has been focused on defining and estimating the mean and covariance functions of these processes, little effort has been devoted to developing goodness-of-fit tests to allow users to assess the models\\' adequacy. We describe a general goodness-of-fit test and related graphical diagnostics for assessing the fit of Bayesian Gaussian process models using pivotal discrepancy measures. Our method is applicable for both regularly and irregularly spaced observation locations on planar and spherical domains. The essential idea behind our method is to evaluate pivotal quantities defined for a realization of a Gaussian random field at parameter values drawn from the posterior distribution. Because the nominal distribution of the resulting pivotal discrepancy measures is known, it is possible to quantitatively assess model fit directly from the output of Markov chain Monte Carlo algorithms used to sample from the posterior distribution on the parameter space. We illustrate our method in a simulation study and in two applications.
A Bayesian model for the analysis of transgenerational epigenetic variation.
Varona, Luis; Munilla, Sebastián; Mouresan, Elena Flavia; González-Rodríguez, Aldemar; Moreno, Carlos; Altarriba, Juan
2015-01-23
Epigenetics has become one of the major areas of biological research. However, the degree of phenotypic variability that is explained by epigenetic processes still remains unclear. From a quantitative genetics perspective, the estimation of variance components is achieved by means of the information provided by the resemblance between relatives. In a previous study, this resemblance was described as a function of the epigenetic variance component and a reset coefficient that indicates the rate of dissipation of epigenetic marks across generations. Given these assumptions, we propose a Bayesian mixed model methodology that allows the estimation of epigenetic variance from a genealogical and phenotypic database. The methodology is based on the development of a T: matrix of epigenetic relationships that depends on the reset coefficient. In addition, we present a simple procedure for the calculation of the inverse of this matrix ( T-1: ) and a Gibbs sampler algorithm that obtains posterior estimates of all the unknowns in the model. The new procedure was used with two simulated data sets and with a beef cattle database. In the simulated populations, the results of the analysis provided marginal posterior distributions that included the population parameters in the regions of highest posterior density. In the case of the beef cattle dataset, the posterior estimate of transgenerational epigenetic variability was very low and a model comparison test indicated that a model that did not included it was the most plausible. Copyright © 2015 Varona et al.
Bayesian model calibration of ramp compression experiments on Z
Brown, Justin; Hund, Lauren
2017-06-01
Bayesian model calibration (BMC) is a statistical framework to estimate inputs for a computational model in the presence of multiple uncertainties, making it well suited to dynamic experiments which must be coupled with numerical simulations to interpret the results. Often, dynamic experiments are diagnosed using velocimetry and this output can be modeled using a hydrocode. Several calibration issues unique to this type of scenario including the functional nature of the output, uncertainty of nuisance parameters within the simulation, and model discrepancy identifiability are addressed, and a novel BMC process is proposed. As a proof of concept, we examine experiments conducted on Sandia National Laboratories' Z-machine which ramp compressed tantalum to peak stresses of 250 GPa. The proposed BMC framework is used to calibrate the cold curve of Ta (with uncertainty), and we conclude that the procedure results in simple, fast, and valid inferences. Sandia National Laboratories is a multi-mission laboratory managed and operated by Sandia Corporation, a wholly owned subsidiary of Lockheed Martin Corporation, for the U.S. Department of Energy's National Nuclear Security Administration under contract DE-AC04-94AL85000.
Fer, I.; Kelly, R.; Andrews, T.; Dietze, M.; Richardson, A. D.
2016-12-01
Our ability to forecast ecosystems is limited by how well we parameterize ecosystem models. Direct measurements for all model parameters are not always possible and inverse estimation of these parameters through Bayesian methods is computationally costly. A solution to computational challenges of Bayesian calibration is to approximate the posterior probability surface using a Gaussian Process that emulates the complex process-based model. Here we report the integration of this method within an ecoinformatics toolbox, Predictive Ecosystem Analyzer (PEcAn), and its application with two ecosystem models: SIPNET and ED2.1. SIPNET is a simple model, allowing application of MCMC methods both to the model itself and to its emulator. We used both approaches to assimilate flux (CO2 and latent heat), soil respiration, and soil carbon data from Bartlett Experimental Forest. This comparison showed that emulator is reliable in terms of convergence to the posterior distribution. A 10000-iteration MCMC analysis with SIPNET itself required more than two orders of magnitude greater computation time than an MCMC run of same length with its emulator. This difference would be greater for a more computationally demanding model. Validation of the emulator-calibrated SIPNET against both the assimilated data and out-of-sample data showed improved fit and reduced uncertainty around model predictions. We next applied the validated emulator method to the ED2, whose complexity precludes standard Bayesian data assimilation. We used the ED2 emulator to assimilate demographic data from a network of inventory plots. For validation of the calibrated ED2, we compared the model to results from Empirical Succession Mapping (ESM), a novel synthesis of successional patterns in Forest Inventory and Analysis data. Our results revealed that while the pre-assimilation ED2 formulation cannot capture the emergent demographic patterns from ESM analysis, constrained model parameters controlling demographic
Application of hierarchical genetic models to Raven and WAIS subtests: a Dutch twin study
Rijsdijk, F.V.; Vernon, P.A.; Boomsma, D.I.
2002-01-01
Hierarchical models of intelligence are highly informative and widely accepted. Application of these models to twin data, however, is sparse. This paper addresses the question of how a genetic hierarchical model fits the Wechsler Adult Intelligence Scale (WAIS) subtests and the Raven Standard
Directory of Open Access Journals (Sweden)
Alejandro Ivan Aguirre-Salado
2017-07-01
Full Text Available We implemented a spatial model for analysing PM 10 maxima across the Mexico City metropolitan area during the period 1995–2016. We assumed that these maxima follow a non-identical generalized extreme value (GEV distribution and modeled the trend by introducing multivariate smoothing spline functions into the probability GEV distribution. A flexible, three-stage hierarchical Bayesian approach was developed to analyse the distribution of the PM 10 maxima in space and time. We evaluated the statistical model’s performance by using a simulation study. The results showed strong evidence of a positive correlation between the PM 10 maxima and the longitude and latitude. The relationship between time and the PM 10 maxima was negative, indicating a decreasing trend over time. Finally, a high risk of PM 10 maxima presenting levels above 1000 μ g/m 3 (return period: 25 yr was observed in the northwestern region of the study area.
Flexible Bayesian Dynamic Modeling of Covariance and Correlation Matrices
Lan, Shiwei
2017-11-08
Modeling covariance (and correlation) matrices is a challenging problem due to the large dimensionality and positive-definiteness constraint. In this paper, we propose a novel Bayesian framework based on decomposing the covariance matrix into variance and correlation matrices. The highlight is that the correlations are represented as products of vectors on unit spheres. We propose a variety of distributions on spheres (e.g. the squared-Dirichlet distribution) to induce flexible prior distributions for covariance matrices that go beyond the commonly used inverse-Wishart prior. To handle the intractability of the resulting posterior, we introduce the adaptive $\\\\Delta$-Spherical Hamiltonian Monte Carlo. We also extend our structured framework to dynamic cases and introduce unit-vector Gaussian process priors for modeling the evolution of correlation among multiple time series. Using an example of Normal-Inverse-Wishart problem, a simulated periodic process, and an analysis of local field potential data (collected from the hippocampus of rats performing a complex sequence memory task), we demonstrated the validity and effectiveness of our proposed framework for (dynamic) modeling covariance and correlation matrices.
Bayesian network model of crowd emotion and negative behavior
Ramli, Nurulhuda; Ghani, Noraida Abdul; Hatta, Zulkarnain Ahmad; Hashim, Intan Hashimah Mohd; Sulong, Jasni; Mahudin, Nor Diana Mohd; Rahman, Shukran Abd; Saad, Zarina Mat
2014-12-01
The effects of overcrowding have become a major concern for event organizers. One aspect of this concern has been the idea that overcrowding can enhance the occurrence of serious incidents during events. As one of the largest Muslim religious gathering attended by pilgrims from all over the world, Hajj has become extremely overcrowded with many incidents being reported. The purpose of this study is to analyze the nature of human emotion and negative behavior resulting from overcrowding during Hajj events from data gathered in Malaysian Hajj Experience Survey in 2013. The sample comprised of 147 Malaysian pilgrims (70 males and 77 females). Utilizing a probabilistic model called Bayesian network, this paper models the dependence structure between different emotions and negative behaviors of pilgrims in the crowd. The model included the following variables of emotion: negative, negative comfortable, positive, positive comfortable and positive spiritual and variables of negative behaviors; aggressive and hazardous acts. The study demonstrated that emotions of negative, negative comfortable, positive spiritual and positive emotion have a direct influence on aggressive behavior whereas emotion of negative comfortable, positive spiritual and positive have a direct influence on hazardous acts behavior. The sensitivity analysis showed that a low level of negative and negative comfortable emotions leads to a lower level of aggressive and hazardous behavior. Findings of the study can be further improved to identify the exact cause and risk factors of crowd-related incidents in preventing crowd disasters during the mass gathering events.
Parameter Estimation of Structural Equation Modeling Using Bayesian Approach
Directory of Open Access Journals (Sweden)
Dewi Kurnia Sari
2016-05-01
Full Text Available Leadership is a process of influencing, directing or giving an example of employees in order to achieve the objectives of the organization and is a key element in the effectiveness of the organization. In addition to the style of leadership, the success of an organization or company in achieving its objectives can also be influenced by the commitment of the organization. Where organizational commitment is a commitment created by each individual for the betterment of the organization. The purpose of this research is to obtain a model of leadership style and organizational commitment to job satisfaction and employee performance, and determine the factors that influence job satisfaction and employee performance using SEM with Bayesian approach. This research was conducted at Statistics FNI employees in Malang, with 15 people. The result of this study showed that the measurement model, all significant indicators measure each latent variable. Meanwhile in the structural model, it was concluded there are a significant difference between the variables of Leadership Style and Organizational Commitment toward Job Satisfaction directly as well as a significant difference between Job Satisfaction on Employee Performance. As for the influence of Leadership Style and variable Organizational Commitment on Employee Performance directly declared insignificant.
Hierarchical modeling and its numerical implementation for layered thin elastic structures
Energy Technology Data Exchange (ETDEWEB)
Cho, Jin-Rae [Hongik University, Sejong (Korea, Republic of)
2017-05-15
Thin elastic structures such as beam- and plate-like structures and laminates are characterized by the small thickness, which lead to classical plate and laminate theories in which the displacement fields through the thickness are assumed linear or higher-order polynomials. These classical theories are either insufficient to represent the complex stress variation through the thickness or may encounter the accuracy-computational cost dilemma. In order to overcome the inherent problem of classical theories, the concept of hierarchical modeling has been emerged. In the hierarchical modeling, the hierarchical models with different model levels are selected and combined within a structure domain, in order to make the modeling error be distributed as uniformly as possible throughout the problem domain. The purpose of current study is to explore the potential of hierarchical modeling for the effective numerical analysis of layered structures such as laminated composite. For this goal, the hierarchical models are constructed and the hierarchical modeling is implemented by selectively adjusting the level of hierarchical models. As well, the major characteristics of hierarchical models are investigated through the numerical experiments.
Feng, Xiaohui; Dietze, Michael
2013-12-01
Relationships between leaf traits and carbon assimilation rates are commonly used to predict primary productivity at scales from the leaf to the globe. We addressed how the shape and magnitude of these relationships vary across temporal, spatial and taxonomic scales to improve estimates of carbon dynamics. Photosynthetic CO2 and light response curves, leaf nitrogen (N), chlorophyll (Chl) concentration and specific leaf area (SLA) of 25 grassland species were measured. In addition, C3 and C4 photosynthesis models were parameterized using a novel hierarchical Bayesian approach to quantify the effects of leaf traits on photosynthetic capacity and parameters at different scales. The effects of plant physiological traits on photosynthetic capacity and parameters varied among species, plant functional types and taxonomic scales. Relationships in the grassland biome were significantly different from the global average. Within-species variability in photosynthetic parameters through the growing season could be attributed to the seasonal changes of leaf traits, especially leaf N and Chl, but these responses followed qualitatively different relationships from the across-species relationship. The results suggest that one broad-scale relationship is not sufficient to characterize ecosystem condition and change at multiple scales. Applying trait relationships without articulating the scales may cause substantial carbon flux estimation errors. © 2013 The Authors. New Phytologist © 2013 New Phytologist Trust.
A biological hierarchical model based underwater moving object detection.
Shen, Jie; Fan, Tanghuai; Tang, Min; Zhang, Qian; Sun, Zhen; Huang, Fengchen
2014-01-01
Underwater moving object detection is the key for many underwater computer vision tasks, such as object recognizing, locating, and tracking. Considering the super ability in visual sensing of the underwater habitats, the visual mechanism of aquatic animals is generally regarded as the cue for establishing bionic models which are more adaptive to the underwater environments. However, the low accuracy rate and the absence of the prior knowledge learning limit their adaptation in underwater applications. Aiming to solve the problems originated from the inhomogeneous lumination and the unstable background, the mechanism of the visual information sensing and processing pattern from the eye of frogs are imitated to produce a hierarchical background model for detecting underwater objects. Firstly, the image is segmented into several subblocks. The intensity information is extracted for establishing background model which could roughly identify the object and the background regions. The texture feature of each pixel in the rough object region is further analyzed to generate the object contour precisely. Experimental results demonstrate that the proposed method gives a better performance. Compared to the traditional Gaussian background model, the completeness of the object detection is 97.92% with only 0.94% of the background region that is included in the detection results.
A Biological Hierarchical Model Based Underwater Moving Object Detection
Directory of Open Access Journals (Sweden)
Jie Shen
2014-01-01
Full Text Available Underwater moving object detection is the key for many underwater computer vision tasks, such as object recognizing, locating, and tracking. Considering the super ability in visual sensing of the underwater habitats, the visual mechanism of aquatic animals is generally regarded as the cue for establishing bionic models which are more adaptive to the underwater environments. However, the low accuracy rate and the absence of the prior knowledge learning limit their adaptation in underwater applications. Aiming to solve the problems originated from the inhomogeneous lumination and the unstable background, the mechanism of the visual information sensing and processing pattern from the eye of frogs are imitated to produce a hierarchical background model for detecting underwater objects. Firstly, the image is segmented into several subblocks. The intensity information is extracted for establishing background model which could roughly identify the object and the background regions. The texture feature of each pixel in the rough object region is further analyzed to generate the object contour precisely. Experimental results demonstrate that the proposed method gives a better performance. Compared to the traditional Gaussian background model, the completeness of the object detection is 97.92% with only 0.94% of the background region that is included in the detection results.
Bayesian Regression of Thermodynamic Models of Redox Active Materials
Energy Technology Data Exchange (ETDEWEB)
Johnston, Katherine [Sandia National Lab. (SNL-NM), Albuquerque, NM (United States)
2017-09-01
Finding a suitable functional redox material is a critical challenge to achieving scalable, economically viable technologies for storing concentrated solar energy in the form of a defected oxide. Demonstrating e ectiveness for thermal storage or solar fuel is largely accomplished by using a thermodynamic model derived from experimental data. The purpose of this project is to test the accuracy of our regression model on representative data sets. Determining the accuracy of the model includes parameter tting the model to the data, comparing the model using di erent numbers of param- eters, and analyzing the entropy and enthalpy calculated from the model. Three data sets were considered in this project: two demonstrating materials for solar fuels by wa- ter splitting and the other of a material for thermal storage. Using Bayesian Inference and Markov Chain Monte Carlo (MCMC), parameter estimation was preformed on the three data sets. Good results were achieved, except some there was some deviations on the edges of the data input ranges. The evidence values were then calculated in a variety of ways and used to compare models with di erent number of parameters. It was believed that at least one of the parameters was unnecessary and comparing evidence values demonstrated that the parameter was need on one data set and not signi cantly helpful on another. The entropy was calculated by taking the derivative in one variable and integrating over another. and its uncertainty was also calculated by evaluating the entropy over multiple MCMC samples. Afterwards, all the parts were written up as a tutorial for the Uncertainty Quanti cation Toolkit (UQTk).
Macroscopic Models of Clique Tree Growth for Bayesian Networks
National Aeronautics and Space Administration — In clique tree clustering, inference consists of propagation in a clique tree compiled from a Bayesian network. In this paper, we develop an analytical approach to...
MRI Based Bayesian Personalization of a Tumor Growth Model.
Le, Matthieu; Delingette, Herve; Kalpathy-Cramer, Jayashree; Gerstner, Elizabeth R; Batchelor, Tracy; Unkelbach, Jan; Ayache, Nicholas
2016-10-01
The mathematical modeling of brain tumor growth has been the topic of numerous research studies. Most of this work focuses on the reaction-diffusion model, which suggests that the diffusion coefficient and the proliferation rate can be related to clinically relevant information. However, estimating the parameters of the reaction-diffusion model is difficult because of the lack of identifiability of the parameters, the uncertainty in the tumor segmentations, and the model approximation, which cannot perfectly capture the complex dynamics of the tumor evolution. Our approach aims at analyzing the uncertainty in the patient specific parameters of a tumor growth model, by sampling from the posterior probability of the parameters knowing the magnetic resonance images of a given patient. The estimation of the posterior probability is based on: 1) a highly parallelized implementation of the reaction-diffusion equation using the Lattice Boltzmann Method (LBM), and 2) a high acceptance rate Monte Carlo technique called Gaussian Process Hamiltonian Monte Carlo (GPHMC). We compare this personalization approach with two commonly used methods based on the spherical asymptotic analysis of the reaction-diffusion model, and on a derivative-free optimization algorithm. We demonstrate the performance of the method on synthetic data, and on seven patients with a glioblastoma, the most aggressive primary brain tumor. This Bayesian personalization produces more informative results. In particular, it provides samples from the regions of interest and highlights the presence of several modes for some patients. In contrast, previous approaches based on optimization strategies fail to reveal the presence of different modes, and correlation between parameters.
Bayesian model of protein primary sequence for secondary structure prediction.
Directory of Open Access Journals (Sweden)
Qiwei Li
Full Text Available Determining the primary structure (i.e., amino acid sequence of a protein has become cheaper, faster, and more accurate. Higher order protein structure provides insight into a protein's function in the cell. Understanding a protein's secondary structure is a first step towards this goal. Therefore, a number of computational prediction methods have been developed to predict secondary structure from just the primary amino acid sequence. The most successful methods use machine learning approaches that are quite accurate, but do not directly incorporate structural information. As a step towards improving secondary structure reduction given the primary structure, we propose a Bayesian model based on the knob-socket model of protein packing in secondary structure. The method considers the packing influence of residues on the secondary structure determination, including those packed close in space but distant in sequence. By performing an assessment of our method on 2 test sets we show how incorporation of multiple sequence alignment data, similarly to PSIPRED, provides balance and improves the accuracy of the predictions. Software implementing the methods is provided as a web application and a stand-alone implementation.
A Bayesian Model of Group Decision-Making
Directory of Open Access Journals (Sweden)
Tadeusz Wibig
2016-01-01
Full Text Available A change in the opinion of a group, treated as a network of communicating agents, caused by the accumulation of new information is expected to depend on communication within the group, cooperation and, possibly, a kind of conformity mechanism. We have developed a mathematical model of the creation of a group decision, including this effect. This is based on a Bayesian description of inference and can be used for both conscious and inattentive acts. This model can be used to study the effect of whether a leader exists or not and other group inhomogeneities, as well as establishing the (statistical significance and quality of a group decision. The proposed evolution equations explain in a straightforward, analytical way some general properties of the general phenomenon of conformity (groupthink. To illustrate this theoretical idea in practice, we created an information technology (IT tool to study the effect of conformity in a small group. As an example, we present results of an experiment performed using a network of students' tablets, which could not only measure group pressure, but also conduct and control collaborative thinking in the group. (original abstract
Nitrate source apportionment in a subtropical watershed using Bayesian model
Energy Technology Data Exchange (ETDEWEB)
Yang, Liping; Han, Jiangpei; Xue, Jianlong; Zeng, Lingzao [College of Environmental and Natural Resource Sciences, Zhejiang Provincial Key Laboratory of Subtropical Soil and Plant Nutrition, Zhejiang University, Hangzhou, 310058 (China); Shi, Jiachun, E-mail: jcshi@zju.edu.cn [College of Environmental and Natural Resource Sciences, Zhejiang Provincial Key Laboratory of Subtropical Soil and Plant Nutrition, Zhejiang University, Hangzhou, 310058 (China); Wu, Laosheng, E-mail: laowu@zju.edu.cn [College of Environmental and Natural Resource Sciences, Zhejiang Provincial Key Laboratory of Subtropical Soil and Plant Nutrition, Zhejiang University, Hangzhou, 310058 (China); Jiang, Yonghai [State Key Laboratory of Environmental Criteria and Risk Assessment, Chinese Research Academy of Environmental Sciences, Beijing, 100012 (China)
2013-10-01
Nitrate (NO{sub 3}{sup −}) pollution in aquatic system is a worldwide problem. The temporal distribution pattern and sources of nitrate are of great concern for water quality. The nitrogen (N) cycling processes in a subtropical watershed located in Changxing County, Zhejiang Province, China were greatly influenced by the temporal variations of precipitation and temperature during the study period (September 2011 to July 2012). The highest NO{sub 3}{sup −} concentration in water was in May (wet season, mean ± SD = 17.45 ± 9.50 mg L{sup −1}) and the lowest concentration occurred in December (dry season, mean ± SD = 10.54 ± 6.28 mg L{sup −1}). Nevertheless, no water sample in the study area exceeds the WHO drinking water limit of 50 mg L{sup −1} NO{sub 3}{sup −}. Four sources of NO{sub 3}{sup −} (atmospheric deposition, AD; soil N, SN; synthetic fertilizer, SF; manure and sewage, M and S) were identified using both hydrochemical characteristics [Cl{sup −}, NO{sub 3}{sup −}, HCO{sub 3}{sup −}, SO{sub 4}{sup 2−}, Ca{sup 2+}, K{sup +}, Mg{sup 2+}, Na{sup +}, dissolved oxygen (DO)] and dual isotope approach (δ{sup 15}N–NO{sub 3}{sup −} and δ{sup 18}O–NO{sub 3}{sup −}). Both chemical and isotopic characteristics indicated that denitrification was not the main N cycling process in the study area. Using a Bayesian model (stable isotope analysis in R, SIAR), the contribution of each source was apportioned. Source apportionment results showed that source contributions differed significantly between the dry and wet season, AD and M and S contributed more in December than in May. In contrast, SN and SF contributed more NO{sub 3}{sup −} to water in May than that in December. M and S and SF were the major contributors in December and May, respectively. Moreover, the shortcomings and uncertainties of SIAR were discussed to provide implications for future works. With the assessment of temporal variation and sources of NO{sub 3}{sup −}, better
A hierarchical network modeling method for railway tunnels safety assessment
Zhou, Jin; Xu, Weixiang; Guo, Xin; Liu, Xumin
2017-02-01
Using network theory to model risk-related knowledge on accidents is regarded as potential very helpful in risk management. A large amount of defects detection data for railway tunnels is collected in autumn every year in China. It is extremely important to discover the regularities knowledge in database. In this paper, based on network theories and by using data mining techniques, a new method is proposed for mining risk-related regularities to support risk management in railway tunnel projects. A hierarchical network (HN) model which takes into account the tunnel structures, tunnel defects, potential failures and accidents is established. An improved Apriori algorithm is designed to rapidly and effectively mine correlations between tunnel structures and tunnel defects. Then an algorithm is presented in order to mine the risk-related regularities table (RRT) from the frequent patterns. At last, a safety assessment method is proposed by consideration of actual defects and possible risks of defects gained from the RRT. This method cannot only generate the quantitative risk results but also reveal the key defects and critical risks of defects. This paper is further development on accident causation network modeling methods which can provide guidance for specific maintenance measure.
Lu, Tingrong
2008-01-01
In Kleinrock and Kamoun's paper, the inverse relation of routing table length index and routing path length index in hierarchical routing model is illustrated. In this paper we give the analytical correlation of routing table length index and routing path length index in hierarchical routing model.
On the Estimation of Hierarchical Latent Regression Models for Large-Scale Assessments
Li, Deping; Oranje, Andreas; Jiang, Yanlin
2009-01-01
To find population proficiency distributions, a two-level hierarchical linear model may be applied to large-scale survey assessments such as the National Assessment of Educational Progress (NAEP). The model and parameter estimation are developed and a simulation was carried out to evaluate parameter recovery. Subsequently, both a hierarchical and…
A note on adding and deleting edges in hierarchical log-linear models
DEFF Research Database (Denmark)
Edwards, David
2012-01-01
The operations of edge addition and deletion for hierarchical log-linear models are defined, and polynomial-time algorithms for the operations are given......The operations of edge addition and deletion for hierarchical log-linear models are defined, and polynomial-time algorithms for the operations are given...
Bayesian inference for partially identified models exploring the limits of limited data
Gustafson, Paul
2015-01-01
Introduction Identification What Is against Us? What Is for Us? Some Simple Examples of Partially Identified ModelsThe Road Ahead The Structure of Inference in Partially Identified Models Bayesian Inference The Structure of Posterior Distributions in PIMs Computational Strategies Strength of Bayesian Updating, Revisited Posterior MomentsCredible Intervals Evaluating the Worth of Inference Partial Identification versus Model Misspecification The Siren Call of Identification Comp
A Bayesian vector error corrections model of the U.S. economy
Tom Stark
1998-01-01
This paper presents a small-scale macroeconometric time-series model that can be used to generate short-term forecasts for U.S. output, inflation, and the rate of unemployment. Drawing on both the Bayesian VAR and vector error corrections (VEC) literature, the author specifies the baseline model as a Bayesian VEC. The author documents the model's forecasting ability over various periods, examines its impulse responses, and considers several reasonable alternative specifications. Based on a ro...
Demeter, R.M.; Kristensen, A.R.; Dijkstra, J.; Oude Lansink, A.G.J.M.; Meuwissen, M.P.M.; Arendonk, van J.A.M.
2011-01-01
Herd optimization models that determine economically optimal insemination and replacement decisions are valuable research tools to study various aspects of farming systems. The aim of this study was to develop a herd optimization and simulation model for dairy cattle. The model determines
Reliability assessment using degradation models: bayesian and classical approaches
Directory of Open Access Journals (Sweden)
Marta Afonso Freitas
2010-04-01
Full Text Available Traditionally, reliability assessment of devices has been based on (accelerated life tests. However, for highly reliable products, little information about reliability is provided by life tests in which few or no failures are typically observed. Since most failures arise from a degradation mechanism at work for which there are characteristics that degrade over time, one alternative is monitor the device for a period of time and assess its reliability from the changes in performance (degradation observed during that period. The goal of this article is to illustrate how degradation data can be modeled and analyzed by using "classical" and Bayesian approaches. Four methods of data analysis based on classical inference are presented. Next we show how Bayesian methods can also be used to provide a natural approach to analyzing degradation data. The approaches are applied to a real data set regarding train wheels degradation.Tradicionalmente, o acesso à confiabilidade de dispositivos tem sido baseado em testes de vida (acelerados. Entretanto, para produtos altamente confiáveis, pouca informação a respeito de sua confiabilidade é fornecida por testes de vida no quais poucas ou nenhumas falhas são observadas. Uma vez que boa parte das falhas é induzida por mecanismos de degradação, uma alternativa é monitorar o dispositivo por um período de tempo e acessar sua confiabilidade através das mudanças em desempenho (degradação observadas durante aquele período. O objetivo deste artigo é ilustrar como dados de degradação podem ser modelados e analisados utilizando-se abordagens "clássicas" e Bayesiana. Quatro métodos de análise de dados baseados em inferência clássica são apresentados. A seguir, mostramos como os métodos Bayesianos podem também ser aplicados para proporcionar uma abordagem natural à análise de dados de degradação. As abordagens são aplicadas a um banco de dados real relacionado à degradação de rodas de trens.
Smania, G; Baiardi, P; Ceci, A; Cella, M; Magni, P
2016-08-01
This study presents a pharmacokinetic-pharmacodynamic based clinical trial simulation framework for evaluating the performance of a fixed-sample Bayesian design (BD) and two alternative Bayesian sequential designs (BSDs) (i.e., a non-hierarchical (NON-H) and a semi-hierarchical (SEMI-H) one). Prior information was elicited from adult trials and weighted based on the expected similarity of response to treatment between the pediatric and adult populations. Study designs were evaluated in terms of: type I and II errors, sample size per arm (SS), trial duration (TD), and estimate precision. No substantial differences were observed between NON-H and SEMI-H. BSDs require, on average, smaller SS and TD compared to the BD, which, on the other hand, guarantees higher estimate precision. When large differences between children and adults are expected, BSDs can return very large SS. Bayesian approaches appear to outperform their frequentist counterparts in the design of pediatric trials even when little weight is given to prior information from adults. © 2016 The Authors CPT: Pharmacometrics & Systems Pharmacology published by Wiley Periodicals, Inc. on behalf of American Society for Clinical Pharmacology and Therapeutics.
Tauber, Sean; Navarro, Daniel J; Perfors, Amy; Steyvers, Mark
2017-07-01
Recent debates in the psychological literature have raised questions about the assumptions that underpin Bayesian models of cognition and what inferences they license about human cognition. In this paper we revisit this topic, arguing that there are 2 qualitatively different ways in which a Bayesian model could be constructed. The most common approach uses a Bayesian model as a normative standard upon which to license a claim about optimality. In the alternative approach, a descriptive Bayesian model need not correspond to any claim that the underlying cognition is optimal or rational, and is used solely as a tool for instantiating a substantive psychological theory. We present 3 case studies in which these 2 perspectives lead to different computational models and license different conclusions about human cognition. We demonstrate how the descriptive Bayesian approach can be used to answer different sorts of questions than the optimal approach, especially when combined with principled tools for model evaluation and model selection. More generally we argue for the importance of making a clear distinction between the 2 perspectives. Considerable confusion results when descriptive models and optimal models are conflated, and if Bayesians are to avoid contributing to this confusion it is important to avoid making normative claims when none are intended. (PsycINFO Database Record (c) 2017 APA, all rights reserved).
Bayesian Safety Risk Modeling of Human-Flightdeck Automation Interaction
Ancel, Ersin; Shih, Ann T.
2015-01-01
Usage of automatic systems in airliners has increased fuel efficiency, added extra capabilities, enhanced safety and reliability, as well as provide improved passenger comfort since its introduction in the late 80's. However, original automation benefits, including reduced flight crew workload, human errors or training requirements, were not achieved as originally expected. Instead, automation introduced new failure modes, redistributed, and sometimes increased workload, brought in new cognitive and attention demands, and increased training requirements. Modern airliners have numerous flight modes, providing more flexibility (and inherently more complexity) to the flight crew. However, the price to pay for the increased flexibility is the need for increased mode awareness, as well as the need to supervise, understand, and predict automated system behavior. Also, over-reliance on automation is linked to manual flight skill degradation and complacency in commercial pilots. As a result, recent accidents involving human errors are often caused by the interactions between humans and the automated systems (e.g., the breakdown in man-machine coordination), deteriorated manual flying skills, and/or loss of situational awareness due to heavy dependence on automated systems. This paper describes the development of the increased complexity and reliance on automation baseline model, named FLAP for FLightdeck Automation Problems. The model development process starts with a comprehensive literature review followed by the construction of a framework comprised of high-level causal factors leading to an automation-related flight anomaly. The framework was then converted into a Bayesian Belief Network (BBN) using the Hugin Software v7.8. The effects of automation on flight crew are incorporated into the model, including flight skill degradation, increased cognitive demand and training requirements along with their interactions. Besides flight crew deficiencies, automation system
A Bayesian network model for predicting aquatic toxicity mode ...
The mode of toxic action (MoA) has been recognized as a key determinant of chemical toxicity but MoA classification in aquatic toxicology has been limited. We developed a Bayesian network model to classify aquatic toxicity mode of action using a recently published dataset containing over one thousand chemicals with MoA assignments for aquatic animal toxicity. Two dimensional theoretical chemical descriptors were generated for each chemical using the Toxicity Estimation Software Tool. The model was developed through augmented Markov blanket discovery from the data set with the MoA broad classifications as a target node. From cross validation, the overall precision for the model was 80.2% with a R2 of 0.959. The best precision was for the AChEI MoA (93.5%) where 257 chemicals out of 275 were correctly classified. Model precision was poorest for the reactivity MoA (48.5%) where 48 out of 99 reactive chemicals were correctly classified. Narcosis represented the largest class within the MoA dataset and had a precision and reliability of 80.0%, reflecting the global precision across all of the MoAs. False negatives for narcosis most often fell into electron transport inhibition, neurotoxicity or reactivity MoAs. False negatives for all other MoAs were most often narcosis. A probabilistic sensitivity analysis was undertaken for each MoA to examine the sensitivity to individual and multiple descriptor findings. The results show that the Markov blanket of a structurally
Owen, Rhiannon K; Tincello, Douglas G; Keith, R Abrams
2015-01-01
Network meta-analysis (NMA) is commonly used in evidence synthesis; however, in situations in which there are a large number of treatment options, which may be subdivided into classes, and relatively few trials, NMAs produce considerable uncertainty in the estimated treatment effects, and consequently, identification of the most beneficial intervention remains inconclusive. To develop and demonstrate the use of evidence synthesis methods to evaluate extensive treatment networks with a limited number of trials, making use of classes. Using Bayesian Markov chain Monte Carlo methods, we build on the existing work of a random effects NMA to develop a three-level hierarchical NMA model that accounts for the exchangeability between treatments within the same class as well as for the residual between-study heterogeneity. We demonstrate the application of these methods to a continuous and binary outcome, using a motivating example of overactive bladder. We illustrate methods for incorporating ordering constraints in increasing doses, model selection, and assessing inconsistency between the direct and indirect evidence. The methods were applied to a data set obtained from a systematic literature review of trials for overactive bladder, evaluating the mean reduction in incontinence episodes from baseline and the number of patients reporting one or more adverse events. The data set involved 72 trials comparing 34 interventions that were categorized into nine classes of interventions, including placebo. Bayesian three-level hierarchical NMAs have the potential to increase the precision in the effect estimates while maintaining the interpretability of the individual interventions for decision making. Copyright © 2015 International Society for Pharmacoeconomics and Outcomes Research (ISPOR). Published by Elsevier Inc. All rights reserved.
U.S. Environmental Protection Agency — The dataset is lake dissolved oxygen concentrations obtained form plots published by Gelda et al. (1996) and lake reaeration model simulated values using Bayesian...
A Bayesian view on acoustic model-based techniques for robust speech recognition
Maas, Roland; Huemmer, Christian; Sehr, Armin; Kellermann, Walter
2015-12-01
This article provides a unifying Bayesian view on various approaches for acoustic model adaptation, missing feature, and uncertainty decoding that are well-known in the literature of robust automatic speech recognition. The representatives of these classes can often be deduced from a Bayesian network that extends the conventional hidden Markov models used in speech recognition. These extensions, in turn, can in many cases be motivated from an underlying observation model that relates clean and distorted feature vectors. By identifying and converting the observation models into a Bayesian network representation, we formulate the corresponding compensation rules. We thus summarize the various approaches as approximations or modifications of the same Bayesian decoding rule leading to a unified view on known derivations as well as to new formulations for certain approaches.
[Tree-Augmented NaÏve Bayesian network model for predicting prostate cancer].
Xiao, Li-Hong; Chen, Pei-Ran; Li, Mei; Gou, Zhong-Ping; Xiang, Liang-Cheng; Li, Yong-Zhong; Feng, Ping
2016-06-01
To evaluate the integrated performance of age, serum PSA, and transrectal ultrasound images in the prediction of prostate cancer using a Tree-Augmented NaÏve (TAN) Bayesian network model. We collected such data as age, serum PSA, transrectal ultrasound findings, and pathological diagnoses from 941 male patients who underwent prostate biopsy from January 2008 to September 2011. Using a TAN Bayesian network model, we analyzed the data for predicting prostate cancer, and compared them with the gold standards of pathological diagnosis. The accuracy, sensitivity, specificity, positive prediction rate, and negative prediction rate of the TAN Bayesian network model were 85.11%, 88.37%, 83.67%, 70.37%, and 94.25%, respectively. Based on age, serum PSA, and transrectal ultrasound images, the TAN Bayesian network model has a high value for the prediction of prostate cancer, and can help improve the clinical screening and diagnosis of the disease.
van der Lans, Ralf
2011-01-01
This note provides two corrections to the pseudo-code of the algorithm for the Bayesian estimation of the multinomial logit model using auxiliary variables as developed by Homes and Held (2006). After incorporating the two corrections, the algorithm works correctly for the multinomial as well as the binary logit model.
Blangiardo, M; Baio, G
2014-01-01
The Eurovision Song Contest is an annual musical competition held among active members of the European Broadcasting Union since 1956. The event is televised live across Europe. Each participating country presents a song and receive a vote based on a combination of tele-voting and jury. Over the years, this has led to speculations of tactical voting, discriminating against some participants and thus inducing bias in the final results. In this paper we investigate the presence of positive or ne...
On stable Pareto laws in a hierarchical model of economy
Chebotarev, A. M.
2007-01-01
This study considers a model of the income distribution of agents whose pairwise interaction is asymmetric and price-invariant. Asymmetric transactions are typical for chain-trading groups who arrange their business such that commodities move from senior to junior partners and money moves in the opposite direction. The price-invariance of transactions means that the probability of a pairwise interaction is a function of the ratio of incomes, which is independent of the price scale or absolute income level. These two features characterize the hierarchical model. The income distribution in this class of models is a well-defined double-Pareto function, which possesses Pareto tails for the upper and lower incomes. For gross and net upper incomes, the model predicts definite values of the Pareto exponents, agross and anet, which are stable with respect to quantitative variation of the pair-interaction. The Pareto exponents are also stable with respect to the choice of a demand function within two classes of status-dependent behavior of agents: linear demand ( agross=1, anet=2) and unlimited slowly varying demand ( agross=anet=1). For the sigmoidal demand that describes limited returns, agross=anet=1+α, with some α>0 satisfying a transcendental equation. The low-income distribution may be singular or vanishing in the neighborhood of the minimal income; in any case, it is L1-integrable and its Pareto exponent is given explicitly. The theory used in the present study is based on a simple balance equation and new results from multiplicative Markov chains and exponential moments of random geometric progressions.
Scale of association: hierarchical linear models and the measurement of ecological systems
Sean M. McMahon; Jeffrey M. Diez
2007-01-01
A fundamental challenge to understanding patterns in ecological systems lies in employing methods that can analyse, test and draw inference from measured associations between variables across scales. Hierarchical linear models (HLM) use advanced estimation algorithms to measure regression relationships and variance-covariance parameters in hierarchically structured...
Bayesian network as a modelling tool for risk management in agriculture
DEFF Research Database (Denmark)
Rasmussen, Svend; Madsen, Anders Læsø; Lund, Mogens
The importance of risk management increases as farmers become more exposed to risk. But risk management is a difficult topic because income risk is the result of the complex interaction of multiple risk factors combined with the effect of an increasing array of possible risk management tools....... In this paper we use Bayesian networks as an integrated modelling approach for representing uncertainty and analysing risk management in agriculture. It is shown how historical farm account data may be efficiently used to estimate conditional probabilities, which are the core elements in Bayesian network models....... We further show how the Bayesian network model RiBay is used for stochastic simulation of farm income, and we demonstrate how RiBay can be used to simulate risk management at the farm level. It is concluded that the key strength of a Bayesian network is the transparency of assumptions...
Smart Annotation of Cyclic Data Using Hierarchical Hidden Markov Models.
Martindale, Christine F; Hoenig, Florian; Strohrmann, Christina; Eskofier, Bjoern M
2017-10-13
Cyclic signals are an intrinsic part of daily life, such as human motion and heart activity. The detailed analysis of them is important for clinical applications such as pathological gait analysis and for sports applications such as performance analysis. Labeled training data for algorithms that analyze these cyclic data come at a high annotation cost due to only limited annotations available under laboratory conditions or requiring manual segmentation of the data under less restricted conditions. This paper presents a smart annotation method that reduces this cost of labeling for sensor-based data, which is applicable to data collected outside of strict laboratory conditions. The method uses semi-supervised learning of sections of cyclic data with a known cycle number. A hierarchical hidden Markov model (hHMM) is used, achieving a mean absolute error of 0.041 ± 0.020 s relative to a manually-annotated reference. The resulting model was also used to simultaneously segment and classify continuous, 'in the wild' data, demonstrating the applicability of using hHMM, trained on limited data sections, to label a complete dataset. This technique achieved comparable results to its fully-supervised equivalent. Our semi-supervised method has the significant advantage of reduced annotation cost. Furthermore, it reduces the opportunity for human error in the labeling process normally required for training of segmentation algorithms. It also lowers the annotation cost of training a model capable of continuous monitoring of cycle characteristics such as those employed to analyze the progress of movement disorders or analysis of running technique.
Smart Annotation of Cyclic Data Using Hierarchical Hidden Markov Models
Directory of Open Access Journals (Sweden)
Christine F. Martindale
2017-10-01
Full Text Available Cyclic signals are an intrinsic part of daily life, such as human motion and heart activity. The detailed analysis of them is important for clinical applications such as pathological gait analysis and for sports applications such as performance analysis. Labeled training data for algorithms that analyze these cyclic data come at a high annotation cost due to only limited annotations available under laboratory conditions or requiring manual segmentation of the data under less restricted conditions. This paper presents a smart annotation method that reduces this cost of labeling for sensor-based data, which is applicable to data collected outside of strict laboratory conditions. The method uses semi-supervised learning of sections of cyclic data with a known cycle number. A hierarchical hidden Markov model (hHMM is used, achieving a mean absolute error of 0.041 ± 0.020 s relative to a manually-annotated reference. The resulting model was also used to simultaneously segment and classify continuous, ‘in the wild’ data, demonstrating the applicability of using hHMM, trained on limited data sections, to label a complete dataset. This technique achieved comparable results to its fully-supervised equivalent. Our semi-supervised method has the significant advantage of reduced annotation cost. Furthermore, it reduces the opportunity for human error in the labeling process normally required for training of segmentation algorithms. It also lowers the annotation cost of training a model capable of continuous monitoring of cycle characteristics such as those employed to analyze the progress of movement disorders or analysis of running technique.
Plant, N. G.; Thieler, E. R.; Gutierrez, B.; Lentz, E. E.; Zeigler, S. L.; Van Dongeren, A.; Fienen, M. N.
2016-12-01
We evaluate the strengths and weaknesses of Bayesian networks that have been used to address scientific and decision-support questions related to coastal geomorphology. We will provide an overview of coastal geomorphology research that has used Bayesian networks and describe what this approach can do and when it works (or fails to work). Over the past decade, Bayesian networks have been formulated to analyze the multi-variate structure and evolution of coastal morphology and associated human and ecological impacts. The approach relates observable system variables to each other by estimating discrete correlations. The resulting Bayesian-networks make predictions that propagate errors, conduct inference via Bayes rule, or both. In scientific applications, the model results are useful for hypothesis testing, using confidence estimates to gage the strength of tests while applications to coastal resource management are aimed at decision-support, where the probabilities of desired ecosystems outcomes are evaluated. The range of Bayesian-network applications to coastal morphology includes emulation of high-resolution wave transformation models to make oceanographic predictions, morphologic response to storms and/or sea-level rise, groundwater response to sea-level rise and morphologic variability, habitat suitability for endangered species, and assessment of monetary or human-life risk associated with storms. All of these examples are based on vast observational data sets, numerical model output, or both. We will discuss the progression of our experiments, which has included testing whether the Bayesian-network approach can be implemented and is appropriate for addressing basic and applied scientific problems and evaluating the hindcast and forecast skill of these implementations. We will present and discuss calibration/validation tests that are used to assess the robustness of Bayesian-network models and we will compare these results to tests of other models. This will
Bayesian Network Based Fault Prognosis via Bond Graph Modeling of High-Speed Railway Traction Device
Directory of Open Access Journals (Sweden)
Yunkai Wu
2015-01-01
component-level faults accurately for a high-speed railway traction system, a fault prognosis approach via Bayesian network and bond graph modeling techniques is proposed. The inherent structure of a railway traction system is represented by bond graph model, based on which a multilayer Bayesian network is developed for fault propagation analysis and fault prediction. For complete and incomplete data sets, two different parameter learning algorithms such as Bayesian estimation and expectation maximization (EM algorithm are adopted to determine the conditional probability table of the Bayesian