A Bayesian Beta-Mixture Model for Nonparametric IRT (BBM-IRT)

ERIC Educational Resources Information Center

Arenson, Ethan A.; Karabatsos, George

2017-01-01

Item response models typically assume that the item characteristic (step) curves follow a logistic or normal cumulative distribution function, which are strictly monotone functions of person test ability. Such assumptions can be overly-restrictive for real item response data. We propose a simple and more flexible Bayesian nonparametric IRT model…

Reweighting Data in the Spirit of Tukey: Using Bayesian Posterior Probabilities as Rasch Residuals for Studying Misfit

ERIC Educational Resources Information Center

Dardick, William R.; Mislevy, Robert J.

2016-01-01

A new variant of the iterative "data = fit + residual" data-analytical approach described by Mosteller and Tukey is proposed and implemented in the context of item response theory psychometric models. Posterior probabilities from a Bayesian mixture model of a Rasch item response theory model and an unscalable latent class are expressed…

Spatio-temporal Bayesian model selection for disease mapping

PubMed Central

Carroll, R; Lawson, AB; Faes, C; Kirby, RS; Aregay, M; Watjou, K

2016-01-01

Spatio-temporal analysis of small area health data often involves choosing a fixed set of predictors prior to the final model fit. In this paper, we propose a spatio-temporal approach of Bayesian model selection to implement model selection for certain areas of the study region as well as certain years in the study time line. Here, we examine the usefulness of this approach by way of a large-scale simulation study accompanied by a case study. Our results suggest that a special case of the model selection methods, a mixture model allowing a weight parameter to indicate if the appropriate linear predictor is spatial, spatio-temporal, or a mixture of the two, offers the best option to fitting these spatio-temporal models. In addition, the case study illustrates the effectiveness of this mixture model within the model selection setting by easily accommodating lifestyle, socio-economic, and physical environmental variables to select a predominantly spatio-temporal linear predictor. PMID:28070156

A hybrid expectation maximisation and MCMC sampling algorithm to implement Bayesian mixture model based genomic prediction and QTL mapping.

PubMed

Wang, Tingting; Chen, Yi-Ping Phoebe; Bowman, Phil J; Goddard, Michael E; Hayes, Ben J

2016-09-21

Bayesian mixture models in which the effects of SNP are assumed to come from normal distributions with different variances are attractive for simultaneous genomic prediction and QTL mapping. These models are usually implemented with Monte Carlo Markov Chain (MCMC) sampling, which requires long compute times with large genomic data sets. Here, we present an efficient approach (termed HyB_BR), which is a hybrid of an Expectation-Maximisation algorithm, followed by a limited number of MCMC without the requirement for burn-in. To test prediction accuracy from HyB_BR, dairy cattle and human disease trait data were used. In the dairy cattle data, there were four quantitative traits (milk volume, protein kg, fat% in milk and fertility) measured in 16,214 cattle from two breeds genotyped for 632,002 SNPs. Validation of genomic predictions was in a subset of cattle either from the reference set or in animals from a third breeds that were not in the reference set. In all cases, HyB_BR gave almost identical accuracies to Bayesian mixture models implemented with full MCMC, however computational time was reduced by up to 1/17 of that required by full MCMC. The SNPs with high posterior probability of a non-zero effect were also very similar between full MCMC and HyB_BR, with several known genes affecting milk production in this category, as well as some novel genes. HyB_BR was also applied to seven human diseases with 4890 individuals genotyped for around 300 K SNPs in a case/control design, from the Welcome Trust Case Control Consortium (WTCCC). In this data set, the results demonstrated again that HyB_BR performed as well as Bayesian mixture models with full MCMC for genomic predictions and genetic architecture inference while reducing the computational time from 45 h with full MCMC to 3 h with HyB_BR. The results for quantitative traits in cattle and disease in humans demonstrate that HyB_BR can perform equally well as Bayesian mixture models implemented with full MCMC in terms of prediction accuracy, but with up to 17 times faster than the full MCMC implementations. The HyB_BR algorithm makes simultaneous genomic prediction, QTL mapping and inference of genetic architecture feasible in large genomic data sets.

The Impact of Various Class-Distinction Features on Model Selection in the Mixture Rasch Model

ERIC Educational Resources Information Center

Choi, In-Hee; Paek, Insu; Cho, Sun-Joo

2017-01-01

The purpose of the current study is to examine the performance of four information criteria (Akaike's information criterion [AIC], corrected AIC [AICC] Bayesian information criterion [BIC], sample-size adjusted BIC [SABIC]) for detecting the correct number of latent classes in the mixture Rasch model through simulations. The simulation study…

A comparison of machine learning and Bayesian modelling for molecular serotyping.

PubMed

Newton, Richard; Wernisch, Lorenz

2017-08-11

Streptococcus pneumoniae is a human pathogen that is a major cause of infant mortality. Identifying the pneumococcal serotype is an important step in monitoring the impact of vaccines used to protect against disease. Genomic microarrays provide an effective method for molecular serotyping. Previously we developed an empirical Bayesian model for the classification of serotypes from a molecular serotyping array. With only few samples available, a model driven approach was the only option. In the meanwhile, several thousand samples have been made available to us, providing an opportunity to investigate serotype classification by machine learning methods, which could complement the Bayesian model. We compare the performance of the original Bayesian model with two machine learning algorithms: Gradient Boosting Machines and Random Forests. We present our results as an example of a generic strategy whereby a preliminary probabilistic model is complemented or replaced by a machine learning classifier once enough data are available. Despite the availability of thousands of serotyping arrays, a problem encountered when applying machine learning methods is the lack of training data containing mixtures of serotypes; due to the large number of possible combinations. Most of the available training data comprises samples with only a single serotype. To overcome the lack of training data we implemented an iterative analysis, creating artificial training data of serotype mixtures by combining raw data from single serotype arrays. With the enhanced training set the machine learning algorithms out perform the original Bayesian model. However, for serotypes currently lacking sufficient training data the best performing implementation was a combination of the results of the Bayesian Model and the Gradient Boosting Machine. As well as being an effective method for classifying biological data, machine learning can also be used as an efficient method for revealing subtle biological insights, which we illustrate with an example.

Modular analysis of the probabilistic genetic interaction network.

PubMed

Hou, Lin; Wang, Lin; Qian, Minping; Li, Dong; Tang, Chao; Zhu, Yunping; Deng, Minghua; Li, Fangting

2011-03-15

Epistatic Miniarray Profiles (EMAP) has enabled the mapping of large-scale genetic interaction networks; however, the quantitative information gained from EMAP cannot be fully exploited since the data are usually interpreted as a discrete network based on an arbitrary hard threshold. To address such limitations, we adopted a mixture modeling procedure to construct a probabilistic genetic interaction network and then implemented a Bayesian approach to identify densely interacting modules in the probabilistic network. Mixture modeling has been demonstrated as an effective soft-threshold technique of EMAP measures. The Bayesian approach was applied to an EMAP dataset studying the early secretory pathway in Saccharomyces cerevisiae. Twenty-seven modules were identified, and 14 of those were enriched by gold standard functional gene sets. We also conducted a detailed comparison with state-of-the-art algorithms, hierarchical cluster and Markov clustering. The experimental results show that the Bayesian approach outperforms others in efficiently recovering biologically significant modules.

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

PubMed

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

1997-03-01

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

Detection of mastitis in dairy cattle by use of mixture models for repeated somatic cell scores: a Bayesian approach via Gibbs sampling.

PubMed

Odegård, J; Jensen, J; Madsen, P; Gianola, D; Klemetsdal, G; Heringstad, B

2003-11-01

The distribution of somatic cell scores could be regarded as a mixture of at least two components depending on a cow's udder health status. A heteroscedastic two-component Bayesian normal mixture model with random effects was developed and implemented via Gibbs sampling. The model was evaluated using datasets consisting of simulated somatic cell score records. Somatic cell score was simulated as a mixture representing two alternative udder health statuses ("healthy" or "diseased"). Animals were assigned randomly to the two components according to the probability of group membership (Pm). Random effects (additive genetic and permanent environment), when included, had identical distributions across mixture components. Posterior probabilities of putative mastitis were estimated for all observations, and model adequacy was evaluated using measures of sensitivity, specificity, and posterior probability of misclassification. Fitting different residual variances in the two mixture components caused some bias in estimation of parameters. When the components were difficult to disentangle, so were their residual variances, causing bias in estimation of Pm and of location parameters of the two underlying distributions. When all variance components were identical across mixture components, the mixture model analyses returned parameter estimates essentially without bias and with a high degree of precision. Including random effects in the model increased the probability of correct classification substantially. No sizable differences in probability of correct classification were found between models in which a single cow effect (ignoring relationships) was fitted and models where this effect was split into genetic and permanent environmental components, utilizing relationship information. When genetic and permanent environmental effects were fitted, the between-replicate variance of estimates of posterior means was smaller because the model accounted for random genetic drift.

A 3-Component Mixture of Rayleigh Distributions: Properties and Estimation in Bayesian Framework

PubMed Central

Aslam, Muhammad; Tahir, Muhammad; Hussain, Zawar; Al-Zahrani, Bander

2015-01-01

To study lifetimes of certain engineering processes, a lifetime model which can accommodate the nature of such processes is desired. The mixture models of underlying lifetime distributions are intuitively more appropriate and appealing to model the heterogeneous nature of process as compared to simple models. This paper is about studying a 3-component mixture of the Rayleigh distributionsin Bayesian perspective. The censored sampling environment is considered due to its popularity in reliability theory and survival analysis. The expressions for the Bayes estimators and their posterior risks are derived under different scenarios. In case the case that no or little prior information is available, elicitation of hyperparameters is given. To examine, numerically, the performance of the Bayes estimators using non-informative and informative priors under different loss functions, we have simulated their statistical properties for different sample sizes and test termination times. In addition, to highlight the practical significance, an illustrative example based on a real-life engineering data is also given. PMID:25993475

A Mixture Rasch Model with a Covariate: A Simulation Study via Bayesian Markov Chain Monte Carlo Estimation

ERIC Educational Resources Information Center

Dai, Yunyun

2013-01-01

Mixtures of item response theory (IRT) models have been proposed as a technique to explore response patterns in test data related to cognitive strategies, instructional sensitivity, and differential item functioning (DIF). Estimation proves challenging due to difficulties in identification and questions of effect size needed to recover underlying…

Nonparametric Bayesian inference for mean residual life functions in survival analysis.

PubMed

Poynor, Valerie; Kottas, Athanasios

2018-01-19

Modeling and inference for survival analysis problems typically revolves around different functions related to the survival distribution. Here, we focus on the mean residual life (MRL) function, which provides the expected remaining lifetime given that a subject has survived (i.e. is event-free) up to a particular time. This function is of direct interest in reliability, medical, and actuarial fields. In addition to its practical interpretation, the MRL function characterizes the survival distribution. We develop general Bayesian nonparametric inference for MRL functions built from a Dirichlet process mixture model for the associated survival distribution. The resulting model for the MRL function admits a representation as a mixture of the kernel MRL functions with time-dependent mixture weights. This model structure allows for a wide range of shapes for the MRL function. Particular emphasis is placed on the selection of the mixture kernel, taken to be a gamma distribution, to obtain desirable properties for the MRL function arising from the mixture model. The inference method is illustrated with a data set of two experimental groups and a data set involving right censoring. The supplementary material available at Biostatistics online provides further results on empirical performance of the model, using simulated data examples. © The Author 2018. Published by Oxford University Press. All rights reserved. For permissions, please e-mail: journals.permissions@oup.com.

Bayesian Regularization for Normal Mixture Estimation and Model-Based Clustering

DTIC Science & Technology

2005-08-04

describe a four-band magnetic resonance image (MRI) consisting of 23,712 pixels of a brain with a tumor 2. Because of the size of the dataset, it is not...the Royal Statistical Society, Series B 56, 363–375. Figueiredo, M. A. T. and A. K. Jain (2002). Unsupervised learning of finite mixture models. IEEE...20 5.4 Brain MRI

An introduction to Bayesian statistics in health psychology.

PubMed

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

2017-09-01

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

Poisson Mixture Regression Models for Heart Disease Prediction.

PubMed

Mufudza, Chipo; Erol, Hamza

2016-01-01

Early heart disease control can be achieved by high disease prediction and diagnosis efficiency. This paper focuses on the use of model based clustering techniques to predict and diagnose heart disease via Poisson mixture regression models. Analysis and application of Poisson mixture regression models is here addressed under two different classes: standard and concomitant variable mixture regression models. Results show that a two-component concomitant variable Poisson mixture regression model predicts heart disease better than both the standard Poisson mixture regression model and the ordinary general linear Poisson regression model due to its low Bayesian Information Criteria value. Furthermore, a Zero Inflated Poisson Mixture Regression model turned out to be the best model for heart prediction over all models as it both clusters individuals into high or low risk category and predicts rate to heart disease componentwise given clusters available. It is deduced that heart disease prediction can be effectively done by identifying the major risks componentwise using Poisson mixture regression model.

Poisson Mixture Regression Models for Heart Disease Prediction

PubMed Central

Erol, Hamza

2016-01-01

Early heart disease control can be achieved by high disease prediction and diagnosis efficiency. This paper focuses on the use of model based clustering techniques to predict and diagnose heart disease via Poisson mixture regression models. Analysis and application of Poisson mixture regression models is here addressed under two different classes: standard and concomitant variable mixture regression models. Results show that a two-component concomitant variable Poisson mixture regression model predicts heart disease better than both the standard Poisson mixture regression model and the ordinary general linear Poisson regression model due to its low Bayesian Information Criteria value. Furthermore, a Zero Inflated Poisson Mixture Regression model turned out to be the best model for heart prediction over all models as it both clusters individuals into high or low risk category and predicts rate to heart disease componentwise given clusters available. It is deduced that heart disease prediction can be effectively done by identifying the major risks componentwise using Poisson mixture regression model. PMID:27999611

BiomeNet: A Bayesian Model for Inference of Metabolic Divergence among Microbial Communities

PubMed Central

Chipman, Hugh; Gu, Hong; Bielawski, Joseph P.

2014-01-01

Metagenomics yields enormous numbers of microbial sequences that can be assigned a metabolic function. Using such data to infer community-level metabolic divergence is hindered by the lack of a suitable statistical framework. Here, we describe a novel hierarchical Bayesian model, called BiomeNet (Bayesian inference of metabolic networks), for inferring differential prevalence of metabolic subnetworks among microbial communities. To infer the structure of community-level metabolic interactions, BiomeNet applies a mixed-membership modelling framework to enzyme abundance information. The basic idea is that the mixture components of the model (metabolic reactions, subnetworks, and networks) are shared across all groups (microbiome samples), but the mixture proportions vary from group to group. Through this framework, the model can capture nested structures within the data. BiomeNet is unique in modeling each metagenome sample as a mixture of complex metabolic systems (metabosystems). The metabosystems are composed of mixtures of tightly connected metabolic subnetworks. BiomeNet differs from other unsupervised methods by allowing researchers to discriminate groups of samples through the metabolic patterns it discovers in the data, and by providing a framework for interpreting them. We describe a collapsed Gibbs sampler for inference of the mixture weights under BiomeNet, and we use simulation to validate the inference algorithm. Application of BiomeNet to human gut metagenomes revealed a metabosystem with greater prevalence among inflammatory bowel disease (IBD) patients. Based on the discriminatory subnetworks for this metabosystem, we inferred that the community is likely to be closely associated with the human gut epithelium, resistant to dietary interventions, and interfere with human uptake of an antioxidant connected to IBD. Because this metabosystem has a greater capacity to exploit host-associated glycans, we speculate that IBD-associated communities might arise from opportunist growth of bacteria that can circumvent the host's nutrient-based mechanism for bacterial partner selection. PMID:25412107

Bayesian Variable Selection for Hierarchical Gene-Environment and Gene-Gene Interactions

PubMed Central

Liu, Changlu; Ma, Jianzhong; Amos, Christopher I.

2014-01-01

We propose a Bayesian hierarchical mixture model framework that allows us to investigate the genetic and environmental effects, gene by gene interactions and gene by environment interactions in the same model. Our approach incorporates the natural hierarchical structure between the main effects and interaction effects into a mixture model, such that our methods tend to remove the irrelevant interaction effects more effectively, resulting in more robust and parsimonious models. We consider both strong and weak hierarchical models. For a strong hierarchical model, both of the main effects between interacting factors must be present for the interactions to be considered in the model development, while for a weak hierarchical model, only one of the two main effects is required to be present for the interaction to be evaluated. Our simulation results show that the proposed strong and weak hierarchical mixture models work well in controlling false positive rates and provide a powerful approach for identifying the predisposing effects and interactions in gene-environment interaction studies, in comparison with the naive model that does not impose this hierarchical constraint in most of the scenarios simulated. We illustrated our approach using data for lung cancer and cutaneous melanoma. PMID:25154630

A Mixtures-of-Trees Framework for Multi-Label Classification

PubMed Central

Hong, Charmgil; Batal, Iyad; Hauskrecht, Milos

2015-01-01

We propose a new probabilistic approach for multi-label classification that aims to represent the class posterior distribution P(Y|X). Our approach uses a mixture of tree-structured Bayesian networks, which can leverage the computational advantages of conditional tree-structured models and the abilities of mixtures to compensate for tree-structured restrictions. We develop algorithms for learning the model from data and for performing multi-label predictions using the learned model. Experiments on multiple datasets demonstrate that our approach outperforms several state-of-the-art multi-label classification methods. PMID:25927011

Critically evaluating the theory and performance of Bayesian analysis of macroevolutionary mixtures

PubMed Central

Moore, Brian R.; Höhna, Sebastian; May, Michael R.; Rannala, Bruce; Huelsenbeck, John P.

2016-01-01

Bayesian analysis of macroevolutionary mixtures (BAMM) has recently taken the study of lineage diversification by storm. BAMM estimates the diversification-rate parameters (speciation and extinction) for every branch of a study phylogeny and infers the number and location of diversification-rate shifts across branches of a tree. Our evaluation of BAMM reveals two major theoretical errors: (i) the likelihood function (which estimates the model parameters from the data) is incorrect, and (ii) the compound Poisson process prior model (which describes the prior distribution of diversification-rate shifts across branches) is incoherent. Using simulation, we demonstrate that these theoretical issues cause statistical pathologies; posterior estimates of the number of diversification-rate shifts are strongly influenced by the assumed prior, and estimates of diversification-rate parameters are unreliable. Moreover, the inability to correctly compute the likelihood or to correctly specify the prior for rate-variable trees precludes the use of Bayesian approaches for testing hypotheses regarding the number and location of diversification-rate shifts using BAMM. PMID:27512038

A Bayesian framework based on a Gaussian mixture model and radial-basis-function Fisher discriminant analysis (BayGmmKda V1.1) for spatial prediction of floods

NASA Astrophysics Data System (ADS)

Tien Bui, Dieu; Hoang, Nhat-Duc

2017-09-01

In this study, a probabilistic model, named as BayGmmKda, is proposed for flood susceptibility assessment in a study area in central Vietnam. The new model is a Bayesian framework constructed by a combination of a Gaussian mixture model (GMM), radial-basis-function Fisher discriminant analysis (RBFDA), and a geographic information system (GIS) database. In the Bayesian framework, GMM is used for modeling the data distribution of flood-influencing factors in the GIS database, whereas RBFDA is utilized to construct a latent variable that aims at enhancing the model performance. As a result, the posterior probabilistic output of the BayGmmKda model is used as flood susceptibility index. Experiment results showed that the proposed hybrid framework is superior to other benchmark models, including the adaptive neuro-fuzzy inference system and the support vector machine. To facilitate the model implementation, a software program of BayGmmKda has been developed in MATLAB. The BayGmmKda program can accurately establish a flood susceptibility map for the study region. Accordingly, local authorities can overlay this susceptibility map onto various land-use maps for the purpose of land-use planning or management.

Item selection via Bayesian IRT models.

PubMed

Arima, Serena

2015-02-10

With reference to a questionnaire that aimed to assess the quality of life for dysarthric speakers, we investigate the usefulness of a model-based procedure for reducing the number of items. We propose a mixed cumulative logit model, which is known in the psychometrics literature as the graded response model: responses to different items are modelled as a function of individual latent traits and as a function of item characteristics, such as their difficulty and their discrimination power. We jointly model the discrimination and the difficulty parameters by using a k-component mixture of normal distributions. Mixture components correspond to disjoint groups of items. Items that belong to the same groups can be considered equivalent in terms of both difficulty and discrimination power. According to decision criteria, we select a subset of items such that the reduced questionnaire is able to provide the same information that the complete questionnaire provides. The model is estimated by using a Bayesian approach, and the choice of the number of mixture components is justified according to information criteria. We illustrate the proposed approach on the basis of data that are collected for 104 dysarthric patients by local health authorities in Lecce and in Milan. Copyright © 2014 John Wiley & Sons, Ltd.

Bayesian mixture modeling of significant p values: A meta-analytic method to estimate the degree of contamination from H₀.

PubMed

Gronau, Quentin Frederik; Duizer, Monique; Bakker, Marjan; Wagenmakers, Eric-Jan

2017-09-01

Publication bias and questionable research practices have long been known to corrupt the published record. One method to assess the extent of this corruption is to examine the meta-analytic collection of significant p values, the so-called p -curve (Simonsohn, Nelson, & Simmons, 2014a). Inspired by statistical research on false-discovery rates, we propose a Bayesian mixture model analysis of the p -curve. Our mixture model assumes that significant p values arise either from the null-hypothesis H ₀ (when their distribution is uniform) or from the alternative hypothesis H1 (when their distribution is accounted for by a simple parametric model). The mixture model estimates the proportion of significant results that originate from H ₀, but it also estimates the probability that each specific p value originates from H ₀. We apply our model to 2 examples. The first concerns the set of 587 significant p values for all t tests published in the 2007 volumes of Psychonomic Bulletin & Review and the Journal of Experimental Psychology: Learning, Memory, and Cognition; the mixture model reveals that p values higher than about .005 are more likely to stem from H ₀ than from H ₁. The second example concerns 159 significant p values from studies on social priming and 130 from yoked control studies. The results from the yoked controls confirm the findings from the first example, whereas the results from the social priming studies are difficult to interpret because they are sensitive to the prior specification. To maximize accessibility, we provide a web application that allows researchers to apply the mixture model to any set of significant p values. (PsycINFO Database Record (c) 2017 APA, all rights reserved).

Application of hierarchical Bayesian unmixing models in river sediment source apportionment

NASA Astrophysics Data System (ADS)

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 process, (3) deriving and using informative priors in sediment fingerprinting context and (4) transparency of the process and replication of model results by other users.

Using Bayesian statistics for modeling PTSD through Latent Growth Mixture Modeling: implementation and discussion.

PubMed

Depaoli, Sarah; van de Schoot, Rens; van Loey, Nancy; Sijbrandij, Marit

2015-01-01

After traumatic events, such as disaster, war trauma, and injuries including burns (which is the focus here), the risk to develop posttraumatic stress disorder (PTSD) is approximately 10% (Breslau & Davis, 1992). Latent Growth Mixture Modeling can be used to classify individuals into distinct groups exhibiting different patterns of PTSD (Galatzer-Levy, 2015). Currently, empirical evidence points to four distinct trajectories of PTSD patterns in those who have experienced burn trauma. These trajectories are labeled as: resilient, recovery, chronic, and delayed onset trajectories (e.g., Bonanno, 2004; Bonanno, Brewin, Kaniasty, & Greca, 2010; Maercker, Gäbler, O'Neil, Schützwohl, & Müller, 2013; Pietrzak et al., 2013). The delayed onset trajectory affects only a small group of individuals, that is, about 4-5% (O'Donnell, Elliott, Lau, & Creamer, 2007). In addition to its low frequency, the later onset of this trajectory may contribute to the fact that these individuals can be easily overlooked by professionals. In this special symposium on Estimating PTSD trajectories (Van de Schoot, 2015a), we illustrate how to properly identify this small group of individuals through the Bayesian estimation framework using previous knowledge through priors (see, e.g., Depaoli & Boyajian, 2014; Van de Schoot, Broere, Perryck, Zondervan-Zwijnenburg, & Van Loey, 2015). We used latent growth mixture modeling (LGMM) (Van de Schoot, 2015b) to estimate PTSD trajectories across 4 years that followed a traumatic burn. We demonstrate and compare results from traditional (maximum likelihood) and Bayesian estimation using priors (see, Depaoli, 2012, 2013). Further, we discuss where priors come from and how to define them in the estimation process. We demonstrate that only the Bayesian approach results in the desired theory-driven solution of PTSD trajectories. Since the priors are chosen subjectively, we also present a sensitivity analysis of the Bayesian results to illustrate how to check the impact of the prior knowledge integrated into the model. We conclude with recommendations and guidelines for researchers looking to implement theory-driven LGMM, and we tailor this discussion to the context of PTSD research.

Bayesian kernel machine regression for estimating the health effects of multi-pollutant mixtures.

PubMed

Bobb, Jennifer F; Valeri, Linda; Claus Henn, Birgit; Christiani, David C; Wright, Robert O; Mazumdar, Maitreyi; Godleski, John J; Coull, Brent A

2015-07-01

Because humans are invariably exposed to complex chemical mixtures, estimating the health effects of multi-pollutant exposures is of critical concern in environmental epidemiology, and to regulatory agencies such as the U.S. Environmental Protection Agency. However, most health effects studies focus on single agents or consider simple two-way interaction models, in part because we lack the statistical methodology to more realistically capture the complexity of mixed exposures. We introduce Bayesian kernel machine regression (BKMR) as a new approach to study mixtures, in which the health outcome is regressed on a flexible function of the mixture (e.g. air pollution or toxic waste) components that is specified using a kernel function. In high-dimensional settings, a novel hierarchical variable selection approach is incorporated to identify important mixture components and account for the correlated structure of the mixture. Simulation studies demonstrate the success of BKMR in estimating the exposure-response function and in identifying the individual components of the mixture responsible for health effects. We demonstrate the features of the method through epidemiology and toxicology applications. © The Author 2014. Published by Oxford University Press. All rights reserved. For permissions, please e-mail: journals.permissions@oup.com.

A Bayesian mixture model for missing data in marine mammal growth analysis

PubMed Central

Shotwell, Mary E.; McFee, Wayne E.; Slate, Elizabeth H.

2016-01-01

Much of what is known about bottle nose dolphin (Tursiops truncatus) anatomy and physiology is based on necropsies from stranding events. Measurements of total body length, total body mass, and age are used to estimate growth. It is more feasible to retrieve and transport smaller animals for total body mass measurement than larger animals, introducing a systematic bias in sampling. Adverse weather events, volunteer availability, and other unforeseen circumstances also contribute to incomplete measurement. We have developed a Bayesian mixture model to describe growth in detected stranded animals using data from both those that are fully measured and those not fully measured. Our approach uses a shared random effect to link the missingness mechanism (i.e. full/partial measurement) to distinct growth curves in the fully and partially measured populations, thereby enabling drawing of strength for estimation. We use simulation to compare our model to complete case analysis and two common multiple imputation methods according to model mean square error. Results indicate that our mixture model provides better fit both when the two populations are present and when they are not. The feasibility and utility of our new method is demonstrated by application to South Carolina strandings data. PMID:28503080

Protein construct storage: Bayesian variable selection and prediction with mixtures.

PubMed

Clyde, M A; Parmigiani, G

1998-07-01

Determining optimal conditions for protein storage while maintaining a high level of protein activity is an important question in pharmaceutical research. A designed experiment based on a space-filling design was conducted to understand the effects of factors affecting protein storage and to establish optimal storage conditions. Different model-selection strategies to identify important factors may lead to very different answers about optimal conditions. Uncertainty about which factors are important, or model uncertainty, can be a critical issue in decision-making. We use Bayesian variable selection methods for linear models to identify important variables in the protein storage data, while accounting for model uncertainty. We also use the Bayesian framework to build predictions based on a large family of models, rather than an individual model, and to evaluate the probability that certain candidate storage conditions are optimal.

Probabilistic modeling of bifurcations in single-cell gene expression data using a Bayesian mixture of factor analyzers.

PubMed

Campbell, Kieran R; Yau, Christopher

2017-03-15

Modeling bifurcations in single-cell transcriptomics data has become an increasingly popular field of research. Several methods have been proposed to infer bifurcation structure from such data, but all rely on heuristic non-probabilistic inference. Here we propose the first generative, fully probabilistic model for such inference based on a Bayesian hierarchical mixture of factor analyzers. Our model exhibits competitive performance on large datasets despite implementing full Markov-Chain Monte Carlo sampling, and its unique hierarchical prior structure enables automatic determination of genes driving the bifurcation process. We additionally propose an Empirical-Bayes like extension that deals with the high levels of zero-inflation in single-cell RNA-seq data and quantify when such models are useful. We apply or model to both real and simulated single-cell gene expression data and compare the results to existing pseudotime methods. Finally, we discuss both the merits and weaknesses of such a unified, probabilistic approach in the context practical bioinformatics analyses.

Mixture class recovery in GMM under varying degrees of class separation: frequentist versus Bayesian estimation.

PubMed

Depaoli, Sarah

2013-06-01

Growth mixture modeling (GMM) represents a technique that is designed to capture change over time for unobserved subgroups (or latent classes) that exhibit qualitatively different patterns of growth. The aim of the current article was to explore the impact of latent class separation (i.e., how similar growth trajectories are across latent classes) on GMM performance. Several estimation conditions were compared: maximum likelihood via the expectation maximization (EM) algorithm and the Bayesian framework implementing diffuse priors, "accurate" informative priors, weakly informative priors, data-driven informative priors, priors reflecting partial-knowledge of parameters, and "inaccurate" (but informative) priors. The main goal was to provide insight about the optimal estimation condition under different degrees of latent class separation for GMM. Results indicated that optimal parameter recovery was obtained though the Bayesian approach using "accurate" informative priors, and partial-knowledge priors showed promise for the recovery of the growth trajectory parameters. Maximum likelihood and the remaining Bayesian estimation conditions yielded poor parameter recovery for the latent class proportions and the growth trajectories. (PsycINFO Database Record (c) 2013 APA, all rights reserved).

CRAFT (complete reduction to amplitude frequency table)--robust and time-efficient Bayesian approach for quantitative mixture analysis by NMR.

PubMed

Krishnamurthy, Krish

2013-12-01

The intrinsic quantitative nature of NMR is increasingly exploited in areas ranging from complex mixture analysis (as in metabolomics and reaction monitoring) to quality assurance/control. Complex NMR spectra are more common than not, and therefore, extraction of quantitative information generally involves significant prior knowledge and/or operator interaction to characterize resonances of interest. Moreover, in most NMR-based metabolomic experiments, the signals from metabolites are normally present as a mixture of overlapping resonances, making quantification difficult. Time-domain Bayesian approaches have been reported to be better than conventional frequency-domain analysis at identifying subtle changes in signal amplitude. We discuss an approach that exploits Bayesian analysis to achieve a complete reduction to amplitude frequency table (CRAFT) in an automated and time-efficient fashion - thus converting the time-domain FID to a frequency-amplitude table. CRAFT uses a two-step approach to FID analysis. First, the FID is digitally filtered and downsampled to several sub FIDs, and secondly, these sub FIDs are then modeled as sums of decaying sinusoids using the Bayesian approach. CRAFT tables can be used for further data mining of quantitative information using fingerprint chemical shifts of compounds of interest and/or statistical analysis of modulation of chemical quantity in a biological study (metabolomics) or process study (reaction monitoring) or quality assurance/control. The basic principles behind this approach as well as results to evaluate the effectiveness of this approach in mixture analysis are presented. Copyright © 2013 John Wiley & Sons, Ltd.

A two-component Bayesian mixture model to identify implausible gestational age.

PubMed

Mohammadian-Khoshnoud, Maryam; Moghimbeigi, Abbas; Faradmal, Javad; Yavangi, Mahnaz

2016-01-01

Background: Birth weight and gestational age are two important variables in obstetric research. The primary measure of gestational age is based on a mother's recall of her last menstrual period. This recall may cause random or systematic errors. Therefore, the objective of this study is to utilize Bayesian mixture model in order to identify implausible gestational age. Methods: In this cross-sectional study, medical documents of 502 preterm infants born and hospitalized in Hamadan Fatemieh Hospital from 2009 to 2013 were gathered. Preterm infants were classified to less than 28 weeks and 28 to 31 weeks. A two-component Bayesian mixture model was utilized to identify implausible gestational age; the first component shows the probability of correct and the second one shows the probability of incorrect classification of gestational ages. The data were analyzed through OpenBUGS 3.2.2 and 'coda' package of R 3.1.1. Results: The mean (SD) of the second component of less than 28 weeks and 28 to 31 weeks were 1179 (0.0123) and 1620 (0.0074), respectively. These values were larger than the mean of the first component for both groups which were 815.9 (0.0123) and 1061 (0.0074), respectively. Conclusion: Errors occurred in recording the gestational ages of these two groups of preterm infants included recording the gestational age less than the actual value at birth. Therefore, developing scientific methods to correct these errors is essential to providing desirable health services and adjusting accurate health indicators.

Bayesian hierarchical modeling for detecting safety signals in clinical trials.

PubMed

Xia, H Amy; Ma, Haijun; Carlin, Bradley P

2011-09-01

Detection of safety signals from clinical trial adverse event data is critical in drug development, but carries a challenging statistical multiplicity problem. Bayesian hierarchical mixture modeling is appealing for its ability to borrow strength across subgroups in the data, as well as moderate extreme findings most likely due merely to chance. We implement such a model for subject incidence (Berry and Berry, 2004 ) using a binomial likelihood, and extend it to subject-year adjusted incidence rate estimation under a Poisson likelihood. We use simulation to choose a signal detection threshold, and illustrate some effective graphics for displaying the flagged signals.

Bayesian nonparametric regression with varying residual density

PubMed Central

Pati, Debdeep; Dunson, David B.

2013-01-01

We consider the problem of robust Bayesian inference on the mean regression function allowing the residual density to change flexibly with predictors. The proposed class of models is based on a Gaussian process prior for the mean regression function and mixtures of Gaussians for the collection of residual densities indexed by predictors. Initially considering the homoscedastic case, we propose priors for the residual density based on probit stick-breaking (PSB) scale mixtures and symmetrized PSB (sPSB) location-scale mixtures. Both priors restrict the residual density to be symmetric about zero, with the sPSB prior more flexible in allowing multimodal densities. We provide sufficient conditions to ensure strong posterior consistency in estimating the regression function under the sPSB prior, generalizing existing theory focused on parametric residual distributions. The PSB and sPSB priors are generalized to allow residual densities to change nonparametrically with predictors through incorporating Gaussian processes in the stick-breaking components. This leads to a robust Bayesian regression procedure that automatically down-weights outliers and influential observations in a locally-adaptive manner. Posterior computation relies on an efficient data augmentation exact block Gibbs sampler. The methods are illustrated using simulated and real data applications. PMID:24465053

Hierarchical Bayesian sparse image reconstruction with application to MRFM.

PubMed

Dobigeon, Nicolas; Hero, Alfred O; Tourneret, Jean-Yves

2009-09-01

This paper presents a hierarchical Bayesian model to reconstruct sparse images when the observations are obtained from linear transformations and corrupted by an additive white Gaussian noise. Our hierarchical Bayes model is well suited to such naturally sparse image applications as it seamlessly accounts for properties such as sparsity and positivity of the image via appropriate Bayes priors. We propose a prior that is based on a weighted mixture of a positive exponential distribution and a mass at zero. The prior has hyperparameters that are tuned automatically by marginalization over the hierarchical Bayesian model. To overcome the complexity of the posterior distribution, a Gibbs sampling strategy is proposed. The Gibbs samples can be used to estimate the image to be recovered, e.g., by maximizing the estimated posterior distribution. In our fully Bayesian approach, the posteriors of all the parameters are available. Thus, our algorithm provides more information than other previously proposed sparse reconstruction methods that only give a point estimate. The performance of the proposed hierarchical Bayesian sparse reconstruction method is illustrated on synthetic data and real data collected from a tobacco virus sample using a prototype MRFM instrument.

Finding Groups Using Model-Based Cluster Analysis: Heterogeneous Emotional Self-Regulatory Processes and Heavy Alcohol Use Risk

ERIC Educational Resources Information Center

Mun, Eun Young; von Eye, Alexander; Bates, Marsha E.; Vaschillo, Evgeny G.

2008-01-01

Model-based cluster analysis is a new clustering procedure to investigate population heterogeneity utilizing finite mixture multivariate normal densities. It is an inferentially based, statistically principled procedure that allows comparison of nonnested models using the Bayesian information criterion to compare multiple models and identify the…

On selecting a prior for the precision parameter of Dirichlet process mixture models

USGS Publications Warehouse

Dorazio, R.M.

2009-01-01

In hierarchical mixture models the Dirichlet process is used to specify latent patterns of heterogeneity, particularly when the distribution of latent parameters is thought to be clustered (multimodal). The parameters of a Dirichlet process include a precision parameter ?? and a base probability measure G0. In problems where ?? is unknown and must be estimated, inferences about the level of clustering can be sensitive to the choice of prior assumed for ??. In this paper an approach is developed for computing a prior for the precision parameter ?? that can be used in the presence or absence of prior information about the level of clustering. This approach is illustrated in an analysis of counts of stream fishes. The results of this fully Bayesian analysis are compared with an empirical Bayes analysis of the same data and with a Bayesian analysis based on an alternative commonly used prior.

Using Latent Class Analysis to Model Temperament Types

ERIC Educational Resources Information Center

Loken, Eric

2004-01-01

Mixture models are appropriate for data that arise from a set of qualitatively different subpopulations. In this study, latent class analysis was applied to observational data from a laboratory assessment of infant temperament at four months of age. The EM algorithm was used to fit the models, and the Bayesian method of posterior predictive checks…

Bayesian Hierarchical Grouping: perceptual grouping as mixture estimation

PubMed Central

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

Overlapping community detection in weighted networks via a Bayesian approach

NASA Astrophysics Data System (ADS)

Chen, Yi; Wang, Xiaolong; Xiang, Xin; Tang, Buzhou; Chen, Qingcai; Fan, Shixi; Bu, Junzhao

2017-02-01

Complex networks as a powerful way to represent complex systems have been widely studied during the past several years. One of the most important tasks of complex network analysis is to detect communities embedded in networks. In the real world, weighted networks are very common and may contain overlapping communities where a node is allowed to belong to multiple communities. In this paper, we propose a novel Bayesian approach, called the Bayesian mixture network (BMN) model, to detect overlapping communities in weighted networks. The advantages of our method are (i) providing soft-partition solutions in weighted networks; (ii) providing soft memberships, which quantify 'how strongly' a node belongs to a community. Experiments on a large number of real and synthetic networks show that our model has the ability in detecting overlapping communities in weighted networks and is competitive with other state-of-the-art models at shedding light on community partition.

A Semi-Parametric Bayesian Mixture Modeling Approach for the Analysis of Judge Mediated Data

ERIC Educational Resources Information Center

Muckle, Timothy Joseph

2010-01-01

Existing methods for the analysis of ordinal-level data arising from judge ratings, such as the Multi-Facet Rasch model (MFRM, or the so-called Facets model) have been widely used in assessment in order to render fair examinee ability estimates in situations where the judges vary in their behavior or severity. However, this model makes certain…

Estimating mono- and bi-phasic regression parameters using a mixture piecewise linear Bayesian hierarchical model

PubMed Central

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. PMID:28723910

Dynamic classification of fetal heart rates by hierarchical Dirichlet process mixture models.

PubMed

Yu, Kezi; Quirk, J Gerald; Djurić, Petar M

2017-01-01

In this paper, we propose an application of non-parametric Bayesian (NPB) models for classification of fetal heart rate (FHR) recordings. More specifically, we propose models that are used to differentiate between FHR recordings that are from fetuses with or without adverse outcomes. In our work, we rely on models based on hierarchical Dirichlet processes (HDP) and the Chinese restaurant process with finite capacity (CRFC). Two mixture models were inferred from real recordings, one that represents healthy and another, non-healthy fetuses. The models were then used to classify new recordings and provide the probability of the fetus being healthy. First, we compared the classification performance of the HDP models with that of support vector machines on real data and concluded that the HDP models achieved better performance. Then we demonstrated the use of mixture models based on CRFC for dynamic classification of the performance of (FHR) recordings in a real-time setting.

Dynamic classification of fetal heart rates by hierarchical Dirichlet process mixture models

PubMed Central

Yu, Kezi; Quirk, J. Gerald

2017-01-01

In this paper, we propose an application of non-parametric Bayesian (NPB) models for classification of fetal heart rate (FHR) recordings. More specifically, we propose models that are used to differentiate between FHR recordings that are from fetuses with or without adverse outcomes. In our work, we rely on models based on hierarchical Dirichlet processes (HDP) and the Chinese restaurant process with finite capacity (CRFC). Two mixture models were inferred from real recordings, one that represents healthy and another, non-healthy fetuses. The models were then used to classify new recordings and provide the probability of the fetus being healthy. First, we compared the classification performance of the HDP models with that of support vector machines on real data and concluded that the HDP models achieved better performance. Then we demonstrated the use of mixture models based on CRFC for dynamic classification of the performance of (FHR) recordings in a real-time setting. PMID:28953927

Bayesian analysis and classification of two Enzyme-Linked Immunosorbent Assay (ELISA) tests without a gold standard

PubMed Central

Zhang, Jingyang; Chaloner, Kathryn; McLinden, James H.; Stapleton, Jack T.

2013-01-01

Reconciling two quantitative ELISA tests for an antibody to an RNA virus, in a situation without a gold standard and where false negatives may occur, is the motivation for this work. False negatives occur when access of the antibody to the binding site is blocked. Based on the mechanism of the assay, a mixture of four bivariate normal distributions is proposed with the mixture probabilities depending on a two-stage latent variable model including the prevalence of the antibody in the population and the probabilities of blocking on each test. There is prior information on the prevalence of the antibody, and also on the probability of false negatives, and so a Bayesian analysis is used. The dependence between the two tests is modeled to be consistent with the biological mechanism. Bayesian decision theory is utilized for classification. The proposed method is applied to the motivating data set to classify the data into two groups: those with and those without the antibody. Simulation studies describe the properties of the estimation and the classification. Sensitivity to the choice of the prior distribution is also addressed by simulation. The same model with two levels of latent variables is applicable in other testing procedures such as quantitative polymerase chain reaction tests where false negatives occur when there is a mutation in the primer sequence. PMID:23592433

Bayesian mixture analysis for metagenomic community profiling.

PubMed

Morfopoulou, Sofia; Plagnol, Vincent

2015-09-15

Deep sequencing of clinical samples is now an established tool for the detection of infectious pathogens, with direct medical applications. The large amount of data generated produces an opportunity to detect species even at very low levels, provided that computational tools can effectively profile the relevant metagenomic communities. Data interpretation is complicated by the fact that short sequencing reads can match multiple organisms and by the lack of completeness of existing databases, in particular for viral pathogens. Here we present metaMix, a Bayesian mixture model framework for resolving complex metagenomic mixtures. We show that the use of parallel Monte Carlo Markov chains for the exploration of the species space enables the identification of the set of species most likely to contribute to the mixture. We demonstrate the greater accuracy of metaMix compared with relevant methods, particularly for profiling complex communities consisting of several related species. We designed metaMix specifically for the analysis of deep transcriptome sequencing datasets, with a focus on viral pathogen detection; however, the principles are generally applicable to all types of metagenomic mixtures. metaMix is implemented as a user friendly R package, freely available on CRAN: http://cran.r-project.org/web/packages/metaMix sofia.morfopoulou.10@ucl.ac.uk Supplementary data are available at Bionformatics online. © The Author 2015. Published by Oxford University Press.

Phylogenetic relationships of South American lizards of the genus Stenocercus (Squamata: Iguania): A new approach using a general mixture model for gene sequence data.

PubMed

Torres-Carvajal, Omar; Schulte, James A; Cadle, John E

2006-04-01

The South American iguanian lizard genus Stenocercus includes 54 species occurring mostly in the Andes and adjacent lowland areas from northern Venezuela and Colombia to central Argentina at elevations of 0-4000m. Small taxon or character sampling has characterized all phylogenetic analyses of Stenocercus, which has long been recognized as sister taxon to the Tropidurus Group. In this study, we use mtDNA sequence data to perform phylogenetic analyses that include 32 species of Stenocercus and 12 outgroup taxa. Monophyly of this genus is strongly supported by maximum parsimony and Bayesian analyses. Evolutionary relationships within Stenocercus are further analyzed with a Bayesian implementation of a general mixture model, which accommodates variability in the pattern of evolution across sites. These analyses indicate a basal split of Stenocercus into two clades, one of which receives very strong statistical support. In addition, we test previous hypotheses using non-parametric and parametric statistical methods, and provide a phylogenetic classification for Stenocercus.

Simultaneous Force Regression and Movement Classification of Fingers via Surface EMG within a Unified Bayesian Framework.

PubMed

Baldacchino, Tara; Jacobs, William R; Anderson, Sean R; Worden, Keith; Rowson, Jennifer

2018-01-01

This contribution presents a novel methodology for myolectric-based control using surface electromyographic (sEMG) signals recorded during finger movements. A multivariate Bayesian mixture of experts (MoE) model is introduced which provides a powerful method for modeling force regression at the fingertips, while also performing finger movement classification as a by-product of the modeling algorithm. Bayesian inference of the model allows uncertainties to be naturally incorporated into the model structure. This method is tested using data from the publicly released NinaPro database which consists of sEMG recordings for 6 degree-of-freedom force activations for 40 intact subjects. The results demonstrate that the MoE model achieves similar performance compared to the benchmark set by the authors of NinaPro for finger force regression. Additionally, inherent to the Bayesian framework is the inclusion of uncertainty in the model parameters, naturally providing confidence bounds on the force regression predictions. Furthermore, the integrated clustering step allows a detailed investigation into classification of the finger movements, without incurring any extra computational effort. Subsequently, a systematic approach to assessing the importance of the number of electrodes needed for accurate control is performed via sensitivity analysis techniques. A slight degradation in regression performance is observed for a reduced number of electrodes, while classification performance is unaffected.

Bayesian spatiotemporal crash frequency models with mixture components for space-time interactions.

PubMed

Cheng, Wen; Gill, Gurdiljot Singh; Zhang, Yongping; Cao, Zhong

2018-03-01

The traffic safety research has developed spatiotemporal models to explore the variations in the spatial pattern of crash risk over time. Many studies observed notable benefits associated with the inclusion of spatial and temporal correlation and their interactions. However, the safety literature lacks sufficient research for the comparison of different temporal treatments and their interaction with spatial component. This study developed four spatiotemporal models with varying complexity due to the different temporal treatments such as (I) linear time trend; (II) quadratic time trend; (III) Autoregressive-1 (AR-1); and (IV) time adjacency. Moreover, the study introduced a flexible two-component mixture for the space-time interaction which allows greater flexibility compared to the traditional linear space-time interaction. The mixture component allows the accommodation of global space-time interaction as well as the departures from the overall spatial and temporal risk patterns. This study performed a comprehensive assessment of mixture models based on the diverse criteria pertaining to goodness-of-fit, cross-validation and evaluation based on in-sample data for predictive accuracy of crash estimates. The assessment of model performance in terms of goodness-of-fit clearly established the superiority of the time-adjacency specification which was evidently more complex due to the addition of information borrowed from neighboring years, but this addition of parameters allowed significant advantage at posterior deviance which subsequently benefited overall fit to crash data. The Base models were also developed to study the comparison between the proposed mixture and traditional space-time components for each temporal model. The mixture models consistently outperformed the corresponding Base models due to the advantages of much lower deviance. For cross-validation comparison of predictive accuracy, linear time trend model was adjudged the best as it recorded the highest value of log pseudo marginal likelihood (LPML). Four other evaluation criteria were considered for typical validation using the same data for model development. Under each criterion, observed crash counts were compared with three types of data containing Bayesian estimated, normal predicted, and model replicated ones. The linear model again performed the best in most scenarios except one case of using model replicated data and two cases involving prediction without including random effects. These phenomena indicated the mediocre performance of linear trend when random effects were excluded for evaluation. This might be due to the flexible mixture space-time interaction which can efficiently absorb the residual variability escaping from the predictable part of the model. The comparison of Base and mixture models in terms of prediction accuracy further bolstered the superiority of the mixture models as the mixture ones generated more precise estimated crash counts across all four models, suggesting that the advantages associated with mixture component at model fit were transferable to prediction accuracy. Finally, the residual analysis demonstrated the consistently superior performance of random effect models which validates the importance of incorporating the correlation structures to account for unobserved heterogeneity. Copyright © 2017 Elsevier Ltd. All rights reserved.

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

USGS Publications Warehouse

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.

The Impact of the Tree Prior on Molecular Dating of Data Sets Containing a Mixture of Inter- and Intraspecies Sampling.

PubMed

Ritchie, Andrew M; Lo, Nathan; Ho, Simon Y W

2017-05-01

In Bayesian phylogenetic analyses of genetic data, prior probability distributions need to be specified for the model parameters, including the tree. When Bayesian methods are used for molecular dating, available tree priors include those designed for species-level data, such as the pure-birth and birth-death priors, and coalescent-based priors designed for population-level data. However, molecular dating methods are frequently applied to data sets that include multiple individuals across multiple species. Such data sets violate the assumptions of both the speciation and coalescent-based tree priors, making it unclear which should be chosen and whether this choice can affect the estimation of node times. To investigate this problem, we used a simulation approach to produce data sets with different proportions of within- and between-species sampling under the multispecies coalescent model. These data sets were then analyzed under pure-birth, birth-death, constant-size coalescent, and skyline coalescent tree priors. We also explored the ability of Bayesian model testing to select the best-performing priors. We confirmed the applicability of our results to empirical data sets from cetaceans, phocids, and coregonid whitefish. Estimates of node times were generally robust to the choice of tree prior, but some combinations of tree priors and sampling schemes led to large differences in the age estimates. In particular, the pure-birth tree prior frequently led to inaccurate estimates for data sets containing a mixture of inter- and intraspecific sampling, whereas the birth-death and skyline coalescent priors produced stable results across all scenarios. Model testing provided an adequate means of rejecting inappropriate tree priors. Our results suggest that tree priors do not strongly affect Bayesian molecular dating results in most cases, even when severely misspecified. However, the choice of tree prior can be significant for the accuracy of dating results in the case of data sets with mixed inter- and intraspecies sampling. [Bayesian phylogenetic methods; model testing; molecular dating; node time; tree prior.]. © The authors 2016. Published by Oxford University Press, on behalf of the Society of Systematic Biologists. All rights reserved. For permissions, please e-mail: journals.permission@oup.com.

Fully Bayesian inference for structural MRI: application to segmentation and statistical analysis of T2-hypointensities.

PubMed

Schmidt, Paul; Schmid, Volker J; Gaser, Christian; Buck, Dorothea; Bührlen, Susanne; Förschler, Annette; Mühlau, Mark

2013-01-01

Aiming at iron-related T2-hypointensity, which is related to normal aging and neurodegenerative processes, we here present two practicable approaches, based on Bayesian inference, for preprocessing and statistical analysis of a complex set of structural MRI data. In particular, Markov Chain Monte Carlo methods were used to simulate posterior distributions. First, we rendered a segmentation algorithm that uses outlier detection based on model checking techniques within a Bayesian mixture model. Second, we rendered an analytical tool comprising a Bayesian regression model with smoothness priors (in the form of Gaussian Markov random fields) mitigating the necessity to smooth data prior to statistical analysis. For validation, we used simulated data and MRI data of 27 healthy controls (age: [Formula: see text]; range, [Formula: see text]). We first observed robust segmentation of both simulated T2-hypointensities and gray-matter regions known to be T2-hypointense. Second, simulated data and images of segmented T2-hypointensity were analyzed. We found not only robust identification of simulated effects but also a biologically plausible age-related increase of T2-hypointensity primarily within the dentate nucleus but also within the globus pallidus, substantia nigra, and red nucleus. Our results indicate that fully Bayesian inference can successfully be applied for preprocessing and statistical analysis of structural MRI data.

Bayesian parameter estimation for the Wnt pathway: an infinite mixture models approach.

PubMed

Koutroumpas, Konstantinos; Ballarini, Paolo; Votsi, Irene; Cournède, Paul-Henry

2016-09-01

Likelihood-free methods, like Approximate Bayesian Computation (ABC), have been extensively used in model-based statistical inference with intractable likelihood functions. When combined with Sequential Monte Carlo (SMC) algorithms they constitute a powerful approach for parameter estimation and model selection of mathematical models of complex biological systems. A crucial step in the ABC-SMC algorithms, significantly affecting their performance, is the propagation of a set of parameter vectors through a sequence of intermediate distributions using Markov kernels. In this article, we employ Dirichlet process mixtures (DPMs) to design optimal transition kernels and we present an ABC-SMC algorithm with DPM kernels. We illustrate the use of the proposed methodology using real data for the canonical Wnt signaling pathway. A multi-compartment model of the pathway is developed and it is compared to an existing model. The results indicate that DPMs are more efficient in the exploration of the parameter space and can significantly improve ABC-SMC performance. In comparison to alternative sampling schemes that are commonly used, the proposed approach can bring potential benefits in the estimation of complex multimodal distributions. The method is used to estimate the parameters and the initial state of two models of the Wnt pathway and it is shown that the multi-compartment model fits better the experimental data. Python scripts for the Dirichlet Process Gaussian Mixture model and the Gibbs sampler are available at https://sites.google.com/site/kkoutroumpas/software konstantinos.koutroumpas@ecp.fr. © The Author 2016. Published by Oxford University Press. All rights reserved. For Permissions, please e-mail: journals.permissions@oup.com.

Bayesian seismic inversion based on rock-physics prior modeling for the joint estimation of acoustic impedance, porosity and lithofacies

DOE Office of Scientific and Technical Information (OSTI.GOV)

Passos de Figueiredo, Leandro, E-mail: leandrop.fgr@gmail.com; Grana, Dario; Santos, Marcio

We propose a Bayesian approach for seismic inversion to estimate acoustic impedance, porosity and lithofacies within the reservoir conditioned to post-stack seismic and well data. The link between elastic and petrophysical properties is given by a joint prior distribution for the logarithm of impedance and porosity, based on a rock-physics model. The well conditioning is performed through a background model obtained by well log interpolation. Two different approaches are presented: in the first approach, the prior is defined by a single Gaussian distribution, whereas in the second approach it is defined by a Gaussian mixture to represent the well datamore » multimodal distribution and link the Gaussian components to different geological lithofacies. The forward model is based on a linearized convolutional model. For the single Gaussian case, we obtain an analytical expression for the posterior distribution, resulting in a fast algorithm to compute the solution of the inverse problem, i.e. the posterior distribution of acoustic impedance and porosity as well as the facies probability given the observed data. For the Gaussian mixture prior, it is not possible to obtain the distributions analytically, hence we propose a Gibbs algorithm to perform the posterior sampling and obtain several reservoir model realizations, allowing an uncertainty analysis of the estimated properties and lithofacies. Both methodologies are applied to a real seismic dataset with three wells to obtain 3D models of acoustic impedance, porosity and lithofacies. The methodologies are validated through a blind well test and compared to a standard Bayesian inversion approach. Using the probability of the reservoir lithofacies, we also compute a 3D isosurface probability model of the main oil reservoir in the studied field.« less

On The Value at Risk Using Bayesian Mixture Laplace Autoregressive Approach for Modelling the Islamic Stock Risk Investment

NASA Astrophysics Data System (ADS)

Miftahurrohmah, Brina; Iriawan, Nur; Fithriasari, Kartika

2017-06-01

Stocks are known as the financial instruments traded in the capital market which have a high level of risk. Their risks are indicated by their uncertainty of their return which have to be accepted by investors in the future. The higher the risk to be faced, the higher the return would be gained. Therefore, the measurements need to be made against the risk. Value at Risk (VaR) as the most popular risk measurement method, is frequently ignore when the pattern of return is not uni-modal Normal. The calculation of the risks using VaR method with the Normal Mixture Autoregressive (MNAR) approach has been considered. This paper proposes VaR method couple with the Mixture Laplace Autoregressive (MLAR) that would be implemented for analysing the first three biggest capitalization Islamic stock return in JII, namely PT. Astra International Tbk (ASII), PT. Telekomunikasi Indonesia Tbk (TLMK), and PT. Unilever Indonesia Tbk (UNVR). Parameter estimation is performed by employing Bayesian Markov Chain Monte Carlo (MCMC) approaches.

Sizing Up the Milky Way: A Bayesian Mixture Model Meta-analysis of Photometric Scale Length Measurements

NASA Astrophysics Data System (ADS)

Licquia, Timothy C.; Newman, Jeffrey A.

2016-11-01

The exponential scale length (L d ) of the Milky Way’s (MW’s) disk is a critical parameter for describing the global physical size of our Galaxy, important both for interpreting other Galactic measurements and helping us to understand how our Galaxy fits into extragalactic contexts. Unfortunately, current estimates span a wide range of values and are often statistically incompatible with one another. Here, we perform a Bayesian meta-analysis to determine an improved, aggregate estimate for L d , utilizing a mixture-model approach to account for the possibility that any one measurement has not properly accounted for all statistical or systematic errors. Within this machinery, we explore a variety of ways of modeling the nature of problematic measurements, and then employ a Bayesian model averaging technique to derive net posterior distributions that incorporate any model-selection uncertainty. Our meta-analysis combines 29 different (15 visible and 14 infrared) photometric measurements of L d available in the literature; these involve a broad assortment of observational data sets, MW models and assumptions, and methodologies, all tabulated herein. Analyzing the visible and infrared measurements separately yields estimates for L d of {2.71}-0.20+0.22 kpc and {2.51}-0.13+0.15 kpc, respectively, whereas considering them all combined yields 2.64 ± 0.13 kpc. The ratio between the visible and infrared scale lengths determined here is very similar to that measured in external spiral galaxies. We use these results to update the model of the Galactic disk from our previous work, constraining its stellar mass to be {4.8}-1.1+1.5× {10}10 M ⊙, and the MW’s total stellar mass to be {5.7}-1.1+1.5× {10}10 M ⊙.

Joint model-based clustering of nonlinear longitudinal trajectories and associated time-to-event data analysis, linked by latent class membership: with application to AIDS clinical studies.

PubMed

Huang, Yangxin; Lu, Xiaosun; Chen, Jiaqing; Liang, Juan; Zangmeister, Miriam

2017-10-27

Longitudinal and time-to-event data are often observed together. Finite mixture models are currently used to analyze nonlinear heterogeneous longitudinal data, which, by releasing the homogeneity restriction of nonlinear mixed-effects (NLME) models, can cluster individuals into one of the pre-specified classes with class membership probabilities. This clustering may have clinical significance, and be associated with clinically important time-to-event data. This article develops a joint modeling approach to a finite mixture of NLME models for longitudinal data and proportional hazard Cox model for time-to-event data, linked by individual latent class indicators, under a Bayesian framework. The proposed joint models and method are applied to a real AIDS clinical trial data set, followed by simulation studies to assess the performance of the proposed joint model and a naive two-step model, in which finite mixture model and Cox model are fitted separately.

A Bayesian approach for convex combination of two Gumbel-Barnett copulas

NASA Astrophysics Data System (ADS)

Fernández, M.; González-López, V. A.

2013-10-01

In this paper it was applied a new Bayesian approach to model the dependence between two variables of interest in public policy: "Gonorrhea Rates per 100,000 Population" and "400% Federal Poverty Level and over" with a small number of paired observations (one pair for each U.S. state). We use a mixture of Gumbel-Barnett copulas suitable to represent situations with weak and negative dependence, which is the case treated here. The methodology allows even making a prediction of the dependence between the variables from one year to another, showing whether there was any alteration in the dependence.

Improved estimation of sediment source contributions by concentration-dependent Bayesian isotopic mixing model

NASA Astrophysics Data System (ADS)

Ram Upadhayay, Hari; Bodé, Samuel; Griepentrog, Marco; Bajracharya, Roshan Man; Blake, Will; Cornelis, Wim; Boeckx, Pascal

2017-04-01

The implementation of compound-specific stable isotope (CSSI) analyses of biotracers (e.g. fatty acids, FAs) as constraints on sediment-source contributions has become increasingly relevant to understand the origin of sediments in catchments. The CSSI fingerprinting of sediment utilizes CSSI signature of biotracer as input in an isotopic mixing model (IMM) to apportion source soil contributions. So far source studies relied on the linear mixing assumptions of CSSI signature of sources to the sediment without accounting for potential effects of source biotracer concentration. Here we evaluated the effect of FAs concentration in sources on the accuracy of source contribution estimations in artificial soil mixture of three well-separated land use sources. Soil samples from land use sources were mixed to create three groups of artificial mixture with known source contributions. Sources and artificial mixture were analysed for δ13C of FAs using gas chromatography-combustion-isotope ratio mass spectrometry. The source contributions to the mixture were estimated using with and without concentration-dependent MixSIAR, a Bayesian isotopic mixing model. The concentration-dependent MixSIAR provided the closest estimates to the known artificial mixture source contributions (mean absolute error, MAE = 10.9%, and standard error, SE = 1.4%). In contrast, the concentration-independent MixSIAR with post mixing correction of tracer proportions based on aggregated concentration of FAs of sources biased the source contributions (MAE = 22.0%, SE = 3.4%). This study highlights the importance of accounting the potential effect of a source FA concentration for isotopic mixing in sediments that adds realisms to mixing model and allows more accurate estimates of contributions of sources to the mixture. The potential influence of FA concentration on CSSI signature of sediments is an important underlying factor that determines whether the isotopic signature of a given source is observable even after equilibrium. Therefore inclusion of FA concentrations of the sources in the IMM formulation is standard procedure for accurate estimation of source contributions. The post model correction approach that dominates the CSSI fingerprinting causes bias, especially if the FAs concentration of sources differs substantially.

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

NASA Astrophysics Data System (ADS)

Sahai, Swupnil

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

A new approach for handling longitudinal count data with zero-inflation and overdispersion: poisson geometric process model.

PubMed

Wan, Wai-Yin; Chan, Jennifer S K

2009-08-01

For time series of count data, correlated measurements, clustering as well as excessive zeros occur simultaneously in biomedical applications. Ignoring such effects might contribute to misleading treatment outcomes. A generalized mixture Poisson geometric process (GMPGP) model and a zero-altered mixture Poisson geometric process (ZMPGP) model are developed from the geometric process model, which was originally developed for modelling positive continuous data and was extended to handle count data. These models are motivated by evaluating the trend development of new tumour counts for bladder cancer patients as well as by identifying useful covariates which affect the count level. The models are implemented using Bayesian method with Markov chain Monte Carlo (MCMC) algorithms and are assessed using deviance information criterion (DIC).

EuroForMix: An open source software based on a continuous model to evaluate STR DNA profiles from a mixture of contributors with artefacts.

PubMed

Bleka, Øyvind; Storvik, Geir; Gill, Peter

2016-03-01

We have released a software named EuroForMix to analyze STR DNA profiles in a user-friendly graphical user interface. The software implements a model to explain the allelic peak height on a continuous scale in order to carry out weight-of-evidence calculations for profiles which could be from a mixture of contributors. Through a properly parameterized model we are able to do inference on mixture proportions, the peak height properties, stutter proportion and degradation. In addition, EuroForMix includes models for allele drop-out, allele drop-in and sub-population structure. EuroForMix supports two inference approaches for likelihood ratio calculations. The first approach uses maximum likelihood estimation of the unknown parameters. The second approach is Bayesian based which requires prior distributions to be specified for the parameters involved. The user may specify any number of known and unknown contributors in the model, however we find that there is a practical computing time limit which restricts the model to a maximum of four unknown contributors. EuroForMix is the first freely open source, continuous model (accommodating peak height, stutter, drop-in, drop-out, population substructure and degradation), to be reported in the literature. It therefore serves an important purpose to act as an unrestricted platform to compare different solutions that are available. The implementation of the continuous model used in the software showed close to identical results to the R-package DNAmixtures, which requires a HUGIN Expert license to be used. An additional feature in EuroForMix is the ability for the user to adapt the Bayesian inference framework by incorporating their own prior information. Copyright © 2015 Elsevier Ireland Ltd. All rights reserved.

An algebraic aspect of Pareto mixture parameter estimation using censored sample: A Bayesian approach.

PubMed

Saleem, Muhammad; Sharif, Kashif; Fahmi, Aliya

2018-04-27

Applications of Pareto distribution are common in reliability, survival and financial studies. In this paper, A Pareto mixture distribution is considered to model a heterogeneous population comprising of two subgroups. Each of two subgroups is characterized by the same functional form with unknown distinct shape and scale parameters. Bayes estimators have been derived using flat and conjugate priors using squared error loss function. Standard errors have also been derived for the Bayes estimators. An interesting feature of this study is the preparation of components of Fisher Information matrix.

A Bayesian hierarchical model for mortality data from cluster-sampling household surveys in humanitarian crises.

PubMed

Heudtlass, Peter; Guha-Sapir, Debarati; Speybroeck, Niko

2018-05-31

The crude death rate (CDR) is one of the defining indicators of humanitarian emergencies. When data from vital registration systems are not available, it is common practice to estimate the CDR from household surveys with cluster-sampling design. However, sample sizes are often too small to compare mortality estimates to emergency thresholds, at least in a frequentist framework. Several authors have proposed Bayesian methods for health surveys in humanitarian crises. Here, we develop an approach specifically for mortality data and cluster-sampling surveys. We describe a Bayesian hierarchical Poisson-Gamma mixture model with generic (weakly informative) priors that could be used as default in absence of any specific prior knowledge, and compare Bayesian and frequentist CDR estimates using five different mortality datasets. We provide an interpretation of the Bayesian estimates in the context of an emergency threshold and demonstrate how to interpret parameters at the cluster level and ways in which informative priors can be introduced. With the same set of weakly informative priors, Bayesian CDR estimates are equivalent to frequentist estimates, for all practical purposes. The probability that the CDR surpasses the emergency threshold can be derived directly from the posterior of the mean of the mixing distribution. All observation in the datasets contribute to the estimation of cluster-level estimates, through the hierarchical structure of the model. In a context of sparse data, Bayesian mortality assessments have advantages over frequentist ones already when using only weakly informative priors. More informative priors offer a formal and transparent way of combining new data with existing data and expert knowledge and can help to improve decision-making in humanitarian crises by complementing frequentist estimates.

Use of genetic data to infer population-specific ecological and phenotypic traits from mixed aggregations

USGS Publications Warehouse

Moran, Paul; Bromaghin, Jeffrey F.; Masuda, Michele

2014-01-01

Many applications in ecological genetics involve sampling individuals from a mixture of multiple biological populations and subsequently associating those individuals with the populations from which they arose. Analytical methods that assign individuals to their putative population of origin have utility in both basic and applied research, providing information about population-specific life history and habitat use, ecotoxins, pathogen and parasite loads, and many other non-genetic ecological, or phenotypic traits. Although the question is initially directed at the origin of individuals, in most cases the ultimate desire is to investigate the distribution of some trait among populations. Current practice is to assign individuals to a population of origin and study properties of the trait among individuals within population strata as if they constituted independent samples. It seemed that approach might bias population-specific trait inference. In this study we made trait inferences directly through modeling, bypassing individual assignment. We extended a Bayesian model for population mixture analysis to incorporate parameters for the phenotypic trait and compared its performance to that of individual assignment with a minimum probability threshold for assignment. The Bayesian mixture model outperformed individual assignment under some trait inference conditions. However, by discarding individuals whose origins are most uncertain, the individual assignment method provided a less complex analytical technique whose performance may be adequate for some common trait inference problems. Our results provide specific guidance for method selection under various genetic relationships among populations with different trait distributions.

Use of Genetic Data to Infer Population-Specific Ecological and Phenotypic Traits from Mixed Aggregations

PubMed Central

Moran, Paul; Bromaghin, Jeffrey F.; Masuda, Michele

2014-01-01

Many applications in ecological genetics involve sampling individuals from a mixture of multiple biological populations and subsequently associating those individuals with the populations from which they arose. Analytical methods that assign individuals to their putative population of origin have utility in both basic and applied research, providing information about population-specific life history and habitat use, ecotoxins, pathogen and parasite loads, and many other non-genetic ecological, or phenotypic traits. Although the question is initially directed at the origin of individuals, in most cases the ultimate desire is to investigate the distribution of some trait among populations. Current practice is to assign individuals to a population of origin and study properties of the trait among individuals within population strata as if they constituted independent samples. It seemed that approach might bias population-specific trait inference. In this study we made trait inferences directly through modeling, bypassing individual assignment. We extended a Bayesian model for population mixture analysis to incorporate parameters for the phenotypic trait and compared its performance to that of individual assignment with a minimum probability threshold for assignment. The Bayesian mixture model outperformed individual assignment under some trait inference conditions. However, by discarding individuals whose origins are most uncertain, the individual assignment method provided a less complex analytical technique whose performance may be adequate for some common trait inference problems. Our results provide specific guidance for method selection under various genetic relationships among populations with different trait distributions. PMID:24905464

Using hierarchical Bayesian multi-species mixture models to estimate tandem hoop-net based habitat associations and detection probabilities of fishes in reservoirs

USGS Publications Warehouse

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.

Infinite von Mises-Fisher Mixture Modeling of Whole Brain fMRI Data.

PubMed

Røge, Rasmus E; Madsen, Kristoffer H; Schmidt, Mikkel N; Mørup, Morten

2017-10-01

Cluster analysis of functional magnetic resonance imaging (fMRI) data is often performed using gaussian mixture models, but when the time series are standardized such that the data reside on a hypersphere, this modeling assumption is questionable. The consequences of ignoring the underlying spherical manifold are rarely analyzed, in part due to the computational challenges imposed by directional statistics. In this letter, we discuss a Bayesian von Mises-Fisher (vMF) mixture model for data on the unit hypersphere and present an efficient inference procedure based on collapsed Markov chain Monte Carlo sampling. Comparing the vMF and gaussian mixture models on synthetic data, we demonstrate that the vMF model has a slight advantage inferring the true underlying clustering when compared to gaussian-based models on data generated from both a mixture of vMFs and a mixture of gaussians subsequently normalized. Thus, when performing model selection, the two models are not in agreement. Analyzing multisubject whole brain resting-state fMRI data from healthy adult subjects, we find that the vMF mixture model is considerably more reliable than the gaussian mixture model when comparing solutions across models trained on different groups of subjects, and again we find that the two models disagree on the optimal number of components. The analysis indicates that the fMRI data support more than a thousand clusters, and we confirm this is not a result of overfitting by demonstrating better prediction on data from held-out subjects. Our results highlight the utility of using directional statistics to model standardized fMRI data and demonstrate that whole brain segmentation of fMRI data requires a very large number of functional units in order to adequately account for the discernible statistical patterns in the data.

Mixture of autoregressive modeling orders and its implication on single trial EEG classification

PubMed Central

Atyabi, Adham; Shic, Frederick; Naples, Adam

2016-01-01

Autoregressive (AR) models are of commonly utilized feature types in Electroencephalogram (EEG) studies due to offering better resolution, smoother spectra and being applicable to short segments of data. Identifying correct AR’s modeling order is an open challenge. Lower model orders poorly represent the signal while higher orders increase noise. Conventional methods for estimating modeling order includes Akaike Information Criterion (AIC), Bayesian Information Criterion (BIC) and Final Prediction Error (FPE). This article assesses the hypothesis that appropriate mixture of multiple AR orders is likely to better represent the true signal compared to any single order. Better spectral representation of underlying EEG patterns can increase utility of AR features in Brain Computer Interface (BCI) systems by increasing timely & correctly responsiveness of such systems to operator’s thoughts. Two mechanisms of Evolutionary-based fusion and Ensemble-based mixture are utilized for identifying such appropriate mixture of modeling orders. The classification performance of the resultant AR-mixtures are assessed against several conventional methods utilized by the community including 1) A well-known set of commonly used orders suggested by the literature, 2) conventional order estimation approaches (e.g., AIC, BIC and FPE), 3) blind mixture of AR features originated from a range of well-known orders. Five datasets from BCI competition III that contain 2, 3 and 4 motor imagery tasks are considered for the assessment. The results indicate superiority of Ensemble-based modeling order mixture and evolutionary-based order fusion methods within all datasets. PMID:28740331

A Bayesian mixture model for chromatin interaction data.

PubMed

Niu, Liang; Lin, Shili

2015-02-01

Chromatin interactions mediated by a particular protein are of interest for studying gene regulation, especially the regulation of genes that are associated with, or known to be causative of, a disease. A recent molecular technique, Chromatin interaction analysis by paired-end tag sequencing (ChIA-PET), that uses chromatin immunoprecipitation (ChIP) and high throughput paired-end sequencing, is able to detect such chromatin interactions genomewide. However, ChIA-PET may generate noise (i.e., pairings of DNA fragments by random chance) in addition to true signal (i.e., pairings of DNA fragments by interactions). In this paper, we propose MC_DIST based on a mixture modeling framework to identify true chromatin interactions from ChIA-PET count data (counts of DNA fragment pairs). The model is cast into a Bayesian framework to take into account the dependency among the data and the available information on protein binding sites and gene promoters to reduce false positives. A simulation study showed that MC_DIST outperforms the previously proposed hypergeometric model in terms of both power and type I error rate. A real data study showed that MC_DIST may identify potential chromatin interactions between protein binding sites and gene promoters that may be missed by the hypergeometric model. An R package implementing the MC_DIST model is available at http://www.stat.osu.edu/~statgen/SOFTWARE/MDM.

Bayesian inference on multiscale models for poisson intensity estimation: applications to photon-limited image denoising.

PubMed

Lefkimmiatis, Stamatios; Maragos, Petros; Papandreou, George

2009-08-01

We present an improved statistical model for analyzing Poisson processes, with applications to photon-limited imaging. We build on previous work, adopting a multiscale representation of the Poisson process in which the ratios of the underlying Poisson intensities (rates) in adjacent scales are modeled as mixtures of conjugate parametric distributions. Our main contributions include: 1) a rigorous and robust regularized expectation-maximization (EM) algorithm for maximum-likelihood estimation of the rate-ratio density parameters directly from the noisy observed Poisson data (counts); 2) extension of the method to work under a multiscale hidden Markov tree model (HMT) which couples the mixture label assignments in consecutive scales, thus modeling interscale coefficient dependencies in the vicinity of image edges; 3) exploration of a 2-D recursive quad-tree image representation, involving Dirichlet-mixture rate-ratio densities, instead of the conventional separable binary-tree image representation involving beta-mixture rate-ratio densities; and 4) a novel multiscale image representation, which we term Poisson-Haar decomposition, that better models the image edge structure, thus yielding improved performance. Experimental results on standard images with artificially simulated Poisson noise and on real photon-limited images demonstrate the effectiveness of the proposed techniques.

BATMAN--an R package for the automated quantification of metabolites from nuclear magnetic resonance spectra using a Bayesian model.

PubMed

Hao, Jie; Astle, William; De Iorio, Maria; Ebbels, Timothy M D

2012-08-01

Nuclear Magnetic Resonance (NMR) spectra are widely used in metabolomics to obtain metabolite profiles in complex biological mixtures. Common methods used to assign and estimate concentrations of metabolites involve either an expert manual peak fitting or extra pre-processing steps, such as peak alignment and binning. Peak fitting is very time consuming and is subject to human error. Conversely, alignment and binning can introduce artefacts and limit immediate biological interpretation of models. We present the Bayesian automated metabolite analyser for NMR spectra (BATMAN), an R package that deconvolutes peaks from one-dimensional NMR spectra, automatically assigns them to specific metabolites from a target list and obtains concentration estimates. The Bayesian model incorporates information on characteristic peak patterns of metabolites and is able to account for shifts in the position of peaks commonly seen in NMR spectra of biological samples. It applies a Markov chain Monte Carlo algorithm to sample from a joint posterior distribution of the model parameters and obtains concentration estimates with reduced error compared with conventional numerical integration and comparable to manual deconvolution by experienced spectroscopists. http://www1.imperial.ac.uk/medicine/people/t.ebbels/ t.ebbels@imperial.ac.uk.

Bayesian informative dropout model for longitudinal binary data with random effects using conditional and joint modeling approaches.

PubMed

Chan, Jennifer S K

2016-05-01

Dropouts are common in longitudinal study. If the dropout probability depends on the missing observations at or after dropout, this type of dropout is called informative (or nonignorable) dropout (ID). Failure to accommodate such dropout mechanism into the model will bias the parameter estimates. We propose a conditional autoregressive model for longitudinal binary data with an ID model such that the probabilities of positive outcomes as well as the drop-out indicator in each occasion are logit linear in some covariates and outcomes. This model adopting a marginal model for outcomes and a conditional model for dropouts is called a selection model. To allow for the heterogeneity and clustering effects, the outcome model is extended to incorporate mixture and random effects. Lastly, the model is further extended to a novel model that models the outcome and dropout jointly such that their dependency is formulated through an odds ratio function. Parameters are estimated by a Bayesian approach implemented using the user-friendly Bayesian software WinBUGS. A methadone clinic dataset is analyzed to illustrate the proposed models. Result shows that the treatment time effect is still significant but weaker after allowing for an ID process in the data. Finally the effect of drop-out on parameter estimates is evaluated through simulation studies. © 2015 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim.

Spatiotemporal multivariate mixture models for Bayesian model selection in disease mapping.

PubMed

Lawson, A B; Carroll, R; Faes, C; Kirby, R S; Aregay, M; Watjou, K

2017-12-01

It is often the case that researchers wish to simultaneously explore the behavior of and estimate overall risk for multiple, related diseases with varying rarity while accounting for potential spatial and/or temporal correlation. In this paper, we propose a flexible class of multivariate spatio-temporal mixture models to fill this role. Further, these models offer flexibility with the potential for model selection as well as the ability to accommodate lifestyle, socio-economic, and physical environmental variables with spatial, temporal, or both structures. Here, we explore the capability of this approach via a large scale simulation study and examine a motivating data example involving three cancers in South Carolina. The results which are focused on four model variants suggest that all models possess the ability to recover simulation ground truth and display improved model fit over two baseline Knorr-Held spatio-temporal interaction model variants in a real data application.

Cure modeling in real-time prediction: How much does it help?

PubMed

Ying, Gui-Shuang; Zhang, Qiang; Lan, Yu; Li, Yimei; Heitjan, Daniel F

2017-08-01

Various parametric and nonparametric modeling approaches exist for real-time prediction in time-to-event clinical trials. Recently, Chen (2016 BMC Biomedical Research Methodology 16) proposed a prediction method based on parametric cure-mixture modeling, intending to cover those situations where it appears that a non-negligible fraction of subjects is cured. In this article we apply a Weibull cure-mixture model to create predictions, demonstrating the approach in RTOG 0129, a randomized trial in head-and-neck cancer. We compare the ultimate realized data in RTOG 0129 to interim predictions from a Weibull cure-mixture model, a standard Weibull model without a cure component, and a nonparametric model based on the Bayesian bootstrap. The standard Weibull model predicted that events would occur earlier than the Weibull cure-mixture model, but the difference was unremarkable until late in the trial when evidence for a cure became clear. Nonparametric predictions often gave undefined predictions or infinite prediction intervals, particularly at early stages of the trial. Simulations suggest that cure modeling can yield better-calibrated prediction intervals when there is a cured component, or the appearance of a cured component, but at a substantial cost in the average width of the intervals. Copyright © 2017 Elsevier Inc. All rights reserved.

Bayesian Peak Picking for NMR Spectra

PubMed Central

Cheng, Yichen; Gao, Xin; Liang, Faming

2013-01-01

Protein structure determination is a very important topic in structural genomics, which helps people to understand varieties of biological functions such as protein-protein interactions, protein–DNA interactions and so on. Nowadays, nuclear magnetic resonance (NMR) has often been used to determine the three-dimensional structures of protein in vivo. This study aims to automate the peak picking step, the most important and tricky step in NMR structure determination. We propose to model the NMR spectrum by a mixture of bivariate Gaussian densities and use the stochastic approximation Monte Carlo algorithm as the computational tool to solve the problem. Under the Bayesian framework, the peak picking problem is casted as a variable selection problem. The proposed method can automatically distinguish true peaks from false ones without preprocessing the data. To the best of our knowledge, this is the first effort in the literature that tackles the peak picking problem for NMR spectrum data using Bayesian method. PMID:24184964

Impact of relationships between test and training animals and among training animals on reliability of genomic prediction.

PubMed

Wu, X; Lund, M S; Sun, D; Zhang, Q; Su, G

2015-10-01

One of the factors affecting the reliability of genomic prediction is the relationship among the animals of interest. This study investigated the reliability of genomic prediction in various scenarios with regard to the relationship between test and training animals, and among animals within the training data set. Different training data sets were generated from EuroGenomics data and a group of Nordic Holstein bulls (born in 2005 and afterwards) as a common test data set. Genomic breeding values were predicted using a genomic best linear unbiased prediction model and a Bayesian mixture model. The results showed that a closer relationship between test and training animals led to a higher reliability of genomic predictions for the test animals, while a closer relationship among training animals resulted in a lower reliability. In addition, the Bayesian mixture model in general led to a slightly higher reliability of genomic prediction, especially for the scenario of distant relationships between training and test animals. Therefore, to prevent a decrease in reliability, constant updates of the training population with animals from more recent generations are required. Moreover, a training population consisting of less-related animals is favourable for reliability of genomic prediction. © 2015 Blackwell Verlag GmbH.

Negative Binomial Process Count and Mixture Modeling.

PubMed

Zhou, Mingyuan; Carin, Lawrence

2015-02-01

The seemingly disjoint problems of count and mixture modeling are united under the negative binomial (NB) process. A gamma process is employed to model the rate measure of a Poisson process, whose normalization provides a random probability measure for mixture modeling and whose marginalization leads to an NB process for count modeling. A draw from the NB process consists of a Poisson distributed finite number of distinct atoms, each of which is associated with a logarithmic distributed number of data samples. We reveal relationships between various count- and mixture-modeling distributions and construct a Poisson-logarithmic bivariate distribution that connects the NB and Chinese restaurant table distributions. Fundamental properties of the models are developed, and we derive efficient Bayesian inference. It is shown that with augmentation and normalization, the NB process and gamma-NB process can be reduced to the Dirichlet process and hierarchical Dirichlet process, respectively. These relationships highlight theoretical, structural, and computational advantages of the NB process. A variety of NB processes, including the beta-geometric, beta-NB, marked-beta-NB, marked-gamma-NB and zero-inflated-NB processes, with distinct sharing mechanisms, are also constructed. These models are applied to topic modeling, with connections made to existing algorithms under Poisson factor analysis. Example results show the importance of inferring both the NB dispersion and probability parameters.

Bayesian Ensemble Trees (BET) for Clustering and Prediction in Heterogeneous Data

PubMed Central

Duan, Leo L.; Clancy, John P.; Szczesniak, Rhonda D.

2016-01-01

We propose a novel “tree-averaging” model that utilizes the ensemble of classification and regression trees (CART). Each constituent tree is estimated with a subset of similar data. We treat this grouping of subsets as Bayesian Ensemble Trees (BET) and model them as a Dirichlet process. We show that BET determines the optimal number of trees by adapting to the data heterogeneity. Compared with the other ensemble methods, BET requires much fewer trees and shows equivalent prediction accuracy using weighted averaging. Moreover, each tree in BET provides variable selection criterion and interpretation for each subset. We developed an efficient estimating procedure with improved estimation strategies in both CART and mixture models. We demonstrate these advantages of BET with simulations and illustrate the approach with a real-world data example involving regression of lung function measurements obtained from patients with cystic fibrosis. Supplemental materials are available online. PMID:27524872

Accounting for non-independent detection when estimating abundance of organisms with a Bayesian approach

USGS Publications Warehouse

Martin, Julien; Royle, J. Andrew; MacKenzie, Darryl I.; Edwards, Holly H.; Kery, Marc; Gardner, Beth

2011-01-01

Summary 1. Binomial mixture models use repeated count data to estimate abundance. They are becoming increasingly popular because they provide a simple and cost-effective way to account for imperfect detection. However, these models assume that individuals are detected independently of each other. This assumption may often be violated in the field. For instance, manatees (Trichechus manatus latirostris) may surface in turbid water (i.e. become available for detection during aerial surveys) in a correlated manner (i.e. in groups). However, correlated behaviour, affecting the non-independence of individual detections, may also be relevant in other systems (e.g. correlated patterns of singing in birds and amphibians). 2. We extend binomial mixture models to account for correlated behaviour and therefore to account for non-independent detection of individuals. We simulated correlated behaviour using beta-binomial random variables. Our approach can be used to simultaneously estimate abundance, detection probability and a correlation parameter. 3. Fitting binomial mixture models to data that followed a beta-binomial distribution resulted in an overestimation of abundance even for moderate levels of correlation. In contrast, the beta-binomial mixture model performed considerably better in our simulation scenarios. We also present a goodness-of-fit procedure to evaluate the fit of beta-binomial mixture models. 4. We illustrate our approach by fitting both binomial and beta-binomial mixture models to aerial survey data of manatees in Florida. We found that the binomial mixture model did not fit the data, whereas there was no evidence of lack of fit for the beta-binomial mixture model. This example helps illustrate the importance of using simulations and assessing goodness-of-fit when analysing ecological data with N-mixture models. Indeed, both the simulations and the goodness-of-fit procedure highlighted the limitations of the standard binomial mixture model for aerial manatee surveys. 5. Overestimation of abundance by binomial mixture models owing to non-independent detections is problematic for ecological studies, but also for conservation. For example, in the case of endangered species, it could lead to inappropriate management decisions, such as downlisting. These issues will be increasingly relevant as more ecologists apply flexible N-mixture models to ecological data.

Bayesian dose-response analysis for epidemiological studies with complex uncertainty in dose estimation.

PubMed

Kwon, Deukwoo; Hoffman, F Owen; Moroz, Brian E; Simon, Steven L

2016-02-10

Most conventional risk analysis methods rely on a single best estimate of exposure per person, which does not allow for adjustment for exposure-related uncertainty. Here, we propose a Bayesian model averaging method to properly quantify the relationship between radiation dose and disease outcomes by accounting for shared and unshared uncertainty in estimated dose. Our Bayesian risk analysis method utilizes multiple realizations of sets (vectors) of doses generated by a two-dimensional Monte Carlo simulation method that properly separates shared and unshared errors in dose estimation. The exposure model used in this work is taken from a study of the risk of thyroid nodules among a cohort of 2376 subjects who were exposed to fallout from nuclear testing in Kazakhstan. We assessed the performance of our method through an extensive series of simulations and comparisons against conventional regression risk analysis methods. When the estimated doses contain relatively small amounts of uncertainty, the Bayesian method using multiple a priori plausible draws of dose vectors gave similar results to the conventional regression-based methods of dose-response analysis. However, when large and complex mixtures of shared and unshared uncertainties are present, the Bayesian method using multiple dose vectors had significantly lower relative bias than conventional regression-based risk analysis methods and better coverage, that is, a markedly increased capability to include the true risk coefficient within the 95% credible interval of the Bayesian-based risk estimate. An evaluation of the dose-response using our method is presented for an epidemiological study of thyroid disease following radiation exposure. Copyright © 2015 John Wiley & Sons, Ltd.

Bayesian Lagrangian Data Assimilation and Drifter Deployment Strategies

NASA Astrophysics Data System (ADS)

Dutt, A.; Lermusiaux, P. F. J.

2017-12-01

Ocean currents transport a variety of natural (e.g. water masses, phytoplankton, zooplankton, sediments, etc.) and man-made materials and other objects (e.g. pollutants, floating debris, search and rescue, etc.). Lagrangian Coherent Structures (LCSs) or the most influential/persistent material lines in a flow, provide a robust approach to characterize such Lagrangian transports and organize classic trajectories. Using the flow-map stochastic advection and a dynamically-orthogonal decomposition, we develop uncertainty prediction schemes for both Eulerian and Lagrangian variables. We then extend our Bayesian Gaussian Mixture Model (GMM)-DO filter to a joint Eulerian-Lagrangian Bayesian data assimilation scheme. The resulting nonlinear filter allows the simultaneous non-Gaussian estimation of Eulerian variables (e.g. velocity, temperature, salinity, etc.) and Lagrangian variables (e.g. drifter/float positions, trajectories, LCSs, etc.). Its results are showcased using a double-gyre flow with a random frequency, a stochastic flow past a cylinder, and realistic ocean examples. We further show how our Bayesian mutual information and adaptive sampling equations provide a rigorous efficient methodology to plan optimal drifter deployment strategies and predict the optimal times, locations, and types of measurements to be collected.

A multivariate spatial mixture model for areal data: examining regional differences in standardized test scores

PubMed Central

Neelon, Brian; Gelfand, Alan E.; Miranda, Marie Lynn

2013-01-01

Summary Researchers in the health and social sciences often wish to examine joint spatial patterns for two or more related outcomes. Examples include infant birth weight and gestational length, psychosocial and behavioral indices, and educational test scores from different cognitive domains. We propose a multivariate spatial mixture model for the joint analysis of continuous individual-level outcomes that are referenced to areal units. The responses are modeled as a finite mixture of multivariate normals, which accommodates a wide range of marginal response distributions and allows investigators to examine covariate effects within subpopulations of interest. The model has a hierarchical structure built at the individual level (i.e., individuals are nested within areal units), and thus incorporates both individual- and areal-level predictors as well as spatial random effects for each mixture component. Conditional autoregressive (CAR) priors on the random effects provide spatial smoothing and allow the shape of the multivariate distribution to vary flexibly across geographic regions. We adopt a Bayesian modeling approach and develop an efficient Markov chain Monte Carlo model fitting algorithm that relies primarily on closed-form full conditionals. We use the model to explore geographic patterns in end-of-grade math and reading test scores among school-age children in North Carolina. PMID:26401059

Using Latent Class Analysis to Model Temperament Types.

PubMed

Loken, Eric

2004-10-01

Mixture models are appropriate for data that arise from a set of qualitatively different subpopulations. In this study, latent class analysis was applied to observational data from a laboratory assessment of infant temperament at four months of age. The EM algorithm was used to fit the models, and the Bayesian method of posterior predictive checks was used for model selection. Results show at least three types of infant temperament, with patterns consistent with those identified by previous researchers who classified the infants using a theoretically based system. Multiple imputation of group memberships is proposed as an alternative to assigning subjects to the latent class with maximum posterior probability in order to reflect variance due to uncertainty in the parameter estimation. Latent class membership at four months of age predicted longitudinal outcomes at four years of age. The example illustrates issues relevant to all mixture models, including estimation, multi-modality, model selection, and comparisons based on the latent group indicators.

Bayesian hierarchical functional data analysis via contaminated informative priors.

PubMed

Scarpa, Bruno; Dunson, David B

2009-09-01

A variety of flexible approaches have been proposed for functional data analysis, allowing both the mean curve and the distribution about the mean to be unknown. Such methods are most useful when there is limited prior information. Motivated by applications to modeling of temperature curves in the menstrual cycle, this article proposes a flexible approach for incorporating prior information in semiparametric Bayesian analyses of hierarchical functional data. The proposed approach is based on specifying the distribution of functions as a mixture of a parametric hierarchical model and a nonparametric contamination. The parametric component is chosen based on prior knowledge, while the contamination is characterized as a functional Dirichlet process. In the motivating application, the contamination component allows unanticipated curve shapes in unhealthy menstrual cycles. Methods are developed for posterior computation, and the approach is applied to data from a European fecundability study.

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

NASA Astrophysics Data System (ADS)

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.

The dynamics of fidelity over the time course of long-term memory.

PubMed

Persaud, Kimele; Hemmer, Pernille

2016-08-01

Bayesian models of cognition assume that prior knowledge about the world influences judgments. Recent approaches have suggested that the loss of fidelity from working to long-term (LT) memory is simply due to an increased rate of guessing (e.g. Brady, Konkle, Gill, Oliva, & Alvarez, 2013). That is, recall is the result of either remembering (with some noise) or guessing. This stands in contrast to Bayesian models of cognition while assume that prior knowledge about the world influences judgments, and that recall is a combination of expectations learned from the environment and noisy memory representations. Here, we evaluate the time course of fidelity in LT episodic memory, and the relative contribution of prior category knowledge and guessing, using a continuous recall paradigm. At an aggregate level, performance reflects a high rate of guessing. However, when aggregate data is partitioned by lag (i.e., the number of presentations from study to test), or is un-aggregated, performance appears to be more complex than just remembering with some noise and guessing. We implemented three models: the standard remember-guess model, a three-component remember-guess model, and a Bayesian mixture model and evaluated these models against the data. The results emphasize the importance of taking into account the influence of prior category knowledge on memory. Copyright © 2016 Elsevier Inc. All rights reserved.

A Hierarchical Bayesian Procedure for Two-Mode Cluster Analysis

ERIC Educational Resources Information Center

DeSarbo, Wayne S.; Fong, Duncan K. H.; Liechty, John; Saxton, M. Kim

2004-01-01

This manuscript introduces a new Bayesian finite mixture methodology for the joint clustering of row and column stimuli/objects associated with two-mode asymmetric proximity, dominance, or profile data. That is, common clusters are derived which partition both the row and column stimuli/objects simultaneously into the same derived set of clusters.…

A unified Bayesian semiparametric approach to assess discrimination ability in survival analysis

PubMed Central

Zhao, Lili; Feng, Dai; Chen, Guoan; Taylor, Jeremy M.G.

2015-01-01

Summary The discriminatory ability of a marker for censored survival data is routinely assessed by the time-dependent ROC curve and the c-index. The time-dependent ROC curve evaluates the ability of a biomarker to predict whether a patient lives past a particular time t. The c-index measures the global concordance of the marker and the survival time regardless of the time point. We propose a Bayesian semiparametric approach to estimate these two measures. The proposed estimators are based on the conditional distribution of the survival time given the biomarker and the empirical biomarker distribution. The conditional distribution is estimated by a linear dependent Dirichlet process mixture model. The resulting ROC curve is smooth as it is estimated by a mixture of parametric functions. The proposed c-index estimator is shown to be more efficient than the commonly used Harrell's c-index since it uses all pairs of data rather than only informative pairs. The proposed estimators are evaluated through simulations and illustrated using a lung cancer dataset. PMID:26676324

Efficient Bayesian mixed model analysis increases association power in large cohorts

PubMed Central

Loh, Po-Ru; Tucker, George; Bulik-Sullivan, Brendan K; Vilhjálmsson, Bjarni J; Finucane, Hilary K; Salem, Rany M; Chasman, Daniel I; Ridker, Paul M; Neale, Benjamin M; Berger, Bonnie; Patterson, Nick; Price, Alkes L

2014-01-01

Linear mixed models are a powerful statistical tool for identifying genetic associations and avoiding confounding. However, existing methods are computationally intractable in large cohorts, and may not optimize power. All existing methods require time cost O(MN2) (where N = #samples and M = #SNPs) and implicitly assume an infinitesimal genetic architecture in which effect sizes are normally distributed, which can limit power. Here, we present a far more efficient mixed model association method, BOLT-LMM, which requires only a small number of O(MN)-time iterations and increases power by modeling more realistic, non-infinitesimal genetic architectures via a Bayesian mixture prior on marker effect sizes. We applied BOLT-LMM to nine quantitative traits in 23,294 samples from the Women’s Genome Health Study (WGHS) and observed significant increases in power, consistent with simulations. Theory and simulations show that the boost in power increases with cohort size, making BOLT-LMM appealing for GWAS in large cohorts. PMID:25642633

Mixture Modeling for Background and Sources Separation in x-ray Astronomical Images

NASA Astrophysics Data System (ADS)

Guglielmetti, Fabrizia; Fischer, Rainer; Dose, Volker

2004-11-01

A probabilistic technique for the joint estimation of background and sources in high-energy astrophysics is described. Bayesian probability theory is applied to gain insight into the coexistence of background and sources through a probabilistic two-component mixture model, which provides consistent uncertainties of background and sources. The present analysis is applied to ROSAT PSPC data (0.1-2.4 keV) in Survey Mode. A background map is modelled using a Thin-Plate spline. Source probability maps are obtained for each pixel (45 arcsec) independently and for larger correlation lengths, revealing faint and extended sources. We will demonstrate that the described probabilistic method allows for detection improvement of faint extended celestial sources compared to the Standard Analysis Software System (SASS) used for the production of the ROSAT All-Sky Survey (RASS) catalogues.

Meta-Analysis of a Continuous Outcome Combining Individual Patient Data and Aggregate Data: A Method Based on Simulated Individual Patient Data

ERIC Educational Resources Information Center

Yamaguchi, Yusuke; Sakamoto, Wataru; Goto, Masashi; Staessen, Jan A.; Wang, Jiguang; Gueyffier, Francois; Riley, Richard D.

2014-01-01

When some trials provide individual patient data (IPD) and the others provide only aggregate data (AD), meta-analysis methods for combining IPD and AD are required. We propose a method that reconstructs the missing IPD for AD trials by a Bayesian sampling procedure and then applies an IPD meta-analysis model to the mixture of simulated IPD and…

Bayesian peak picking for NMR spectra.

PubMed

Cheng, Yichen; Gao, Xin; Liang, Faming

2014-02-01

Protein structure determination is a very important topic in structural genomics, which helps people to understand varieties of biological functions such as protein-protein interactions, protein-DNA interactions and so on. Nowadays, nuclear magnetic resonance (NMR) has often been used to determine the three-dimensional structures of protein in vivo. This study aims to automate the peak picking step, the most important and tricky step in NMR structure determination. We propose to model the NMR spectrum by a mixture of bivariate Gaussian densities and use the stochastic approximation Monte Carlo algorithm as the computational tool to solve the problem. Under the Bayesian framework, the peak picking problem is casted as a variable selection problem. The proposed method can automatically distinguish true peaks from false ones without preprocessing the data. To the best of our knowledge, this is the first effort in the literature that tackles the peak picking problem for NMR spectrum data using Bayesian method. Copyright © 2013. Production and hosting by Elsevier Ltd.

Learning coefficient of generalization error in Bayesian estimation and vandermonde matrix-type singularity.

PubMed

Aoyagi, Miki; Nagata, Kenji

2012-06-01

The term algebraic statistics arises from the study of probabilistic models and techniques for statistical inference using methods from algebra and geometry (Sturmfels, 2009 ). The purpose of our study is to consider the generalization error and stochastic complexity in learning theory by using the log-canonical threshold in algebraic geometry. Such thresholds correspond to the main term of the generalization error in Bayesian estimation, which is called a learning coefficient (Watanabe, 2001a , 2001b ). The learning coefficient serves to measure the learning efficiencies in hierarchical learning models. In this letter, we consider learning coefficients for Vandermonde matrix-type singularities, by using a new approach: focusing on the generators of the ideal, which defines singularities. We give tight new bound values of learning coefficients for the Vandermonde matrix-type singularities and the explicit values with certain conditions. By applying our results, we can show the learning coefficients of three-layered neural networks and normal mixture models.

Bayesian model averaging using particle filtering and Gaussian mixture modeling: Theory, concepts, and simulation experiments

NASA Astrophysics Data System (ADS)

Rings, Joerg; Vrugt, Jasper A.; Schoups, Gerrit; Huisman, Johan A.; Vereecken, Harry

2012-05-01

Bayesian model averaging (BMA) is a standard method for combining predictive distributions from different models. In recent years, this method has enjoyed widespread application and use in many fields of study to improve the spread-skill relationship of forecast ensembles. The BMA predictive probability density function (pdf) of any quantity of interest is a weighted average of pdfs centered around the individual (possibly bias-corrected) forecasts, where the weights are equal to posterior probabilities of the models generating the forecasts, and reflect the individual models skill over a training (calibration) period. The original BMA approach presented by Raftery et al. (2005) assumes that the conditional pdf of each individual model is adequately described with a rather standard Gaussian or Gamma statistical distribution, possibly with a heteroscedastic variance. Here we analyze the advantages of using BMA with a flexible representation of the conditional pdf. A joint particle filtering and Gaussian mixture modeling framework is presented to derive analytically, as closely and consistently as possible, the evolving forecast density (conditional pdf) of each constituent ensemble member. The median forecasts and evolving conditional pdfs of the constituent models are subsequently combined using BMA to derive one overall predictive distribution. This paper introduces the theory and concepts of this new ensemble postprocessing method, and demonstrates its usefulness and applicability by numerical simulation of the rainfall-runoff transformation using discharge data from three different catchments in the contiguous United States. The revised BMA method receives significantly lower-prediction errors than the original default BMA method (due to filtering) with predictive uncertainty intervals that are substantially smaller but still statistically coherent (due to the use of a time-variant conditional pdf).

Bayesian depth estimation from monocular natural images.

PubMed

Su, Che-Chun; Cormack, Lawrence K; Bovik, Alan C

2017-05-01

Estimating an accurate and naturalistic dense depth map from a single monocular photographic image is a difficult problem. Nevertheless, human observers have little difficulty understanding the depth structure implied by photographs. Two-dimensional (2D) images of the real-world environment contain significant statistical information regarding the three-dimensional (3D) structure of the world that the vision system likely exploits to compute perceived depth, monocularly as well as binocularly. Toward understanding how this might be accomplished, we propose a Bayesian model of monocular depth computation that recovers detailed 3D scene structures by extracting reliable, robust, depth-sensitive statistical features from single natural images. These features are derived using well-accepted univariate natural scene statistics (NSS) models and recent bivariate/correlation NSS models that describe the relationships between 2D photographic images and their associated depth maps. This is accomplished by building a dictionary of canonical local depth patterns from which NSS features are extracted as prior information. The dictionary is used to create a multivariate Gaussian mixture (MGM) likelihood model that associates local image features with depth patterns. A simple Bayesian predictor is then used to form spatial depth estimates. The depth results produced by the model, despite its simplicity, correlate well with ground-truth depths measured by a current-generation terrestrial light detection and ranging (LIDAR) scanner. Such a strong form of statistical depth information could be used by the visual system when creating overall estimated depth maps incorporating stereopsis, accommodation, and other conditions. Indeed, even in isolation, the Bayesian predictor delivers depth estimates that are competitive with state-of-the-art "computer vision" methods that utilize highly engineered image features and sophisticated machine learning algorithms.

Dirichlet Process Gaussian-mixture model: An application to localizing coalescing binary neutron stars with gravitational-wave observations

NASA Astrophysics Data System (ADS)

Del Pozzo, W.; Berry, C. P. L.; Ghosh, A.; Haines, T. S. F.; Singer, L. P.; Vecchio, A.

2018-06-01

We reconstruct posterior distributions for the position (sky area and distance) of a simulated set of binary neutron-star gravitational-waves signals observed with Advanced LIGO and Advanced Virgo. We use a Dirichlet Process Gaussian-mixture model, a fully Bayesian non-parametric method that can be used to estimate probability density functions with a flexible set of assumptions. The ability to reliably reconstruct the source position is important for multimessenger astronomy, as recently demonstrated with GW170817. We show that for detector networks comparable to the early operation of Advanced LIGO and Advanced Virgo, typical localization volumes are ˜104-105 Mpc3 corresponding to ˜102-103 potential host galaxies. The localization volume is a strong function of the network signal-to-noise ratio, scaling roughly ∝ϱnet-6. Fractional localizations improve with the addition of further detectors to the network. Our Dirichlet Process Gaussian-mixture model can be adopted for localizing events detected during future gravitational-wave observing runs, and used to facilitate prompt multimessenger follow-up.

A Hierarchical Bayesian Model for Calibrating Estimates of Species Divergence Times

PubMed Central

Heath, Tracy A.

2012-01-01

In Bayesian divergence time estimation methods, incorporating calibrating information from the fossil record is commonly done by assigning prior densities to ancestral nodes in the tree. Calibration prior densities are typically parametric distributions offset by minimum age estimates provided by the fossil record. Specification of the parameters of calibration densities requires the user to quantify his or her prior knowledge of the age of the ancestral node relative to the age of its calibrating fossil. The values of these parameters can, potentially, result in biased estimates of node ages if they lead to overly informative prior distributions. Accordingly, determining parameter values that lead to adequate prior densities is not straightforward. In this study, I present a hierarchical Bayesian model for calibrating divergence time analyses with multiple fossil age constraints. This approach applies a Dirichlet process prior as a hyperprior on the parameters of calibration prior densities. Specifically, this model assumes that the rate parameters of exponential prior distributions on calibrated nodes are distributed according to a Dirichlet process, whereby the rate parameters are clustered into distinct parameter categories. Both simulated and biological data are analyzed to evaluate the performance of the Dirichlet process hyperprior. Compared with fixed exponential prior densities, the hierarchical Bayesian approach results in more accurate and precise estimates of internal node ages. When this hyperprior is applied using Markov chain Monte Carlo methods, the ages of calibrated nodes are sampled from mixtures of exponential distributions and uncertainty in the values of calibration density parameters is taken into account. PMID:22334343

Hierarchical Bayesian Approach To Reduce Uncertainty in the Aquatic Effect Assessment of Realistic Chemical Mixtures.

PubMed

Oldenkamp, Rik; Hendriks, Harrie W M; van de Meent, Dik; Ragas, Ad M J

2015-09-01

Species in the aquatic environment differ in their toxicological sensitivity to the various chemicals they encounter. In aquatic risk assessment, this interspecies variation is often quantified via species sensitivity distributions. Because the information available for the characterization of these distributions is typically limited, optimal use of information is essential to reduce uncertainty involved in the assessment. In the present study, we show that the credibility intervals on the estimated potentially affected fraction of species after exposure to a mixture of chemicals at environmentally relevant surface water concentrations can be extremely wide if a classical approach is followed, in which each chemical in the mixture is considered in isolation. As an alternative, we propose a hierarchical Bayesian approach, in which knowledge on the toxicity of chemicals other than those assessed is incorporated. A case study with a mixture of 13 pharmaceuticals demonstrates that this hierarchical approach results in more realistic estimations of the potentially affected fraction, as a result of reduced uncertainty in species sensitivity distributions for data-poor chemicals.

A Bayesian Hybrid Adaptive Randomisation Design for Clinical Trials with Survival Outcomes.

PubMed

Moatti, M; Chevret, S; Zohar, S; Rosenberger, W F

2016-01-01

Response-adaptive randomisation designs have been proposed to improve the efficiency of phase III randomised clinical trials and improve the outcomes of the clinical trial population. In the setting of failure time outcomes, Zhang and Rosenberger (2007) developed a response-adaptive randomisation approach that targets an optimal allocation, based on a fixed sample size. The aim of this research is to propose a response-adaptive randomisation procedure for survival trials with an interim monitoring plan, based on the following optimal criterion: for fixed variance of the estimated log hazard ratio, what allocation minimizes the expected hazard of failure? We demonstrate the utility of the design by redesigning a clinical trial on multiple myeloma. To handle continuous monitoring of data, we propose a Bayesian response-adaptive randomisation procedure, where the log hazard ratio is the effect measure of interest. Combining the prior with the normal likelihood, the mean posterior estimate of the log hazard ratio allows derivation of the optimal target allocation. We perform a simulation study to assess and compare the performance of this proposed Bayesian hybrid adaptive design to those of fixed, sequential or adaptive - either frequentist or fully Bayesian - designs. Non informative normal priors of the log hazard ratio were used, as well as mixture of enthusiastic and skeptical priors. Stopping rules based on the posterior distribution of the log hazard ratio were computed. The method is then illustrated by redesigning a phase III randomised clinical trial of chemotherapy in patients with multiple myeloma, with mixture of normal priors elicited from experts. As expected, there was a reduction in the proportion of observed deaths in the adaptive vs. non-adaptive designs; this reduction was maximized using a Bayes mixture prior, with no clear-cut improvement by using a fully Bayesian procedure. The use of stopping rules allows a slight decrease in the observed proportion of deaths under the alternate hypothesis compared with the adaptive designs with no stopping rules. Such Bayesian hybrid adaptive survival trials may be promising alternatives to traditional designs, reducing the duration of survival trials, as well as optimizing the ethical concerns for patients enrolled in the trial.

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

PubMed

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

2011-06-01

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.

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

PubMed Central

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

Accuracy of latent-variable estimation in Bayesian semi-supervised learning.

PubMed

Yamazaki, Keisuke

2015-09-01

Hierarchical probabilistic models, such as Gaussian mixture models, are widely used for unsupervised learning tasks. These models consist of observable and latent variables, which represent the observable data and the underlying data-generation process, respectively. Unsupervised learning tasks, such as cluster analysis, are regarded as estimations of latent variables based on the observable ones. The estimation of latent variables in semi-supervised learning, where some labels are observed, will be more precise than that in unsupervised, and one of the concerns is to clarify the effect of the labeled data. However, there has not been sufficient theoretical analysis of the accuracy of the estimation of latent variables. In a previous study, a distribution-based error function was formulated, and its asymptotic form was calculated for unsupervised learning with generative models. It has been shown that, for the estimation of latent variables, the Bayes method is more accurate than the maximum-likelihood method. The present paper reveals the asymptotic forms of the error function in Bayesian semi-supervised learning for both discriminative and generative models. The results show that the generative model, which uses all of the given data, performs better when the model is well specified. Copyright © 2015 Elsevier Ltd. All rights reserved.

Comparing nonparametric Bayesian tree priors for clonal reconstruction of tumors.

PubMed

Deshwar, Amit G; Vembu, Shankar; Morris, Quaid

2015-01-01

Statistical machine learning methods, especially nonparametric Bayesian methods, have become increasingly popular to infer clonal population structure of tumors. Here we describe the treeCRP, an extension of the Chinese restaurant process (CRP), a popular construction used in nonparametric mixture models, to infer the phylogeny and genotype of major subclonal lineages represented in the population of cancer cells. We also propose new split-merge updates tailored to the subclonal reconstruction problem that improve the mixing time of Markov chains. In comparisons with the tree-structured stick breaking prior used in PhyloSub, we demonstrate superior mixing and running time using the treeCRP with our new split-merge procedures. We also show that given the same number of samples, TSSB and treeCRP have similar ability to recover the subclonal structure of a tumor…

Bayesian deconvolution and quantification of metabolites in complex 1D NMR spectra using BATMAN.

PubMed

Hao, Jie; Liebeke, Manuel; Astle, William; De Iorio, Maria; Bundy, Jacob G; Ebbels, Timothy M D

2014-01-01

Data processing for 1D NMR spectra is a key bottleneck for metabolomic and other complex-mixture studies, particularly where quantitative data on individual metabolites are required. We present a protocol for automated metabolite deconvolution and quantification from complex NMR spectra by using the Bayesian automated metabolite analyzer for NMR (BATMAN) R package. BATMAN models resonances on the basis of a user-controllable set of templates, each of which specifies the chemical shifts, J-couplings and relative peak intensities for a single metabolite. Peaks are allowed to shift position slightly between spectra, and peak widths are allowed to vary by user-specified amounts. NMR signals not captured by the templates are modeled non-parametrically by using wavelets. The protocol covers setting up user template libraries, optimizing algorithmic input parameters, improving prior information on peak positions, quality control and evaluation of outputs. The outputs include relative concentration estimates for named metabolites together with associated Bayesian uncertainty estimates, as well as the fit of the remainder of the spectrum using wavelets. Graphical diagnostics allow the user to examine the quality of the fit for multiple spectra simultaneously. This approach offers a workflow to analyze large numbers of spectra and is expected to be useful in a wide range of metabolomics studies.

Spot counting on fluorescence in situ hybridization in suspension images using Gaussian mixture model

NASA Astrophysics Data System (ADS)

Liu, Sijia; Sa, Ruhan; Maguire, Orla; Minderman, Hans; Chaudhary, Vipin

2015-03-01

Cytogenetic abnormalities are important diagnostic and prognostic criteria for acute myeloid leukemia (AML). A flow cytometry-based imaging approach for FISH in suspension (FISH-IS) was established that enables the automated analysis of several log-magnitude higher number of cells compared to the microscopy-based approaches. The rotational positioning can occur leading to discordance between spot count. As a solution of counting error from overlapping spots, in this study, a Gaussian Mixture Model based classification method is proposed. The Akaike information criterion (AIC) and Bayesian information criterion (BIC) of GMM are used as global image features of this classification method. Via Random Forest classifier, the result shows that the proposed method is able to detect closely overlapping spots which cannot be separated by existing image segmentation based spot detection methods. The experiment results show that by the proposed method we can obtain a significant improvement in spot counting accuracy.

Speech Enhancement, Gain, and Noise Spectrum Adaptation Using Approximate Bayesian Estimation

PubMed Central

Hao, Jiucang; Attias, Hagai; Nagarajan, Srikantan; Lee, Te-Won; Sejnowski, Terrence J.

2010-01-01

This paper presents a new approximate Bayesian estimator for enhancing a noisy speech signal. The speech model is assumed to be a Gaussian mixture model (GMM) in the log-spectral domain. This is in contrast to most current models in frequency domain. Exact signal estimation is a computationally intractable problem. We derive three approximations to enhance the efficiency of signal estimation. The Gaussian approximation transforms the log-spectral domain GMM into the frequency domain using minimal Kullback–Leiber (KL)-divergency criterion. The frequency domain Laplace method computes the maximum a posteriori (MAP) estimator for the spectral amplitude. Correspondingly, the log-spectral domain Laplace method computes the MAP estimator for the log-spectral amplitude. Further, the gain and noise spectrum adaptation are implemented using the expectation–maximization (EM) algorithm within the GMM under Gaussian approximation. The proposed algorithms are evaluated by applying them to enhance the speeches corrupted by the speech-shaped noise (SSN). The experimental results demonstrate that the proposed algorithms offer improved signal-to-noise ratio, lower word recognition error rate, and less spectral distortion. PMID:20428253

Probability density function characterization for aggregated large-scale wind power based on Weibull mixtures

DOE PAGES

Gomez-Lazaro, Emilio; Bueso, Maria C.; Kessler, Mathieu; ...

2016-02-02

Here, the Weibull probability distribution has been widely applied to characterize wind speeds for wind energy resources. Wind power generation modeling is different, however, due in particular to power curve limitations, wind turbine control methods, and transmission system operation requirements. These differences are even greater for aggregated wind power generation in power systems with high wind penetration. Consequently, models based on one-Weibull component can provide poor characterizations for aggregated wind power generation. With this aim, the present paper focuses on discussing Weibull mixtures to characterize the probability density function (PDF) for aggregated wind power generation. PDFs of wind power datamore » are firstly classified attending to hourly and seasonal patterns. The selection of the number of components in the mixture is analyzed through two well-known different criteria: the Akaike information criterion (AIC) and the Bayesian information criterion (BIC). Finally, the optimal number of Weibull components for maximum likelihood is explored for the defined patterns, including the estimated weight, scale, and shape parameters. Results show that multi-Weibull models are more suitable to characterize aggregated wind power data due to the impact of distributed generation, variety of wind speed values and wind power curtailment.« less

Model-based Clustering of Categorical Time Series with Multinomial Logit Classification

NASA Astrophysics Data System (ADS)

Frühwirth-Schnatter, Sylvia; Pamminger, Christoph; Winter-Ebmer, Rudolf; Weber, Andrea

2010-09-01

A common problem in many areas of applied statistics is to identify groups of similar time series in a panel of time series. However, distance-based clustering methods cannot easily be extended to time series data, where an appropriate distance-measure is rather difficult to define, particularly for discrete-valued time series. Markov chain clustering, proposed by Pamminger and Frühwirth-Schnatter [6], is an approach for clustering discrete-valued time series obtained by observing a categorical variable with several states. This model-based clustering method is based on finite mixtures of first-order time-homogeneous Markov chain models. In order to further explain group membership we present an extension to the approach of Pamminger and Frühwirth-Schnatter [6] by formulating a probabilistic model for the latent group indicators within the Bayesian classification rule by using a multinomial logit model. The parameters are estimated for a fixed number of clusters within a Bayesian framework using an Markov chain Monte Carlo (MCMC) sampling scheme representing a (full) Gibbs-type sampler which involves only draws from standard distributions. Finally, an application to a panel of Austrian wage mobility data is presented which leads to an interesting segmentation of the Austrian labour market.

What are hierarchical models and how do we analyze them?

USGS Publications Warehouse

Royle, Andy

2016-01-01

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

The Topp-Leone generalized Rayleigh cure rate model and its application

NASA Astrophysics Data System (ADS)

Nanthaprut, Pimwarat; Bodhisuwan, Winai; Patummasut, Mena

2017-11-01

Cure rate model is one of the survival analysis when model consider a proportion of the censored data. In clinical trials, the data represent time to recurrence of event or death of patients are used to improve the efficiency of treatments. Each dataset can be separated into two groups: censored and uncensored data. In this work, the new mixture cure rate model is introduced based on the Topp-Leone generalized Rayleigh distribution. The Bayesian approach is employed to estimate its parameters. In addition, a breast cancer dataset is analyzed for model illustration purpose. According to the deviance information criterion, the Topp-Leone generalized Rayleigh cure rate model shows better result than the Weibull and exponential cure rate models.

Estimating abundance in the presence of species uncertainty

USGS Publications Warehouse

Chambert, Thierry A.; Hossack, Blake R.; Fishback, LeeAnn; Davenport, Jon M.

2016-01-01

1.N-mixture models have become a popular method for estimating abundance of free-ranging animals that are not marked or identified individually. These models have been used on count data for single species that can be identified with certainty. However, co-occurring species often look similar during one or more life stages, making it difficult to assign species for all recorded captures. This uncertainty creates problems for estimating species-specific abundance and it can often limit life stages to which we can make inference. 2.We present a new extension of N-mixture models that accounts for species uncertainty. In addition to estimating site-specific abundances and detection probabilities, this model allows estimating probability of correct assignment of species identity. We implement this hierarchical model in a Bayesian framework and provide all code for running the model in BUGS-language programs. 3.We present an application of the model on count data from two sympatric freshwater fishes, the brook stickleback (Culaea inconstans) and the ninespine stickleback (Pungitius pungitius), ad illustrate implementation of covariate effects (habitat characteristics). In addition, we used a simulation study to validate the model and illustrate potential sample size issues. We also compared, for both real and simulated data, estimates provided by our model to those obtained by a simple N-mixture model when captures of unknown species identification were discarded. In the latter case, abundance estimates appeared highly biased and very imprecise, while our new model provided unbiased estimates with higher precision. 4.This extension of the N-mixture model should be useful for a wide variety of studies and taxa, as species uncertainty is a common issue. It should notably help improve investigation of abundance and vital rate characteristics of organisms’ early life stages, which are sometimes more difficult to identify than adults.

Multimodal, high-dimensional, model-based, Bayesian inverse problems with applications in biomechanics

NASA Astrophysics Data System (ADS)

Franck, I. M.; Koutsourelakis, P. S.

2017-01-01

This paper is concerned with the numerical solution of model-based, Bayesian inverse problems. We are particularly interested in cases where the cost of each likelihood evaluation (forward-model call) is expensive and the number of unknown (latent) variables is high. This is the setting in many problems in computational physics where forward models with nonlinear PDEs are used and the parameters to be calibrated involve spatio-temporarily varying coefficients, which upon discretization give rise to a high-dimensional vector of unknowns. One of the consequences of the well-documented ill-posedness of inverse problems is the possibility of multiple solutions. While such information is contained in the posterior density in Bayesian formulations, the discovery of a single mode, let alone multiple, poses a formidable computational task. The goal of the present paper is two-fold. On one hand, we propose approximate, adaptive inference strategies using mixture densities to capture multi-modal posteriors. On the other, we extend our work in [1] with regard to effective dimensionality reduction techniques that reveal low-dimensional subspaces where the posterior variance is mostly concentrated. We validate the proposed model by employing Importance Sampling which confirms that the bias introduced is small and can be efficiently corrected if the analyst wishes to do so. We demonstrate the performance of the proposed strategy in nonlinear elastography where the identification of the mechanical properties of biological materials can inform non-invasive, medical diagnosis. The discovery of multiple modes (solutions) in such problems is critical in achieving the diagnostic objectives.

Examining Gene-Environment Interactions in Comorbid Depressive and Disruptive Behavior Disorders using a Bayesian Approach

PubMed Central

Adrian, Molly; Kiff, Cara; Glazner, Chris; Kohen, Ruth; Tracy, Julia Helen; Zhou, Chuan; McCauley, Elizabeth; Stoep, Ann Vander

2015-01-01

Objective The objective of this study was to apply a Bayesian statistical analytic approach that minimizes multiple testing problems to explore the combined effects of chronic low familial support and variants in 12 candidate genes on risk for a common and debilitating childhood mental health condition. Method Bayesian mixture modeling was used to examine gene by environment interactions among genetic variants and environmental factors (family support) associated in previous studies with the occurrence of comorbid depression and disruptive behavior disorders youth, using a sample of 255 children. Results One main effects, variants in the oxytocin receptor (OXTR, rs53576) was associated with increased risk for comorbid disorders. Two significant gene x environment and one signification gene x gene interaction emerged. Variants in the nicotinic acetylcholine receptor α5 subunit (CHRNA5, rs16969968) and in the glucocorticoid receptor chaperone protein FK506 binding protein 5 (FKBP5, rs4713902) interacted with chronic low family support in association with child mental health status. One gene x gene interaction, 5-HTTLPR variant of the serotonin transporter (SERT/SLC6A4) in combination with μ opioid receptor (OPRM1, rs1799971) was associated with comorbid depression and conduct problems. Conclusions Results indicate that Bayesian modeling is a feasible strategy for conducting behavioral genetics research. This approach, combined with an optimized genetic selection strategy (Vrieze, Iacono, & McGue, 2012), revealed genetic variants involved in stress regulation ( FKBP5, SERTxOPMR), social bonding (OXTR), and nicotine responsivity (CHRNA5) in predicting comorbid status. PMID:26228411

Bayesian multivariate Poisson abundance models for T-cell receptor data.

PubMed

Greene, Joshua; Birtwistle, Marc R; Ignatowicz, Leszek; Rempala, Grzegorz A

2013-06-07

A major feature of an adaptive immune system is its ability to generate B- and T-cell clones capable of recognizing and neutralizing specific antigens. These clones recognize antigens with the help of the surface molecules, called antigen receptors, acquired individually during the clonal development process. In order to ensure a response to a broad range of antigens, the number of different receptor molecules is extremely large, resulting in a huge clonal diversity of both B- and T-cell receptor populations and making their experimental comparisons statistically challenging. To facilitate such comparisons, we propose a flexible parametric model of multivariate count data and illustrate its use in a simultaneous analysis of multiple antigen receptor populations derived from mammalian T-cells. The model relies on a representation of the observed receptor counts as a multivariate Poisson abundance mixture (m PAM). A Bayesian parameter fitting procedure is proposed, based on the complete posterior likelihood, rather than the conditional one used typically in similar settings. The new procedure is shown to be considerably more efficient than its conditional counterpart (as measured by the Fisher information) in the regions of m PAM parameter space relevant to model T-cell data. Copyright © 2013 Elsevier Ltd. All rights reserved.

A Bayesian Joint Model of Menstrual Cycle Length and Fecundity

PubMed Central

Lum, Kirsten J.; Sundaram, Rajeshwari; Louis, Germaine M. Buck; Louis, Thomas A.

2015-01-01

Summary Menstrual cycle length (MCL) has been shown to play an important role in couple fecundity, which is the biologic capacity for reproduction irrespective of pregnancy intentions. However, a comprehensive assessment of its role requires a fecundity model that accounts for male and female attributes and the couple’s intercourse pattern relative to the ovulation day. To this end, we employ a Bayesian joint model for MCL and pregnancy. MCLs follow a scale multiplied (accelerated) mixture model with Gaussian and Gumbel components; the pregnancy model includes MCL as a covariate and computes the cycle-specific probability of pregnancy in a menstrual cycle conditional on the pattern of intercourse and no previous fertilization. Day-specific fertilization probability is modeled using natural, cubic splines. We analyze data from the Longitudinal Investigation of Fertility and the Environment Study (the LIFE Study), a couple based prospective pregnancy study, and find a statistically significant quadratic relation between fecundity and menstrual cycle length, after adjustment for intercourse pattern and other attributes, including male semen quality, both partner’s age, and active smoking status (determined by baseline cotinine level 100ng/mL). We compare results to those produced by a more basic model and show the advantages of a more comprehensive approach. PMID:26295923

Assessing variation in life-history tactics within a population using mixture regression models: a practical guide for evolutionary ecologists.

PubMed

Hamel, Sandra; Yoccoz, Nigel G; Gaillard, Jean-Michel

2017-05-01

Mixed models are now well-established methods in ecology and evolution because they allow accounting for and quantifying within- and between-individual variation. However, the required normal distribution of the random effects can often be violated by the presence of clusters among subjects, which leads to multi-modal distributions. In such cases, using what is known as mixture regression models might offer a more appropriate approach. These models are widely used in psychology, sociology, and medicine to describe the diversity of trajectories occurring within a population over time (e.g. psychological development, growth). In ecology and evolution, however, these models are seldom used even though understanding changes in individual trajectories is an active area of research in life-history studies. Our aim is to demonstrate the value of using mixture models to describe variation in individual life-history tactics within a population, and hence to promote the use of these models by ecologists and evolutionary ecologists. We first ran a set of simulations to determine whether and when a mixture model allows teasing apart latent clustering, and to contrast the precision and accuracy of estimates obtained from mixture models versus mixed models under a wide range of ecological contexts. We then used empirical data from long-term studies of large mammals to illustrate the potential of using mixture models for assessing within-population variation in life-history tactics. Mixture models performed well in most cases, except for variables following a Bernoulli distribution and when sample size was small. The four selection criteria we evaluated [Akaike information criterion (AIC), Bayesian information criterion (BIC), and two bootstrap methods] performed similarly well, selecting the right number of clusters in most ecological situations. We then showed that the normality of random effects implicitly assumed by evolutionary ecologists when using mixed models was often violated in life-history data. Mixed models were quite robust to this violation in the sense that fixed effects were unbiased at the population level. However, fixed effects at the cluster level and random effects were better estimated using mixture models. Our empirical analyses demonstrated that using mixture models facilitates the identification of the diversity of growth and reproductive tactics occurring within a population. Therefore, using this modelling framework allows testing for the presence of clusters and, when clusters occur, provides reliable estimates of fixed and random effects for each cluster of the population. In the presence or expectation of clusters, using mixture models offers a suitable extension of mixed models, particularly when evolutionary ecologists aim at identifying how ecological and evolutionary processes change within a population. Mixture regression models therefore provide a valuable addition to the statistical toolbox of evolutionary ecologists. As these models are complex and have their own limitations, we provide recommendations to guide future users. © 2016 Cambridge Philosophical Society.

Speech Enhancement Using Gaussian Scale Mixture Models

PubMed Central

Hao, Jiucang; Lee, Te-Won; Sejnowski, Terrence J.

2011-01-01

This paper presents a novel probabilistic approach to speech enhancement. Instead of a deterministic logarithmic relationship, we assume a probabilistic relationship between the frequency coefficients and the log-spectra. The speech model in the log-spectral domain is a Gaussian mixture model (GMM). The frequency coefficients obey a zero-mean Gaussian whose covariance equals to the exponential of the log-spectra. This results in a Gaussian scale mixture model (GSMM) for the speech signal in the frequency domain, since the log-spectra can be regarded as scaling factors. The probabilistic relation between frequency coefficients and log-spectra allows these to be treated as two random variables, both to be estimated from the noisy signals. Expectation-maximization (EM) was used to train the GSMM and Bayesian inference was used to compute the posterior signal distribution. Because exact inference of this full probabilistic model is computationally intractable, we developed two approaches to enhance the efficiency: the Laplace method and a variational approximation. The proposed methods were applied to enhance speech corrupted by Gaussian noise and speech-shaped noise (SSN). For both approximations, signals reconstructed from the estimated frequency coefficients provided higher signal-to-noise ratio (SNR) and those reconstructed from the estimated log-spectra produced lower word recognition error rate because the log-spectra fit the inputs to the recognizer better. Our algorithms effectively reduced the SSN, which algorithms based on spectral analysis were not able to suppress. PMID:21359139

Unsupervised Bayesian linear unmixing of gene expression microarrays.

PubMed

Bazot, Cécile; Dobigeon, Nicolas; Tourneret, Jean-Yves; Zaas, Aimee K; Ginsburg, Geoffrey S; Hero, Alfred O

2013-03-19

This paper introduces a new constrained model and the corresponding algorithm, called unsupervised Bayesian linear unmixing (uBLU), to identify biological signatures from high dimensional assays like gene expression microarrays. The basis for uBLU is a Bayesian model for the data samples which are represented as an additive mixture of random positive gene signatures, called factors, with random positive mixing coefficients, called factor scores, that specify the relative contribution of each signature to a specific sample. The particularity of the proposed method is that uBLU constrains the factor loadings to be non-negative and the factor scores to be probability distributions over the factors. Furthermore, it also provides estimates of the number of factors. A Gibbs sampling strategy is adopted here to generate random samples according to the posterior distribution of the factors, factor scores, and number of factors. These samples are then used to estimate all the unknown parameters. Firstly, the proposed uBLU method is applied to several simulated datasets with known ground truth and compared with previous factor decomposition methods, such as principal component analysis (PCA), non negative matrix factorization (NMF), Bayesian factor regression modeling (BFRM), and the gradient-based algorithm for general matrix factorization (GB-GMF). Secondly, we illustrate the application of uBLU on a real time-evolving gene expression dataset from a recent viral challenge study in which individuals have been inoculated with influenza A/H3N2/Wisconsin. We show that the uBLU method significantly outperforms the other methods on the simulated and real data sets considered here. The results obtained on synthetic and real data illustrate the accuracy of the proposed uBLU method when compared to other factor decomposition methods from the literature (PCA, NMF, BFRM, and GB-GMF). The uBLU method identifies an inflammatory component closely associated with clinical symptom scores collected during the study. Using a constrained model allows recovery of all the inflammatory genes in a single factor.

Marginally specified priors for non-parametric Bayesian estimation

PubMed Central

Kessler, David C.; Hoff, Peter D.; Dunson, David B.

2014-01-01

Summary Prior specification for non-parametric Bayesian inference involves the difficult task of quantifying prior knowledge about a parameter of high, often infinite, dimension. A statistician is unlikely to have informed opinions about all aspects of such a parameter but will have real information about functionals of the parameter, such as the population mean or variance. The paper proposes a new framework for non-parametric Bayes inference in which the prior distribution for a possibly infinite dimensional parameter is decomposed into two parts: an informative prior on a finite set of functionals, and a non-parametric conditional prior for the parameter given the functionals. Such priors can be easily constructed from standard non-parametric prior distributions in common use and inherit the large support of the standard priors on which they are based. Additionally, posterior approximations under these informative priors can generally be made via minor adjustments to existing Markov chain approximation algorithms for standard non-parametric prior distributions. We illustrate the use of such priors in the context of multivariate density estimation using Dirichlet process mixture models, and in the modelling of high dimensional sparse contingency tables. PMID:25663813

Analysis of Spin Financial Market by GARCH Model

NASA Astrophysics Data System (ADS)

Takaishi, Tetsuya

2013-08-01

A spin model is used for simulations of financial markets. To determine return volatility in the spin financial market we use the GARCH model often used for volatility estimation in empirical finance. We apply the Bayesian inference performed by the Markov Chain Monte Carlo method to the parameter estimation of the GARCH model. It is found that volatility determined by the GARCH model exhibits "volatility clustering" also observed in the real financial markets. Using volatility determined by the GARCH model we examine the mixture-of-distribution hypothesis (MDH) suggested for the asset return dynamics. We find that the returns standardized by volatility are approximately standard normal random variables. Moreover we find that the absolute standardized returns show no significant autocorrelation. These findings are consistent with the view of the MDH for the return dynamics.

Estimating the periodic components of a biomedical signal through inverse problem modelling and Bayesian inference with sparsity enforcing prior

NASA Astrophysics Data System (ADS)

Dumitru, Mircea; Djafari, Ali-Mohammad

2015-01-01

The recent developments in chronobiology need a periodic components variation analysis for the signals expressing the biological rhythms. A precise estimation of the periodic components vector is required. The classical approaches, based on FFT methods, are inefficient considering the particularities of the data (short length). In this paper we propose a new method, using the sparsity prior information (reduced number of non-zero values components). The considered law is the Student-t distribution, viewed as a marginal distribution of a Infinite Gaussian Scale Mixture (IGSM) defined via a hidden variable representing the inverse variances and modelled as a Gamma Distribution. The hyperparameters are modelled using the conjugate priors, i.e. using Inverse Gamma Distributions. The expression of the joint posterior law of the unknown periodic components vector, hidden variables and hyperparameters is obtained and then the unknowns are estimated via Joint Maximum A Posteriori (JMAP) and Posterior Mean (PM). For the PM estimator, the expression of the posterior law is approximated by a separable one, via the Bayesian Variational Approximation (BVA), using the Kullback-Leibler (KL) divergence. Finally we show the results on synthetic data in cancer treatment applications.

Genomic selection and complex trait prediction using a fast EM algorithm applied to genome-wide markers

PubMed Central

2010-01-01

Background The information provided by dense genome-wide markers using high throughput technology is of considerable potential in human disease studies and livestock breeding programs. Genome-wide association studies relate individual single nucleotide polymorphisms (SNP) from dense SNP panels to individual measurements of complex traits, with the underlying assumption being that any association is caused by linkage disequilibrium (LD) between SNP and quantitative trait loci (QTL) affecting the trait. Often SNP are in genomic regions of no trait variation. Whole genome Bayesian models are an effective way of incorporating this and other important prior information into modelling. However a full Bayesian analysis is often not feasible due to the large computational time involved. Results This article proposes an expectation-maximization (EM) algorithm called emBayesB which allows only a proportion of SNP to be in LD with QTL and incorporates prior information about the distribution of SNP effects. The posterior probability of being in LD with at least one QTL is calculated for each SNP along with estimates of the hyperparameters for the mixture prior. A simulated example of genomic selection from an international workshop is used to demonstrate the features of the EM algorithm. The accuracy of prediction is comparable to a full Bayesian analysis but the EM algorithm is considerably faster. The EM algorithm was accurate in locating QTL which explained more than 1% of the total genetic variation. A computational algorithm for very large SNP panels is described. Conclusions emBayesB is a fast and accurate EM algorithm for implementing genomic selection and predicting complex traits by mapping QTL in genome-wide dense SNP marker data. Its accuracy is similar to Bayesian methods but it takes only a fraction of the time. PMID:20969788

A combined reconstruction-classification method for diffuse optical tomography.

PubMed

Hiltunen, P; Prince, S J D; Arridge, S

2009-11-07

We present a combined classification and reconstruction algorithm for diffuse optical tomography (DOT). DOT is a nonlinear ill-posed inverse problem. Therefore, some regularization is needed. We present a mixture of Gaussians prior, which regularizes the DOT reconstruction step. During each iteration, the parameters of a mixture model are estimated. These associate each reconstructed pixel with one of several classes based on the current estimate of the optical parameters. This classification is exploited to form a new prior distribution to regularize the reconstruction step and update the optical parameters. The algorithm can be described as an iteration between an optimization scheme with zeroth-order variable mean and variance Tikhonov regularization and an expectation-maximization scheme for estimation of the model parameters. We describe the algorithm in a general Bayesian framework. Results from simulated test cases and phantom measurements show that the algorithm enhances the contrast of the reconstructed images with good spatial accuracy. The probabilistic classifications of each image contain only a few misclassified pixels.

Risk Estimation for Lung Cancer in Libya: Analysis Based on Standardized Morbidity Ratio, Poisson-Gamma Model, BYM Model and Mixture Model

PubMed

Alhdiri, Maryam Ahmed; Samat, Nor Azah; Mohamed, Zulkifley

2017-03-01

Cancer is the most rapidly spreading disease in the world, especially in developing countries, including Libya. Cancer represents a significant burden on patients, families, and their societies. This disease can be controlled if detected early. Therefore, disease mapping has recently become an important method in the fields of public health research and disease epidemiology. The correct choice of statistical model is a very important step to producing a good map of a disease. Libya was selected to perform this work and to examine its geographical variation in the incidence of lung cancer. The objective of this paper is to estimate the relative risk for lung cancer. Four statistical models to estimate the relative risk for lung cancer and population censuses of the study area for the time period 2006 to 2011 were used in this work. They are initially known as Standardized Morbidity Ratio, which is the most popular statistic, which used in the field of disease mapping, Poisson-gamma model, which is one of the earliest applications of Bayesian methodology, Besag, York and Mollie (BYM) model and Mixture model. As an initial step, this study begins by providing a review of all proposed models, which we then apply to lung cancer data in Libya. Maps, tables and graph, goodness-of-fit (GOF) were used to compare and present the preliminary results. This GOF is common in statistical modelling to compare fitted models. The main general results presented in this study show that the Poisson-gamma model, BYM model, and Mixture model can overcome the problem of the first model (SMR) when there is no observed lung cancer case in certain districts. Results show that the Mixture model is most robust and provides better relative risk estimates across a range of models. Creative Commons Attribution License

Risk Estimation for Lung Cancer in Libya: Analysis Based on Standardized Morbidity Ratio, Poisson-Gamma Model, BYM Model and Mixture Model

PubMed Central

Alhdiri, Maryam Ahmed; Samat, Nor Azah; Mohamed, Zulkifley

2017-01-01

Cancer is the most rapidly spreading disease in the world, especially in developing countries, including Libya. Cancer represents a significant burden on patients, families, and their societies. This disease can be controlled if detected early. Therefore, disease mapping has recently become an important method in the fields of public health research and disease epidemiology. The correct choice of statistical model is a very important step to producing a good map of a disease. Libya was selected to perform this work and to examine its geographical variation in the incidence of lung cancer. The objective of this paper is to estimate the relative risk for lung cancer. Four statistical models to estimate the relative risk for lung cancer and population censuses of the study area for the time period 2006 to 2011 were used in this work. They are initially known as Standardized Morbidity Ratio, which is the most popular statistic, which used in the field of disease mapping, Poisson-gamma model, which is one of the earliest applications of Bayesian methodology, Besag, York and Mollie (BYM) model and Mixture model. As an initial step, this study begins by providing a review of all proposed models, which we then apply to lung cancer data in Libya. Maps, tables and graph, goodness-of-fit (GOF) were used to compare and present the preliminary results. This GOF is common in statistical modelling to compare fitted models. The main general results presented in this study show that the Poisson-gamma model, BYM model, and Mixture model can overcome the problem of the first model (SMR) when there is no observed lung cancer case in certain districts. Results show that the Mixture model is most robust and provides better relative risk estimates across a range of models. PMID:28440974

Multiple model cardinalized probability hypothesis density filter

NASA Astrophysics Data System (ADS)

Georgescu, Ramona; Willett, Peter

2011-09-01

The Probability Hypothesis Density (PHD) filter propagates the first-moment approximation to the multi-target Bayesian posterior distribution while the Cardinalized PHD (CPHD) filter propagates both the posterior likelihood of (an unlabeled) target state and the posterior probability mass function of the number of targets. Extensions of the PHD filter to the multiple model (MM) framework have been published and were implemented either with a Sequential Monte Carlo or a Gaussian Mixture approach. In this work, we introduce the multiple model version of the more elaborate CPHD filter. We present the derivation of the prediction and update steps of the MMCPHD particularized for the case of two target motion models and proceed to show that in the case of a single model, the new MMCPHD equations reduce to the original CPHD equations.

Multiple co-clustering based on nonparametric mixture models with heterogeneous marginal distributions

PubMed Central

Yoshimoto, Junichiro; Shimizu, Yu; Okada, Go; Takamura, Masahiro; Okamoto, Yasumasa; Yamawaki, Shigeto; Doya, Kenji

2017-01-01

We propose a novel method for multiple clustering, which is useful for analysis of high-dimensional data containing heterogeneous types of features. Our method is based on nonparametric Bayesian mixture models in which features are automatically partitioned (into views) for each clustering solution. This feature partition works as feature selection for a particular clustering solution, which screens out irrelevant features. To make our method applicable to high-dimensional data, a co-clustering structure is newly introduced for each view. Further, the outstanding novelty of our method is that we simultaneously model different distribution families, such as Gaussian, Poisson, and multinomial distributions in each cluster block, which widens areas of application to real data. We apply the proposed method to synthetic and real data, and show that our method outperforms other multiple clustering methods both in recovering true cluster structures and in computation time. Finally, we apply our method to a depression dataset with no true cluster structure available, from which useful inferences are drawn about possible clustering structures of the data. PMID:29049392

Moving beyond qualitative evaluations of Bayesian models of cognition.

PubMed

Hemmer, Pernille; Tauber, Sean; Steyvers, Mark

2015-06-01

Bayesian models of cognition provide a powerful way to understand the behavior and goals of individuals from a computational point of view. Much of the focus in the Bayesian cognitive modeling approach has been on qualitative model evaluations, where predictions from the models are compared to data that is often averaged over individuals. In many cognitive tasks, however, there are pervasive individual differences. We introduce an approach to directly infer individual differences related to subjective mental representations within the framework of Bayesian models of cognition. In this approach, Bayesian data analysis methods are used to estimate cognitive parameters and motivate the inference process within a Bayesian cognitive model. We illustrate this integrative Bayesian approach on a model of memory. We apply the model to behavioral data from a memory experiment involving the recall of heights of people. A cross-validation analysis shows that the Bayesian memory model with inferred subjective priors predicts withheld data better than a Bayesian model where the priors are based on environmental statistics. In addition, the model with inferred priors at the individual subject level led to the best overall generalization performance, suggesting that individual differences are important to consider in Bayesian models of cognition.

Histogram equalization with Bayesian estimation for noise robust speech recognition.

PubMed

Suh, Youngjoo; Kim, Hoirin

2018-02-01

The histogram equalization approach is an efficient feature normalization technique for noise robust automatic speech recognition. However, it suffers from performance degradation when some fundamental conditions are not satisfied in the test environment. To remedy these limitations of the original histogram equalization methods, class-based histogram equalization approach has been proposed. Although this approach showed substantial performance improvement under noise environments, it still suffers from performance degradation due to the overfitting problem when test data are insufficient. To address this issue, the proposed histogram equalization technique employs the Bayesian estimation method in the test cumulative distribution function estimation. It was reported in a previous study conducted on the Aurora-4 task that the proposed approach provided substantial performance gains in speech recognition systems based on the acoustic modeling of the Gaussian mixture model-hidden Markov model. In this work, the proposed approach was examined in speech recognition systems with deep neural network-hidden Markov model (DNN-HMM), the current mainstream speech recognition approach where it also showed meaningful performance improvement over the conventional maximum likelihood estimation-based method. The fusion of the proposed features with the mel-frequency cepstral coefficients provided additional performance gains in DNN-HMM systems, which otherwise suffer from performance degradation in the clean test condition.

Bayesian Modeling of Temporal Coherence in Videos for Entity Discovery and Summarization.

PubMed

Mitra, Adway; Biswas, Soma; Bhattacharyya, Chiranjib

2017-03-01

A video is understood by users in terms of entities present in it. Entity Discovery is the task of building appearance model for each entity (e.g., a person), and finding all its occurrences in the video. We represent a video as a sequence of tracklets, each spanning 10-20 frames, and associated with one entity. We pose Entity Discovery as tracklet clustering, and approach it by leveraging Temporal Coherence (TC): the property that temporally neighboring tracklets are likely to be associated with the same entity. Our major contributions are the first Bayesian nonparametric models for TC at tracklet-level. We extend Chinese Restaurant Process (CRP) to TC-CRP, and further to Temporally Coherent Chinese Restaurant Franchise (TC-CRF) to jointly model entities and temporal segments using mixture components and sparse distributions. For discovering persons in TV serial videos without meta-data like scripts, these methods show considerable improvement over state-of-the-art approaches to tracklet clustering in terms of clustering accuracy, cluster purity and entity coverage. The proposed methods can perform online tracklet clustering on streaming videos unlike existing approaches, and can automatically reject false tracklets. Finally we discuss entity-driven video summarization- where temporal segments of the video are selected based on the discovered entities, to create a semantically meaningful summary.

Semantic Indexing of Multimedia Content Using Visual, Audio, and Text Cues

NASA Astrophysics Data System (ADS)

Adams, W. H.; Iyengar, Giridharan; Lin, Ching-Yung; Naphade, Milind Ramesh; Neti, Chalapathy; Nock, Harriet J.; Smith, John R.

2003-12-01

We present a learning-based approach to the semantic indexing of multimedia content using cues derived from audio, visual, and text features. We approach the problem by developing a set of statistical models for a predefined lexicon. Novel concepts are then mapped in terms of the concepts in the lexicon. To achieve robust detection of concepts, we exploit features from multiple modalities, namely, audio, video, and text. Concept representations are modeled using Gaussian mixture models (GMM), hidden Markov models (HMM), and support vector machines (SVM). Models such as Bayesian networks and SVMs are used in a late-fusion approach to model concepts that are not explicitly modeled in terms of features. Our experiments indicate promise in the proposed classification and fusion methodologies: our proposed fusion scheme achieves more than 10% relative improvement over the best unimodal concept detector.

Development and comparison of Bayesian modularization method in uncertainty assessment of hydrological models

NASA Astrophysics Data System (ADS)

Li, L.; Xu, C.-Y.; Engeland, K.

2012-04-01

With respect to model calibration, parameter estimation and analysis of uncertainty sources, different approaches have been used in hydrological models. Bayesian method is one of the most widely used methods for uncertainty assessment of hydrological models, which incorporates different sources of information into a single analysis through Bayesian theorem. However, none of these applications can well treat the uncertainty in extreme flows of hydrological models' simulations. This study proposes a Bayesian modularization method approach in uncertainty assessment of conceptual hydrological models by considering the extreme flows. It includes a comprehensive comparison and evaluation of uncertainty assessments by a new Bayesian modularization method approach and traditional Bayesian models using the Metropolis Hasting (MH) algorithm with the daily hydrological model WASMOD. Three likelihood functions are used in combination with traditional Bayesian: the AR (1) plus Normal and time period independent model (Model 1), the AR (1) plus Normal and time period dependent model (Model 2) and the AR (1) plus multi-normal model (Model 3). The results reveal that (1) the simulations derived from Bayesian modularization method are more accurate with the highest Nash-Sutcliffe efficiency value, and (2) the Bayesian modularization method performs best in uncertainty estimates of entire flows and in terms of the application and computational efficiency. The study thus introduces a new approach for reducing the extreme flow's effect on the discharge uncertainty assessment of hydrological models via Bayesian. Keywords: extreme flow, uncertainty assessment, Bayesian modularization, hydrological model, WASMOD

Large-scale monitoring of shorebird populations using count data and N-mixture models: Black Oystercatcher (Haematopus bachmani) surveys by land and sea

USGS Publications Warehouse

Lyons, James E.; Andrew, Royle J.; Thomas, Susan M.; Elliott-Smith, Elise; Evenson, Joseph R.; Kelly, Elizabeth G.; Milner, Ruth L.; Nysewander, David R.; Andres, Brad A.

2012-01-01

Large-scale monitoring of bird populations is often based on count data collected across spatial scales that may include multiple physiographic regions and habitat types. Monitoring at large spatial scales may require multiple survey platforms (e.g., from boats and land when monitoring coastal species) and multiple survey methods. It becomes especially important to explicitly account for detection probability when analyzing count data that have been collected using multiple survey platforms or methods. We evaluated a new analytical framework, N-mixture models, to estimate actual abundance while accounting for multiple detection biases. During May 2006, we made repeated counts of Black Oystercatchers (Haematopus bachmani) from boats in the Puget Sound area of Washington (n = 55 sites) and from land along the coast of Oregon (n = 56 sites). We used a Bayesian analysis of N-mixture models to (1) assess detection probability as a function of environmental and survey covariates and (2) estimate total Black Oystercatcher abundance during the breeding season in the two regions. Probability of detecting individuals during boat-based surveys was 0.75 (95% credible interval: 0.42–0.91) and was not influenced by tidal stage. Detection probability from surveys conducted on foot was 0.68 (0.39–0.90); the latter was not influenced by fog, wind, or number of observers but was ~35% lower during rain. The estimated population size was 321 birds (262–511) in Washington and 311 (276–382) in Oregon. N-mixture models provide a flexible framework for modeling count data and covariates in large-scale bird monitoring programs designed to understand population change.

Use of Principal Components Analysis and Kriging to Predict Groundwater-Sourced Rural Drinking Water Quality in Saskatchewan

PubMed Central

McLeod, Lianne; Bharadwaj, Lalita; Epp, Tasha; Waldner, Cheryl L.

2017-01-01

Groundwater drinking water supply surveillance data were accessed to summarize water quality delivered as public and private water supplies in southern Saskatchewan as part of an exposure assessment for epidemiologic analyses of associations between water quality and type 2 diabetes or cardiovascular disease. Arsenic in drinking water has been linked to a variety of chronic diseases and previous studies have identified multiple wells with arsenic above the drinking water standard of 0.01 mg/L; therefore, arsenic concentrations were of specific interest. Principal components analysis was applied to obtain principal component (PC) scores to summarize mixtures of correlated parameters identified as health standards and those identified as aesthetic objectives in the Saskatchewan Drinking Water Quality Standards and Objective. Ordinary, universal, and empirical Bayesian kriging were used to interpolate arsenic concentrations and PC scores in southern Saskatchewan, and the results were compared. Empirical Bayesian kriging performed best across all analyses, based on having the greatest number of variables for which the root mean square error was lowest. While all of the kriging methods appeared to underestimate high values of arsenic and PC scores, empirical Bayesian kriging was chosen to summarize large scale geographic trends in groundwater-sourced drinking water quality and assess exposure to mixtures of trace metals and ions. PMID:28914824

Use of Principal Components Analysis and Kriging to Predict Groundwater-Sourced Rural Drinking Water Quality in Saskatchewan.

PubMed

McLeod, Lianne; Bharadwaj, Lalita; Epp, Tasha; Waldner, Cheryl L

2017-09-15

Groundwater drinking water supply surveillance data were accessed to summarize water quality delivered as public and private water supplies in southern Saskatchewan as part of an exposure assessment for epidemiologic analyses of associations between water quality and type 2 diabetes or cardiovascular disease. Arsenic in drinking water has been linked to a variety of chronic diseases and previous studies have identified multiple wells with arsenic above the drinking water standard of 0.01 mg/L; therefore, arsenic concentrations were of specific interest. Principal components analysis was applied to obtain principal component (PC) scores to summarize mixtures of correlated parameters identified as health standards and those identified as aesthetic objectives in the Saskatchewan Drinking Water Quality Standards and Objective. Ordinary, universal, and empirical Bayesian kriging were used to interpolate arsenic concentrations and PC scores in southern Saskatchewan, and the results were compared. Empirical Bayesian kriging performed best across all analyses, based on having the greatest number of variables for which the root mean square error was lowest. While all of the kriging methods appeared to underestimate high values of arsenic and PC scores, empirical Bayesian kriging was chosen to summarize large scale geographic trends in groundwater-sourced drinking water quality and assess exposure to mixtures of trace metals and ions.

Mechanism-based classification of PAH mixtures to predict carcinogenic potential

DOE PAGES

Tilton, Susan C.; Siddens, Lisbeth K.; Krueger, Sharon K.; ...

2015-04-22

We have previously shown that relative potency factors and DNA adduct measurements are inadequate for predicting carcinogenicity of certain polycyclic aromatic hydrocarbons (PAHs) and PAH mixtures, particularly those that function through alternate pathways or exhibit greater promotional activity compared to benzo[ a]pyrene (BaP). Therefore, we developed a pathway based approach for classification of tumor outcome after dermal exposure to PAH/mixtures. FVB/N mice were exposed to dibenzo[ def,p]chrysene (DBC), BaP or environmental PAH mixtures (Mix 1-3) following a two-stage initiation/promotion skin tumor protocol. Resulting tumor incidence could be categorized by carcinogenic potency as DBC>>BaP=Mix2=Mix3>Mix1=Control, based on statistical significance. Gene expression profilesmore » measured in skin of mice collected 12 h post-initiation were compared to tumor outcome for identification of short-term bioactivity profiles. A Bayesian integration model was utilized to identify biological pathways predictive of PAH carcinogenic potential during initiation. Integration of probability matrices from four enriched pathways (p<0.05) for DNA damage, apoptosis, response to chemical stimulus and interferon gamma signaling resulted in the highest classification accuracy with leave-one-out cross validation. This pathway-driven approach was successfully utilized to distinguish early regulatory events during initiation prognostic for tumor outcome and provides proof-of-concept for using short-term initiation studies to classify carcinogenic potential of environmental PAH mixtures. As a result, these data further provide a ‘source-to outcome’ model that could be used to predict PAH interactions during tumorigenesis and provide an example of how mode-of-action based risk assessment could be employed for environmental PAH mixtures.« less

Mechanism-Based Classification of PAH Mixtures to Predict Carcinogenic Potential.

PubMed

Tilton, Susan C; Siddens, Lisbeth K; Krueger, Sharon K; Larkin, Andrew J; Löhr, Christiane V; Williams, David E; Baird, William M; Waters, Katrina M

2015-07-01

We have previously shown that relative potency factors and DNA adduct measurements are inadequate for predicting carcinogenicity of certain polycyclic aromatic hydrocarbons (PAHs) and PAH mixtures, particularly those that function through alternate pathways or exhibit greater promotional activity compared to benzo[a]pyrene (BaP). Therefore, we developed a pathway-based approach for classification of tumor outcome after dermal exposure to PAH/mixtures. FVB/N mice were exposed to dibenzo[def,p]chrysene (DBC), BaP, or environmental PAH mixtures (Mix 1-3) following a 2-stage initiation/promotion skin tumor protocol. Resulting tumor incidence could be categorized by carcinogenic potency as DBC > BaP = Mix2 = Mix3 > Mix1 = Control, based on statistical significance. Gene expression profiles measured in skin of mice collected 12 h post-initiation were compared with tumor outcome for identification of short-term bioactivity profiles. A Bayesian integration model was utilized to identify biological pathways predictive of PAH carcinogenic potential during initiation. Integration of probability matrices from four enriched pathways (P < .05) for DNA damage, apoptosis, response to chemical stimulus, and interferon gamma signaling resulted in the highest classification accuracy with leave-one-out cross validation. This pathway-driven approach was successfully utilized to distinguish early regulatory events during initiation prognostic for tumor outcome and provides proof-of-concept for using short-term initiation studies to classify carcinogenic potential of environmental PAH mixtures. These data further provide a 'source-to-outcome' model that could be used to predict PAH interactions during tumorigenesis and provide an example of how mode-of-action-based risk assessment could be employed for environmental PAH mixtures. © The Author 2015. Published by Oxford University Press on behalf of the Society of Toxicology. All rights reserved. For Permissions, please e-mail: journals.permissions@oup.com.

A Bayesian Nonparametric Approach to Test Equating

ERIC Educational Resources Information Center

Karabatsos, George; Walker, Stephen G.

2009-01-01

A Bayesian nonparametric model is introduced for score equating. It is applicable to all major equating designs, and has advantages over previous equating models. Unlike the previous models, the Bayesian model accounts for positive dependence between distributions of scores from two tests. The Bayesian model and the previous equating models are…

Model Diagnostics for Bayesian Networks

ERIC Educational Resources Information Center

Sinharay, Sandip

2006-01-01

Bayesian networks are frequently used in educational assessments primarily for learning about students' knowledge and skills. There is a lack of works on assessing fit of Bayesian networks. This article employs the posterior predictive model checking method, a popular Bayesian model checking tool, to assess fit of simple Bayesian networks. A…

Pattern analysis of community health center location in Surabaya using spatial Poisson point process

NASA Astrophysics Data System (ADS)

Kusumaningrum, Choriah Margareta; Iriawan, Nur; Winahju, Wiwiek Setya

2017-11-01

Community health center (puskesmas) is one of the closest health service facilities for the community, which provide healthcare for population on sub-district level as one of the government-mandated community health clinics located across Indonesia. The increasing number of this puskesmas does not directly comply the fulfillment of basic health services needed in such region. Ideally, a puskesmas has to cover up to maximum 30,000 people. The number of puskesmas in Surabaya indicates an unbalance spread in all of the area. This research aims to analyze the spread of puskesmas in Surabaya using spatial Poisson point process model in order to get the effective location of Surabaya's puskesmas which based on their location. The results of the analysis showed that the distribution pattern of puskesmas in Surabaya is non-homogeneous Poisson process and is approched by mixture Poisson model. Based on the estimated model obtained by using Bayesian mixture model couple with MCMC process, some characteristics of each puskesmas have no significant influence as factors to decide the addition of health center in such location. Some factors related to the areas of sub-districts have to be considered as covariate to make a decision adding the puskesmas in Surabaya.

Informative Bayesian Type A uncertainty evaluation, especially applicable to a small number of observations

NASA Astrophysics Data System (ADS)

Cox, M.; Shirono, K.

2017-10-01

A criticism levelled at the Guide to the Expression of Uncertainty in Measurement (GUM) is that it is based on a mixture of frequentist and Bayesian thinking. In particular, the GUM’s Type A (statistical) uncertainty evaluations are frequentist, whereas the Type B evaluations, using state-of-knowledge distributions, are Bayesian. In contrast, making the GUM fully Bayesian implies, among other things, that a conventional objective Bayesian approach to Type A uncertainty evaluation for a number n of observations leads to the impractical consequence that n must be at least equal to 4, thus presenting a difficulty for many metrologists. This paper presents a Bayesian analysis of Type A uncertainty evaluation that applies for all n ≥slant 2 , as in the frequentist analysis in the current GUM. The analysis is based on assuming that the observations are drawn from a normal distribution (as in the conventional objective Bayesian analysis), but uses an informative prior based on lower and upper bounds for the standard deviation of the sampling distribution for the quantity under consideration. The main outcome of the analysis is a closed-form mathematical expression for the factor by which the standard deviation of the mean observation should be multiplied to calculate the required standard uncertainty. Metrological examples are used to illustrate the approach, which is straightforward to apply using a formula or look-up table.

Mixture distributions of wind speed in the UAE

NASA Astrophysics Data System (ADS)

Shin, J.; Ouarda, T.; Lee, T. S.

2013-12-01

Wind speed probability distribution is commonly used to estimate potential wind energy. The 2-parameter Weibull distribution has been most widely used to characterize the distribution of wind speed. However, it is unable to properly model wind speed regimes when wind speed distribution presents bimodal and kurtotic shapes. Several studies have concluded that the Weibull distribution should not be used for frequency analysis of wind speed without investigation of wind speed distribution. Due to these mixture distributional characteristics of wind speed data, the application of mixture distributions should be further investigated in the frequency analysis of wind speed. A number of studies have investigated the potential wind energy in different parts of the Arabian Peninsula. Mixture distributional characteristics of wind speed were detected from some of these studies. Nevertheless, mixture distributions have not been employed for wind speed modeling in the Arabian Peninsula. In order to improve our understanding of wind energy potential in Arabian Peninsula, mixture distributions should be tested for the frequency analysis of wind speed. The aim of the current study is to assess the suitability of mixture distributions for the frequency analysis of wind speed in the UAE. Hourly mean wind speed data at 10-m height from 7 stations were used in the current study. The Weibull and Kappa distributions were employed as representatives of the conventional non-mixture distributions. 10 mixture distributions are used and constructed by mixing four probability distributions such as Normal, Gamma, Weibull and Extreme value type-one (EV-1) distributions. Three parameter estimation methods such as Expectation Maximization algorithm, Least Squares method and Meta-Heuristic Maximum Likelihood (MHML) method were employed to estimate the parameters of the mixture distributions. In order to compare the goodness-of-fit of tested distributions and parameter estimation methods for sample wind data, the adjusted coefficient of determination, Bayesian Information Criterion (BIC) and Chi-squared statistics were computed. Results indicate that MHML presents the best performance of parameter estimation for the used mixture distributions. In most of the employed 7 stations, mixture distributions give the best fit. When the wind speed regime shows mixture distributional characteristics, most of these regimes present the kurtotic statistical characteristic. Particularly, applications of mixture distributions for these stations show a significant improvement in explaining the whole wind speed regime. In addition, the Weibull-Weibull mixture distribution presents the best fit for the wind speed data in the UAE.

Effects of additional data on Bayesian clustering.

PubMed

Yamazaki, Keisuke

2017-10-01

Hierarchical probabilistic models, such as mixture models, are used for cluster analysis. These models have two types of variables: observable and latent. In cluster analysis, the latent variable is estimated, and it is expected that additional information will improve the accuracy of the estimation of the latent variable. Many proposed learning methods are able to use additional data; these include semi-supervised learning and transfer learning. However, from a statistical point of view, a complex probabilistic model that encompasses both the initial and additional data might be less accurate due to having a higher-dimensional parameter. The present paper presents a theoretical analysis of the accuracy of such a model and clarifies which factor has the greatest effect on its accuracy, the advantages of obtaining additional data, and the disadvantages of increasing the complexity. Copyright © 2017 Elsevier Ltd. All rights reserved.

Bayesian Model Averaging for Propensity Score Analysis

ERIC Educational Resources Information Center

Kaplan, David; Chen, Jianshen

2013-01-01

The purpose of this study is to explore Bayesian model averaging in the propensity score context. Previous research on Bayesian propensity score analysis does not take into account model uncertainty. In this regard, an internally consistent Bayesian framework for model building and estimation must also account for model uncertainty. The…

Quantitative assessment of Pb sources in isotopic mixtures using a Bayesian mixing model.

PubMed

Longman, Jack; Veres, Daniel; Ersek, Vasile; Phillips, Donald L; Chauvel, Catherine; Tamas, Calin G

2018-04-18

Lead (Pb) isotopes provide valuable insights into the origin of Pb within a sample, typically allowing for reliable fingerprinting of their source. This is useful for a variety of applications, from tracing sources of pollution-related Pb, to the origins of Pb in archaeological artefacts. However, current approaches investigate source proportions via graphical means, or simple mixing models. As such, an approach, which quantitatively assesses source proportions and fingerprints the signature of analysed Pb, especially for larger numbers of sources, would be valuable. Here we use an advanced Bayesian isotope mixing model for three such applications: tracing dust sources in pre-anthropogenic environmental samples, tracking changing ore exploitation during the Roman period, and identifying the source of Pb in a Roman-age mining artefact. These examples indicate this approach can understand changing Pb sources deposited during both pre-anthropogenic times, when natural cycling of Pb dominated, and the Roman period, one marked by significant anthropogenic pollution. Our archaeometric investigation indicates clear input of Pb from Romanian ores previously speculated, but not proven, to have been the Pb source. Our approach can be applied to a range of disciplines, providing a new method for robustly tracing sources of Pb observed within a variety of environments.

Bayesian demosaicing using Gaussian scale mixture priors with local adaptivity in the dual tree complex wavelet packet transform domain

NASA Astrophysics Data System (ADS)

Goossens, Bart; Aelterman, Jan; Luong, Hiep; Pizurica, Aleksandra; Philips, Wilfried

2013-02-01

In digital cameras and mobile phones, there is an ongoing trend to increase the image resolution, decrease the sensor size and to use lower exposure times. Because smaller sensors inherently lead to more noise and a worse spatial resolution, digital post-processing techniques are required to resolve many of the artifacts. Color filter arrays (CFAs), which use alternating patterns of color filters, are very popular because of price and power consumption reasons. However, color filter arrays require the use of a post-processing technique such as demosaicing to recover full resolution RGB images. Recently, there has been some interest in techniques that jointly perform the demosaicing and denoising. This has the advantage that the demosaicing and denoising can be performed optimally (e.g. in the MSE sense) for the considered noise model, while avoiding artifacts introduced when using demosaicing and denoising sequentially. In this paper, we will continue the research line of the wavelet-based demosaicing techniques. These approaches are computationally simple and very suited for combination with denoising. Therefore, we will derive Bayesian Minimum Squared Error (MMSE) joint demosaicing and denoising rules in the complex wavelet packet domain, taking local adaptivity into account. As an image model, we will use Gaussian Scale Mixtures, thereby taking advantage of the directionality of the complex wavelets. Our results show that this technique is well capable of reconstructing fine details in the image, while removing all of the noise, at a relatively low computational cost. In particular, the complete reconstruction (including color correction, white balancing etc) of a 12 megapixel RAW image takes 3.5 sec on a recent mid-range GPU.

Automated Assessment of Disease Progression in Acute Myeloid Leukemia by Probabilistic Analysis of Flow Cytometry Data

PubMed Central

Rajwa, Bartek; Wallace, Paul K.; Griffiths, Elizabeth A.; Dundar, Murat

2017-01-01

Objective Flow cytometry (FC) is a widely acknowledged technology in diagnosis of acute myeloid leukemia (AML) and has been indispensable in determining progression of the disease. Although FC plays a key role as a post-therapy prognosticator and evaluator of therapeutic efficacy, the manual analysis of cytometry data is a barrier to optimization of reproducibility and objectivity. This study investigates the utility of our recently introduced non-parametric Bayesian framework in accurately predicting the direction of change in disease progression in AML patients using FC data. Methods The highly flexible non-parametric Bayesian model based on the infinite mixture of infinite Gaussian mixtures is used for jointly modeling data from multiple FC samples to automatically identify functionally distinct cell populations and their local realizations. Phenotype vectors are obtained by characterizing each sample by the proportions of recovered cell populations, which are in turn used to predict the direction of change in disease progression for each patient. Results We used 200 diseased and non-diseased immunophenotypic panels for training and tested the system with 36 additional AML cases collected at multiple time points. The proposed framework identified the change in direction of disease progression with accuracies of 90% (9 out of 10) for relapsing cases and 100% (26 out of 26) for the remaining cases. Conclusions We believe that these promising results are an important first step towards the development of automated predictive systems for disease monitoring and continuous response evaluation. Significance Automated measurement and monitoring of therapeutic response is critical not only for objective evaluation of disease status prognosis but also for timely assessment of treatment strategies. PMID:27416585

An adaptive importance sampling algorithm for Bayesian inversion with multimodal distributions

DOE PAGES

Li, Weixuan; Lin, Guang

2015-03-21

Parametric uncertainties are encountered in the simulations of many physical systems, and may be reduced by an inverse modeling procedure that calibrates the simulation results to observations on the real system being simulated. Following Bayes’ rule, a general approach for inverse modeling problems is to sample from the posterior distribution of the uncertain model parameters given the observations. However, the large number of repetitive forward simulations required in the sampling process could pose a prohibitive computational burden. This difficulty is particularly challenging when the posterior is multimodal. We present in this paper an adaptive importance sampling algorithm to tackle thesemore » challenges. Two essential ingredients of the algorithm are: 1) a Gaussian mixture (GM) model adaptively constructed as the proposal distribution to approximate the possibly multimodal target posterior, and 2) a mixture of polynomial chaos (PC) expansions, built according to the GM proposal, as a surrogate model to alleviate the computational burden caused by computational-demanding forward model evaluations. In three illustrative examples, the proposed adaptive importance sampling algorithm demonstrates its capabilities of automatically finding a GM proposal with an appropriate number of modes for the specific problem under study, and obtaining a sample accurately and efficiently representing the posterior with limited number of forward simulations.« less

Probabilistic Elastic Part Model: A Pose-Invariant Representation for Real-World Face Verification.

PubMed

Li, Haoxiang; Hua, Gang

2018-04-01

Pose variation remains to be a major challenge for real-world face recognition. We approach this problem through a probabilistic elastic part model. We extract local descriptors (e.g., LBP or SIFT) from densely sampled multi-scale image patches. By augmenting each descriptor with its location, a Gaussian mixture model (GMM) is trained to capture the spatial-appearance distribution of the face parts of all face images in the training corpus, namely the probabilistic elastic part (PEP) model. Each mixture component of the GMM is confined to be a spherical Gaussian to balance the influence of the appearance and the location terms, which naturally defines a part. Given one or multiple face images of the same subject, the PEP-model builds its PEP representation by sequentially concatenating descriptors identified by each Gaussian component in a maximum likelihood sense. We further propose a joint Bayesian adaptation algorithm to adapt the universally trained GMM to better model the pose variations between the target pair of faces/face tracks, which consistently improves face verification accuracy. Our experiments show that we achieve state-of-the-art face verification accuracy with the proposed representations on the Labeled Face in the Wild (LFW) dataset, the YouTube video face database, and the CMU MultiPIE dataset.

An adaptive importance sampling algorithm for Bayesian inversion with multimodal distributions

DOE Office of Scientific and Technical Information (OSTI.GOV)

Li, Weixuan; Lin, Guang, E-mail: guanglin@purdue.edu

2015-08-01

Parametric uncertainties are encountered in the simulations of many physical systems, and may be reduced by an inverse modeling procedure that calibrates the simulation results to observations on the real system being simulated. Following Bayes' rule, a general approach for inverse modeling problems is to sample from the posterior distribution of the uncertain model parameters given the observations. However, the large number of repetitive forward simulations required in the sampling process could pose a prohibitive computational burden. This difficulty is particularly challenging when the posterior is multimodal. We present in this paper an adaptive importance sampling algorithm to tackle thesemore » challenges. Two essential ingredients of the algorithm are: 1) a Gaussian mixture (GM) model adaptively constructed as the proposal distribution to approximate the possibly multimodal target posterior, and 2) a mixture of polynomial chaos (PC) expansions, built according to the GM proposal, as a surrogate model to alleviate the computational burden caused by computational-demanding forward model evaluations. In three illustrative examples, the proposed adaptive importance sampling algorithm demonstrates its capabilities of automatically finding a GM proposal with an appropriate number of modes for the specific problem under study, and obtaining a sample accurately and efficiently representing the posterior with limited number of forward simulations.« less

Bayesian Inference for Functional Dynamics Exploring in fMRI Data.

PubMed

Guo, Xuan; Liu, Bing; Chen, Le; Chen, Guantao; Pan, Yi; Zhang, Jing

2016-01-01

This paper aims to review state-of-the-art Bayesian-inference-based methods applied to functional magnetic resonance imaging (fMRI) data. Particularly, we focus on one specific long-standing challenge in the computational modeling of fMRI datasets: how to effectively explore typical functional interactions from fMRI time series and the corresponding boundaries of temporal segments. Bayesian inference is a method of statistical inference which has been shown to be a powerful tool to encode dependence relationships among the variables with uncertainty. Here we provide an introduction to a group of Bayesian-inference-based methods for fMRI data analysis, which were designed to detect magnitude or functional connectivity change points and to infer their functional interaction patterns based on corresponding temporal boundaries. We also provide a comparison of three popular Bayesian models, that is, Bayesian Magnitude Change Point Model (BMCPM), Bayesian Connectivity Change Point Model (BCCPM), and Dynamic Bayesian Variable Partition Model (DBVPM), and give a summary of their applications. We envision that more delicate Bayesian inference models will be emerging and play increasingly important roles in modeling brain functions in the years to come.

Using a multinomial tree model for detecting mixtures in perceptual detection

PubMed Central

Chechile, Richard A.

2014-01-01

In the area of memory research there have been two rival approaches for memory measurement—signal detection theory (SDT) and multinomial processing trees (MPT). Both approaches provide measures for the quality of the memory representation, and both approaches provide for corrections for response bias. In recent years there has been a strong case advanced for the MPT approach because of the finding of stochastic mixtures on both target-present and target-absent tests. In this paper a case is made that perceptual detection, like memory recognition, involves a mixture of processes that are readily represented as a MPT model. The Chechile (2004) 6P memory measurement model is modified in order to apply to the case of perceptual detection. This new MPT model is called the Perceptual Detection (PD) model. The properties of the PD model are developed, and the model is applied to some existing data of a radiologist examining CT scans. The PD model brings out novel features that were absent from a standard SDT analysis. Also the topic of optimal parameter estimation on an individual-observer basis is explored with Monte Carlo simulations. These simulations reveal that the mean of the Bayesian posterior distribution is a more accurate estimator than the corresponding maximum likelihood estimator (MLE). Monte Carlo simulations also indicate that model estimates based on only the data from an individual observer can be improved upon (in the sense of being more accurate) by an adjustment that takes into account the parameter estimate based on the data pooled across all the observers. The adjustment of the estimate for an individual is discussed as an analogous statistical effect to the improvement over the individual MLE demonstrated by the James–Stein shrinkage estimator in the case of the multiple-group normal model. PMID:25018741

Bayesian analysis of Jolly-Seber type models

USGS Publications Warehouse

Matechou, Eleni; Nicholls, Geoff K.; Morgan, Byron J. T.; Collazo, Jaime A.; Lyons, James E.

2016-01-01

We propose the use of finite mixtures of continuous distributions in modelling the process by which new individuals, that arrive in groups, become part of a wildlife population. We demonstrate this approach using a data set of migrating semipalmated sandpipers (Calidris pussila) for which we extend existing stopover models to allow for individuals to have different behaviour in terms of their stopover duration at the site. We demonstrate the use of reversible jump MCMC methods to derive posterior distributions for the model parameters and the models, simultaneously. The algorithm moves between models with different numbers of arrival groups as well as between models with different numbers of behavioural groups. The approach is shown to provide new ecological insights about the stopover behaviour of semipalmated sandpipers but is generally applicable to any population in which animals arrive in groups and potentially exhibit heterogeneity in terms of one or more other processes.

DOE Office of Scientific and Technical Information (OSTI.GOV)

Crain, Steven P.; Yang, Shuang-Hong; Zha, Hongyuan

Access to health information by consumers is ham- pered by a fundamental language gap. Current attempts to close the gap leverage consumer oriented health information, which does not, however, have good coverage of slang medical terminology. In this paper, we present a Bayesian model to automatically align documents with different dialects (slang, com- mon and technical) while extracting their semantic topics. The proposed diaTM model enables effective information retrieval, even when the query contains slang words, by explicitly modeling the mixtures of dialects in documents and the joint influence of dialects and topics on word selection. Simulations us- ing consumermore » questions to retrieve medical information from a corpus of medical documents show that diaTM achieves a 25% improvement in information retrieval relevance by nDCG@5 over an LDA baseline.« less

Informative priors on fetal fraction increase power of the noninvasive prenatal screen.

PubMed

Xu, Hanli; Wang, Shaowei; Ma, Lin-Lin; Huang, Shuai; Liang, Lin; Liu, Qian; Liu, Yang-Yang; Liu, Ke-Di; Tan, Ze-Min; Ban, Hao; Guan, Yongtao; Lu, Zuhong

2017-11-09

PurposeNoninvasive prenatal screening (NIPS) sequences a mixture of the maternal and fetal cell-free DNA. Fetal trisomy can be detected by examining chromosomal dosages estimated from sequencing reads. The traditional method uses the Z-test, which compares a subject against a set of euploid controls, where the information of fetal fraction is not fully utilized. Here we present a Bayesian method that leverages informative priors on the fetal fraction.MethodOur Bayesian method combines the Z-test likelihood and informative priors of the fetal fraction, which are learned from the sex chromosomes, to compute Bayes factors. Bayesian framework can account for nongenetic risk factors through the prior odds, and our method can report individual positive/negative predictive values.ResultsOur Bayesian method has more power than the Z-test method. We analyzed 3,405 NIPS samples and spotted at least 9 (of 51) possible Z-test false positives.ConclusionBayesian NIPS is more powerful than the Z-test method, is able to account for nongenetic risk factors through prior odds, and can report individual positive/negative predictive values.Genetics in Medicine advance online publication, 9 November 2017; doi:10.1038/gim.2017.186.

Sample size and classification error for Bayesian change-point models with unlabelled sub-groups and incomplete follow-up.

PubMed

White, Simon R; Muniz-Terrera, Graciela; Matthews, Fiona E

2018-05-01

Many medical (and ecological) processes involve the change of shape, whereby one trajectory changes into another trajectory at a specific time point. There has been little investigation into the study design needed to investigate these models. We consider the class of fixed effect change-point models with an underlying shape comprised two joined linear segments, also known as broken-stick models. We extend this model to include two sub-groups with different trajectories at the change-point, a change and no change class, and also include a missingness model to account for individuals with incomplete follow-up. Through a simulation study, we consider the relationship of sample size to the estimates of the underlying shape, the existence of a change-point, and the classification-error of sub-group labels. We use a Bayesian framework to account for the missing labels, and the analysis of each simulation is performed using standard Markov chain Monte Carlo techniques. Our simulation study is inspired by cognitive decline as measured by the Mini-Mental State Examination, where our extended model is appropriate due to the commonly observed mixture of individuals within studies who do or do not exhibit accelerated decline. We find that even for studies of modest size ( n = 500, with 50 individuals observed past the change-point) in the fixed effect setting, a change-point can be detected and reliably estimated across a range of observation-errors.

Characterization of background concentrations of contaminants using a mixture of normal distributions.

PubMed

Qian, Song S; Lyons, Regan E

2006-10-01

We present a Bayesian approach for characterizing background contaminant concentration distributions using data from sites that may have been contaminated. Our method, focused on estimation, resolves several technical problems of the existing methods sanctioned by the U.S. Environmental Protection Agency (USEPA) (a hypothesis testing based method), resulting in a simple and quick procedure for estimating background contaminant concentrations. The proposed Bayesian method is applied to two data sets from a federal facility regulated under the Resource Conservation and Restoration Act. The results are compared to background distributions identified using existing methods recommended by the USEPA. The two data sets represent low and moderate levels of censorship in the data. Although an unbiased estimator is elusive, we show that the proposed Bayesian estimation method will have a smaller bias than the EPA recommended method.

Uncertainty quantification of reaction mechanisms accounting for correlations introduced by rate rules and fitted Arrhenius parameters

DOE PAGES

Prager, Jens; Najm, Habib N.; Sargsyan, Khachik; ...

2013-02-23

We study correlations among uncertain Arrhenius rate parameters in a chemical model for hydrocarbon fuel-air combustion. We consider correlations induced by the use of rate rules for modeling reaction rate constants, as well as those resulting from fitting rate expressions to empirical measurements arriving at a joint probability density for all Arrhenius parameters. We focus on homogeneous ignition in a fuel-air mixture at constant-pressure. We also outline a general methodology for this analysis using polynomial chaos and Bayesian inference methods. Finally, we examine the uncertainties in both the Arrhenius parameters and in predicted ignition time, outlining the role of correlations,more » and considering both accuracy and computational efficiency.« less

Bayesian structural equation modeling in sport and exercise psychology.

PubMed

Stenling, Andreas; Ivarsson, Andreas; Johnson, Urban; Lindwall, Magnus

2015-08-01

Bayesian statistics is on the rise in mainstream psychology, but applications in sport and exercise psychology research are scarce. In this article, the foundations of Bayesian analysis are introduced, and we will illustrate how to apply Bayesian structural equation modeling in a sport and exercise psychology setting. More specifically, we contrasted a confirmatory factor analysis on the Sport Motivation Scale II estimated with the most commonly used estimator, maximum likelihood, and a Bayesian approach with weakly informative priors for cross-loadings and correlated residuals. The results indicated that the model with Bayesian estimation and weakly informative priors provided a good fit to the data, whereas the model estimated with a maximum likelihood estimator did not produce a well-fitting model. The reasons for this discrepancy between maximum likelihood and Bayesian estimation are discussed as well as potential advantages and caveats with the Bayesian approach.

Bayesian model reduction and empirical Bayes for group (DCM) studies

PubMed Central

Friston, Karl J.; Litvak, Vladimir; Oswal, Ashwini; Razi, Adeel; Stephan, Klaas E.; van Wijk, Bernadette C.M.; Ziegler, Gabriel; Zeidman, Peter

2016-01-01

This technical note describes some Bayesian procedures for the analysis of group studies that use nonlinear models at the first (within-subject) level – e.g., dynamic causal models – and linear models at subsequent (between-subject) levels. Its focus is on using Bayesian model reduction to finesse the inversion of multiple models of a single dataset or a single (hierarchical or empirical Bayes) model of multiple datasets. These applications of Bayesian model reduction allow one to consider parametric random effects and make inferences about group effects very efficiently (in a few seconds). We provide the relatively straightforward theoretical background to these procedures and illustrate their application using a worked example. This example uses a simulated mismatch negativity study of schizophrenia. We illustrate the robustness of Bayesian model reduction to violations of the (commonly used) Laplace assumption in dynamic causal modelling and show how its recursive application can facilitate both classical and Bayesian inference about group differences. Finally, we consider the application of these empirical Bayesian procedures to classification and prediction. PMID:26569570

An introduction to using Bayesian linear regression with clinical data.

PubMed

Baldwin, Scott A; Larson, Michael J

2017-11-01

Statistical training psychology focuses on frequentist methods. Bayesian methods are an alternative to standard frequentist methods. This article provides researchers with an introduction to fundamental ideas in Bayesian modeling. We use data from an electroencephalogram (EEG) and anxiety study to illustrate Bayesian models. Specifically, the models examine the relationship between error-related negativity (ERN), a particular event-related potential, and trait anxiety. Methodological topics covered include: how to set up a regression model in a Bayesian framework, specifying priors, examining convergence of the model, visualizing and interpreting posterior distributions, interval estimates, expected and predicted values, and model comparison tools. We also discuss situations where Bayesian methods can outperform frequentist methods as well has how to specify more complicated regression models. Finally, we conclude with recommendations about reporting guidelines for those using Bayesian methods in their own research. We provide data and R code for replicating our analyses. Copyright © 2017 Elsevier Ltd. All rights reserved.

A Bayesian model for time-to-event data with informative censoring

PubMed Central

Kaciroti, Niko A.; Raghunathan, Trivellore E.; Taylor, Jeremy M. G.; Julius, Stevo

2012-01-01

Randomized trials with dropouts or censored data and discrete time-to-event type outcomes are frequently analyzed using the Kaplan–Meier or product limit (PL) estimation method. However, the PL method assumes that the censoring mechanism is noninformative and when this assumption is violated, the inferences may not be valid. We propose an expanded PL method using a Bayesian framework to incorporate informative censoring mechanism and perform sensitivity analysis on estimates of the cumulative incidence curves. The expanded method uses a model, which can be viewed as a pattern mixture model, where odds for having an event during the follow-up interval (tk−1,tk], conditional on being at risk at tk−1, differ across the patterns of missing data. The sensitivity parameters relate the odds of an event, between subjects from a missing-data pattern with the observed subjects for each interval. The large number of the sensitivity parameters is reduced by considering them as random and assumed to follow a log-normal distribution with prespecified mean and variance. Then we vary the mean and variance to explore sensitivity of inferences. The missing at random (MAR) mechanism is a special case of the expanded model, thus allowing exploration of the sensitivity to inferences as departures from the inferences under the MAR assumption. The proposed approach is applied to data from the TRial Of Preventing HYpertension. PMID:22223746

Identification of degenerate neuronal systems based on intersubject variability.

PubMed

Noppeney, Uta; Penny, Will D; Price, Cathy J; Flandin, Guillaume; Friston, Karl J

2006-04-15

Group studies implicitly assume that all subjects activate one common system to sustain a particular cognitive task. Intersubject variability is generally treated as well-behaved and uninteresting noise. However, intersubject variability might result from subjects engaging different degenerate neuronal systems that are each sufficient for task performance. This would produce a multimodal distribution of intersubject variability. We have explored this idea with the help of Gaussian Mixture Modeling and Bayesian model comparison procedures. We illustrate our approach using a crossmodal priming paradigm, in which subjects perform a semantic decision on environmental sounds or their spoken names that were preceded by a semantically congruent or incongruent picture or written name. All subjects consistently activated the superior temporal gyri bilaterally, the left fusiform gyrus and the inferior frontal sulcus. Comparing a One and Two Gaussian Mixture Model of the unexplained residuals provided very strong evidence for two groups with distinct activation patterns: 6 subjects exhibited additional activations in the superior temporal sulci bilaterally, the right superior frontal and central sulcus. 11 subjects showed increased activation in the striate and the right inferior parietal cortex. These results suggest that semantic decisions on auditory-visual compound stimuli might be accomplished by two overlapping degenerate neuronal systems.

Construction of environmental risk score beyond standard linear models using machine learning methods: application to metal mixtures, oxidative stress and cardiovascular disease in NHANES.

PubMed

Park, Sung Kyun; Zhao, Zhangchen; Mukherjee, Bhramar

2017-09-26

There is growing concern of health effects of exposure to pollutant mixtures. We initially proposed an Environmental Risk Score (ERS) as a summary measure to examine the risk of exposure to multi-pollutants in epidemiologic research considering only pollutant main effects. We expand the ERS by consideration of pollutant-pollutant interactions using modern machine learning methods. We illustrate the multi-pollutant approaches to predicting a marker of oxidative stress (gamma-glutamyl transferase (GGT)), a common disease pathway linking environmental exposure and numerous health endpoints. We examined 20 metal biomarkers measured in urine or whole blood from 6 cycles of the National Health and Nutrition Examination Survey (NHANES 2003-2004 to 2013-2014, n = 9664). We randomly split the data evenly into training and testing sets and constructed ERS's of metal mixtures for GGT using adaptive elastic-net with main effects and pairwise interactions (AENET-I), Bayesian additive regression tree (BART), Bayesian kernel machine regression (BKMR), and Super Learner in the training set and evaluated their performances in the testing set. We also evaluated the associations between GGT-ERS and cardiovascular endpoints. ERS based on AENET-I performed better than other approaches in terms of prediction errors in the testing set. Important metals identified in relation to GGT include cadmium (urine), dimethylarsonic acid, monomethylarsonic acid, cobalt, and barium. All ERS's showed significant associations with systolic and diastolic blood pressure and hypertension. For hypertension, one SD increase in each ERS from AENET-I, BART and SuperLearner were associated with odds ratios of 1.26 (95% CI, 1.15, 1.38), 1.17 (1.09, 1.25), and 1.30 (1.20, 1.40), respectively. ERS's showed non-significant positive associations with mortality outcomes. ERS is a useful tool for characterizing cumulative risk from pollutant mixtures, with accounting for statistical challenges such as high degrees of correlations and pollutant-pollutant interactions. ERS constructed for an intermediate marker like GGT is predictive of related disease endpoints.

Uncertainty Quantification in Climate Modeling and Projection

DOE Office of Scientific and Technical Information (OSTI.GOV)

Qian, Yun; Jackson, Charles; Giorgi, Filippo

The projection of future climate is one of the most complex problems undertaken by the scientific community. Although scientists have been striving to better understand the physical basis of the climate system and to improve climate models, the overall uncertainty in projections of future climate has not been significantly reduced (e.g., from the IPCC AR4 to AR5). With the rapid increase of complexity in Earth system models, reducing uncertainties in climate projections becomes extremely challenging. Since uncertainties always exist in climate models, interpreting the strengths and limitations of future climate projections is key to evaluating risks, and climate change informationmore » for use in Vulnerability, Impact, and Adaptation (VIA) studies should be provided with both well-characterized and well-quantified uncertainty. The workshop aimed at providing participants, many of them from developing countries, information on strategies to quantify the uncertainty in climate model projections and assess the reliability of climate change information for decision-making. The program included a mixture of lectures on fundamental concepts in Bayesian inference and sampling, applications, and hands-on computer laboratory exercises employing software packages for Bayesian inference, Markov Chain Monte Carlo methods, and global sensitivity analyses. The lectures covered a range of scientific issues underlying the evaluation of uncertainties in climate projections, such as the effects of uncertain initial and boundary conditions, uncertain physics, and limitations of observational records. Progress in quantitatively estimating uncertainties in hydrologic, land surface, and atmospheric models at both regional and global scales was also reviewed. The application of Uncertainty Quantification (UQ) concepts to coupled climate system models is still in its infancy. The Coupled Model Intercomparison Project (CMIP) multi-model ensemble currently represents the primary data for assessing reliability and uncertainties of climate change information. An alternative approach is to generate similar ensembles by perturbing parameters within a single-model framework. One of workshop’s objectives was to give participants a deeper understanding of these approaches within a Bayesian statistical framework. However, there remain significant challenges still to be resolved before UQ can be applied in a convincing way to climate models and their projections.« less

Development and comparison in uncertainty assessment based Bayesian modularization method in hydrological modeling

NASA Astrophysics Data System (ADS)

Li, Lu; Xu, Chong-Yu; Engeland, Kolbjørn

2013-04-01

SummaryWith respect to model calibration, parameter estimation and analysis of uncertainty sources, various regression and probabilistic approaches are used in hydrological modeling. A family of Bayesian methods, which incorporates different sources of information into a single analysis through Bayes' theorem, is widely used for uncertainty assessment. However, none of these approaches can well treat the impact of high flows in hydrological modeling. This study proposes a Bayesian modularization uncertainty assessment approach in which the highest streamflow observations are treated as suspect information that should not influence the inference of the main bulk of the model parameters. This study includes a comprehensive comparison and evaluation of uncertainty assessments by our new Bayesian modularization method and standard Bayesian methods using the Metropolis-Hastings (MH) algorithm with the daily hydrological model WASMOD. Three likelihood functions were used in combination with standard Bayesian method: the AR(1) plus Normal model independent of time (Model 1), the AR(1) plus Normal model dependent on time (Model 2) and the AR(1) plus Multi-normal model (Model 3). The results reveal that the Bayesian modularization method provides the most accurate streamflow estimates measured by the Nash-Sutcliffe efficiency and provide the best in uncertainty estimates for low, medium and entire flows compared to standard Bayesian methods. The study thus provides a new approach for reducing the impact of high flows on the discharge uncertainty assessment of hydrological models via Bayesian method.

Bayesian models: A statistical primer for ecologists

USGS Publications Warehouse

Hobbs, N. Thompson; Hooten, Mevin B.

2015-01-01

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

A Poisson nonnegative matrix factorization method with parameter subspace clustering constraint for endmember extraction in hyperspectral imagery

NASA Astrophysics Data System (ADS)

Sun, Weiwei; Ma, Jun; Yang, Gang; Du, Bo; Zhang, Liangpei

2017-06-01

A new Bayesian method named Poisson Nonnegative Matrix Factorization with Parameter Subspace Clustering Constraint (PNMF-PSCC) has been presented to extract endmembers from Hyperspectral Imagery (HSI). First, the method integrates the liner spectral mixture model with the Bayesian framework and it formulates endmember extraction into a Bayesian inference problem. Second, the Parameter Subspace Clustering Constraint (PSCC) is incorporated into the statistical program to consider the clustering of all pixels in the parameter subspace. The PSCC could enlarge differences among ground objects and helps finding endmembers with smaller spectrum divergences. Meanwhile, the PNMF-PSCC method utilizes the Poisson distribution as the prior knowledge of spectral signals to better explain the quantum nature of light in imaging spectrometer. Third, the optimization problem of PNMF-PSCC is formulated into maximizing the joint density via the Maximum A Posterior (MAP) estimator. The program is finally solved by iteratively optimizing two sub-problems via the Alternating Direction Method of Multipliers (ADMM) framework and the FURTHESTSUM initialization scheme. Five state-of-the art methods are implemented to make comparisons with the performance of PNMF-PSCC on both the synthetic and real HSI datasets. Experimental results show that the PNMF-PSCC outperforms all the five methods in Spectral Angle Distance (SAD) and Root-Mean-Square-Error (RMSE), and especially it could identify good endmembers for ground objects with smaller spectrum divergences.

Bayesian model reduction and empirical Bayes for group (DCM) studies.

PubMed

Friston, Karl J; Litvak, Vladimir; Oswal, Ashwini; Razi, Adeel; Stephan, Klaas E; van Wijk, Bernadette C M; Ziegler, Gabriel; Zeidman, Peter

2016-03-01

This technical note describes some Bayesian procedures for the analysis of group studies that use nonlinear models at the first (within-subject) level - e.g., dynamic causal models - and linear models at subsequent (between-subject) levels. Its focus is on using Bayesian model reduction to finesse the inversion of multiple models of a single dataset or a single (hierarchical or empirical Bayes) model of multiple datasets. These applications of Bayesian model reduction allow one to consider parametric random effects and make inferences about group effects very efficiently (in a few seconds). We provide the relatively straightforward theoretical background to these procedures and illustrate their application using a worked example. This example uses a simulated mismatch negativity study of schizophrenia. We illustrate the robustness of Bayesian model reduction to violations of the (commonly used) Laplace assumption in dynamic causal modelling and show how its recursive application can facilitate both classical and Bayesian inference about group differences. Finally, we consider the application of these empirical Bayesian procedures to classification and prediction. Copyright © 2015 The Authors. Published by Elsevier Inc. All rights reserved.

Adaptive Annealed Importance Sampling for Multimodal Posterior Exploration and Model Selection with Application to Extrasolar Planet Detection

NASA Astrophysics Data System (ADS)

Liu, Bin

2014-07-01

We describe an algorithm that can adaptively provide mixture summaries of multimodal posterior distributions. The parameter space of the involved posteriors ranges in size from a few dimensions to dozens of dimensions. This work was motivated by an astrophysical problem called extrasolar planet (exoplanet) detection, wherein the computation of stochastic integrals that are required for Bayesian model comparison is challenging. The difficulty comes from the highly nonlinear models that lead to multimodal posterior distributions. We resort to importance sampling (IS) to estimate the integrals, and thus translate the problem to be how to find a parametric approximation of the posterior. To capture the multimodal structure in the posterior, we initialize a mixture proposal distribution and then tailor its parameters elaborately to make it resemble the posterior to the greatest extent possible. We use the effective sample size (ESS) calculated based on the IS draws to measure the degree of approximation. The bigger the ESS is, the better the proposal resembles the posterior. A difficulty within this tailoring operation lies in the adjustment of the number of mixing components in the mixture proposal. Brute force methods just preset it as a large constant, which leads to an increase in the required computational resources. We provide an iterative delete/merge/add process, which works in tandem with an expectation-maximization step to tailor such a number online. The efficiency of our proposed method is tested via both simulation studies and real exoplanet data analysis.

Bayesian Data-Model Fit Assessment for Structural Equation Modeling

ERIC Educational Resources Information Center

Levy, Roy

2011-01-01

Bayesian approaches to modeling are receiving an increasing amount of attention in the areas of model construction and estimation in factor analysis, structural equation modeling (SEM), and related latent variable models. However, model diagnostics and model criticism remain relatively understudied aspects of Bayesian SEM. This article describes…

CLUSTERING SOUTH AFRICAN HOUSEHOLDS BASED ON THEIR ASSET STATUS USING LATENT VARIABLE MODELS

PubMed Central

McParland, Damien; Gormley, Isobel Claire; McCormick, Tyler H.; Clark, Samuel J.; Kabudula, Chodziwadziwa Whiteson; Collinson, Mark A.

2014-01-01

The Agincourt Health and Demographic Surveillance System has since 2001 conducted a biannual household asset survey in order to quantify household socio-economic status (SES) in a rural population living in northeast South Africa. The survey contains binary, ordinal and nominal items. In the absence of income or expenditure data, the SES landscape in the study population is explored and described by clustering the households into homogeneous groups based on their asset status. A model-based approach to clustering the Agincourt households, based on latent variable models, is proposed. In the case of modeling binary or ordinal items, item response theory models are employed. For nominal survey items, a factor analysis model, similar in nature to a multinomial probit model, is used. Both model types have an underlying latent variable structure—this similarity is exploited and the models are combined to produce a hybrid model capable of handling mixed data types. Further, a mixture of the hybrid models is considered to provide clustering capabilities within the context of mixed binary, ordinal and nominal response data. The proposed model is termed a mixture of factor analyzers for mixed data (MFA-MD). The MFA-MD model is applied to the survey data to cluster the Agincourt households into homogeneous groups. The model is estimated within the Bayesian paradigm, using a Markov chain Monte Carlo algorithm. Intuitive groupings result, providing insight to the different socio-economic strata within the Agincourt region. PMID:25485026

Confident difference criterion: a new Bayesian differentially expressed gene selection algorithm with applications.

PubMed

Yu, Fang; Chen, Ming-Hui; Kuo, Lynn; Talbott, Heather; Davis, John S

2015-08-07

Recently, the Bayesian method becomes more popular for analyzing high dimensional gene expression data as it allows us to borrow information across different genes and provides powerful estimators for evaluating gene expression levels. It is crucial to develop a simple but efficient gene selection algorithm for detecting differentially expressed (DE) genes based on the Bayesian estimators. In this paper, by extending the two-criterion idea of Chen et al. (Chen M-H, Ibrahim JG, Chi Y-Y. A new class of mixture models for differential gene expression in DNA microarray data. J Stat Plan Inference. 2008;138:387-404), we propose two new gene selection algorithms for general Bayesian models and name these new methods as the confident difference criterion methods. One is based on the standardized differences between two mean expression values among genes; the other adds the differences between two variances to it. The proposed confident difference criterion methods first evaluate the posterior probability of a gene having different gene expressions between competitive samples and then declare a gene to be DE if the posterior probability is large. The theoretical connection between the proposed first method based on the means and the Bayes factor approach proposed by Yu et al. (Yu F, Chen M-H, Kuo L. Detecting differentially expressed genes using alibrated Bayes factors. Statistica Sinica. 2008;18:783-802) is established under the normal-normal-model with equal variances between two samples. The empirical performance of the proposed methods is examined and compared to those of several existing methods via several simulations. The results from these simulation studies show that the proposed confident difference criterion methods outperform the existing methods when comparing gene expressions across different conditions for both microarray studies and sequence-based high-throughput studies. A real dataset is used to further demonstrate the proposed methodology. In the real data application, the confident difference criterion methods successfully identified more clinically important DE genes than the other methods. The confident difference criterion method proposed in this paper provides a new efficient approach for both microarray studies and sequence-based high-throughput studies to identify differentially expressed genes.

Bootstrap study of genome-enabled prediction reliabilities using haplotype blocks across Nordic Red cattle breeds.

PubMed

Cuyabano, B C D; Su, G; Rosa, G J M; Lund, M S; Gianola, D

2015-10-01

This study compared the accuracy of genome-enabled prediction models using individual single nucleotide polymorphisms (SNP) or haplotype blocks as covariates when using either a single breed or a combined population of Nordic Red cattle. The main objective was to compare predictions of breeding values of complex traits using a combined training population with haplotype blocks, with predictions using a single breed as training population and individual SNP as predictors. To compare the prediction reliabilities, bootstrap samples were taken from the test data set. With the bootstrapped samples of prediction reliabilities, we built and graphed confidence ellipses to allow comparisons. Finally, measures of statistical distances were used to calculate the gain in predictive ability. Our analyses are innovative in the context of assessment of predictive models, allowing a better understanding of prediction reliabilities and providing a statistical basis to effectively calibrate whether one prediction scenario is indeed more accurate than another. An ANOVA indicated that use of haplotype blocks produced significant gains mainly when Bayesian mixture models were used but not when Bayesian BLUP was fitted to the data. Furthermore, when haplotype blocks were used to train prediction models in a combined Nordic Red cattle population, we obtained up to a statistically significant 5.5% average gain in prediction accuracy, over predictions using individual SNP and training the model with a single breed. Copyright © 2015 American Dairy Science Association. Published by Elsevier Inc. All rights reserved.

Putting Priors in Mixture Density Mercer Kernels

NASA Technical Reports Server (NTRS)

Srivastava, Ashok N.; Schumann, Johann; Fischer, Bernd

2004-01-01

This paper presents a new methodology for automatic knowledge driven data mining based on the theory of Mercer Kernels, which are highly nonlinear symmetric positive definite mappings from the original image space to a very high, possibly infinite dimensional feature space. We describe a new method called Mixture Density Mercer Kernels to learn kernel function directly from data, rather than using predefined kernels. These data adaptive kernels can en- code prior knowledge in the kernel using a Bayesian formulation, thus allowing for physical information to be encoded in the model. We compare the results with existing algorithms on data from the Sloan Digital Sky Survey (SDSS). The code for these experiments has been generated with the AUTOBAYES tool, which automatically generates efficient and documented C/C++ code from abstract statistical model specifications. The core of the system is a schema library which contains template for learning and knowledge discovery algorithms like different versions of EM, or numeric optimization methods like conjugate gradient methods. The template instantiation is supported by symbolic- algebraic computations, which allows AUTOBAYES to find closed-form solutions and, where possible, to integrate them into the code. The results show that the Mixture Density Mercer-Kernel described here outperforms tree-based classification in distinguishing high-redshift galaxies from low- redshift galaxies by approximately 16% on test data, bagged trees by approximately 7%, and bagged trees built on a much larger sample of data by approximately 2%.

Bayesian multimodel inference for dose-response studies

USGS Publications Warehouse

Link, W.A.; Albers, P.H.

2007-01-01

Statistical inference in dose?response studies is model-based: The analyst posits a mathematical model of the relation between exposure and response, estimates parameters of the model, and reports conclusions conditional on the model. Such analyses rarely include any accounting for the uncertainties associated with model selection. The Bayesian inferential system provides a convenient framework for model selection and multimodel inference. In this paper we briefly describe the Bayesian paradigm and Bayesian multimodel inference. We then present a family of models for multinomial dose?response data and apply Bayesian multimodel inferential methods to the analysis of data on the reproductive success of American kestrels (Falco sparveriuss) exposed to various sublethal dietary concentrations of methylmercury.

A guide to Bayesian model selection for ecologists

USGS Publications Warehouse

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.

A Gaussian mixture model based adaptive classifier for fNIRS brain-computer interfaces and its testing via simulation

NASA Astrophysics Data System (ADS)

Li, Zheng; Jiang, Yi-han; Duan, Lian; Zhu, Chao-zhe

2017-08-01

Objective. Functional near infra-red spectroscopy (fNIRS) is a promising brain imaging technology for brain-computer interfaces (BCI). Future clinical uses of fNIRS will likely require operation over long time spans, during which neural activation patterns may change. However, current decoders for fNIRS signals are not designed to handle changing activation patterns. The objective of this study is to test via simulations a new adaptive decoder for fNIRS signals, the Gaussian mixture model adaptive classifier (GMMAC). Approach. GMMAC can simultaneously classify and track activation pattern changes without the need for ground-truth labels. This adaptive classifier uses computationally efficient variational Bayesian inference to label new data points and update mixture model parameters, using the previous model parameters as priors. We test GMMAC in simulations in which neural activation patterns change over time and compare to static decoders and unsupervised adaptive linear discriminant analysis classifiers. Main results. Our simulation experiments show GMMAC can accurately decode under time-varying activation patterns: shifts of activation region, expansions of activation region, and combined contractions and shifts of activation region. Furthermore, the experiments show the proposed method can track the changing shape of the activation region. Compared to prior work, GMMAC performed significantly better than the other unsupervised adaptive classifiers on a difficult activation pattern change simulation: 99% versus  <54% in two-choice classification accuracy. Significance. We believe GMMAC will be useful for clinical fNIRS-based brain-computer interfaces, including neurofeedback training systems, where operation over long time spans is required.

Bayesian Local Contamination Models for Multivariate Outliers

PubMed Central

Page, Garritt L.; Dunson, David B.

2013-01-01

In studies where data are generated from multiple locations or sources it is common for there to exist observations that are quite unlike the majority. Motivated by the application of establishing a reference value in an inter-laboratory setting when outlying labs are present, we propose a local contamination model that is able to accommodate unusual multivariate realizations in a flexible way. The proposed method models the process level of a hierarchical model using a mixture with a parametric component and a possibly nonparametric contamination. Much of the flexibility in the methodology is achieved by allowing varying random subsets of the elements in the lab-specific mean vectors to be allocated to the contamination component. Computational methods are developed and the methodology is compared to three other possible approaches using a simulation study. We apply the proposed method to a NIST/NOAA sponsored inter-laboratory study which motivated the methodological development. PMID:24363465

On the Adequacy of Bayesian Evaluations of Categorization Models: Reply to Vanpaemel and Lee (2012)

ERIC Educational Resources Information Center

Wills, Andy J.; Pothos, Emmanuel M.

2012-01-01

Vanpaemel and Lee (2012) argued, and we agree, that the comparison of formal models can be facilitated by Bayesian methods. However, Bayesian methods neither precede nor supplant our proposals (Wills & Pothos, 2012), as Bayesian methods can be applied both to our proposals and to their polar opposites. Furthermore, the use of Bayesian methods to…

A mixture of sparse coding models explaining properties of face neurons related to holistic and parts-based processing

PubMed Central

2017-01-01

Experimental studies have revealed evidence of both parts-based and holistic representations of objects and faces in the primate visual system. However, it is still a mystery how such seemingly contradictory types of processing can coexist within a single system. Here, we propose a novel theory called mixture of sparse coding models, inspired by the formation of category-specific subregions in the inferotemporal (IT) cortex. We developed a hierarchical network that constructed a mixture of two sparse coding submodels on top of a simple Gabor analysis. The submodels were each trained with face or non-face object images, which resulted in separate representations of facial parts and object parts. Importantly, evoked neural activities were modeled by Bayesian inference, which had a top-down explaining-away effect that enabled recognition of an individual part to depend strongly on the category of the whole input. We show that this explaining-away effect was indeed crucial for the units in the face submodel to exhibit significant selectivity to face images over object images in a similar way to actual face-selective neurons in the macaque IT cortex. Furthermore, the model explained, qualitatively and quantitatively, several tuning properties to facial features found in the middle patch of face processing in IT as documented by Freiwald, Tsao, and Livingstone (2009). These included, in particular, tuning to only a small number of facial features that were often related to geometrically large parts like face outline and hair, preference and anti-preference of extreme facial features (e.g., very large/small inter-eye distance), and reduction of the gain of feature tuning for partial face stimuli compared to whole face stimuli. Thus, we hypothesize that the coding principle of facial features in the middle patch of face processing in the macaque IT cortex may be closely related to mixture of sparse coding models. PMID:28742816

A mixture of sparse coding models explaining properties of face neurons related to holistic and parts-based processing.

PubMed

Hosoya, Haruo; Hyvärinen, Aapo

2017-07-01

Experimental studies have revealed evidence of both parts-based and holistic representations of objects and faces in the primate visual system. However, it is still a mystery how such seemingly contradictory types of processing can coexist within a single system. Here, we propose a novel theory called mixture of sparse coding models, inspired by the formation of category-specific subregions in the inferotemporal (IT) cortex. We developed a hierarchical network that constructed a mixture of two sparse coding submodels on top of a simple Gabor analysis. The submodels were each trained with face or non-face object images, which resulted in separate representations of facial parts and object parts. Importantly, evoked neural activities were modeled by Bayesian inference, which had a top-down explaining-away effect that enabled recognition of an individual part to depend strongly on the category of the whole input. We show that this explaining-away effect was indeed crucial for the units in the face submodel to exhibit significant selectivity to face images over object images in a similar way to actual face-selective neurons in the macaque IT cortex. Furthermore, the model explained, qualitatively and quantitatively, several tuning properties to facial features found in the middle patch of face processing in IT as documented by Freiwald, Tsao, and Livingstone (2009). These included, in particular, tuning to only a small number of facial features that were often related to geometrically large parts like face outline and hair, preference and anti-preference of extreme facial features (e.g., very large/small inter-eye distance), and reduction of the gain of feature tuning for partial face stimuli compared to whole face stimuli. Thus, we hypothesize that the coding principle of facial features in the middle patch of face processing in the macaque IT cortex may be closely related to mixture of sparse coding models.

Uncertainty aggregation and reduction in structure-material performance prediction

NASA Astrophysics Data System (ADS)

Hu, Zhen; Mahadevan, Sankaran; Ao, Dan

2018-02-01

An uncertainty aggregation and reduction framework is presented for structure-material performance prediction. Different types of uncertainty sources, structural analysis model, and material performance prediction model are connected through a Bayesian network for systematic uncertainty aggregation analysis. To reduce the uncertainty in the computational structure-material performance prediction model, Bayesian updating using experimental observation data is investigated based on the Bayesian network. It is observed that the Bayesian updating results will have large error if the model cannot accurately represent the actual physics, and that this error will be propagated to the predicted performance distribution. To address this issue, this paper proposes a novel uncertainty reduction method by integrating Bayesian calibration with model validation adaptively. The observation domain of the quantity of interest is first discretized into multiple segments. An adaptive algorithm is then developed to perform model validation and Bayesian updating over these observation segments sequentially. Only information from observation segments where the model prediction is highly reliable is used for Bayesian updating; this is found to increase the effectiveness and efficiency of uncertainty reduction. A composite rotorcraft hub component fatigue life prediction model, which combines a finite element structural analysis model and a material damage model, is used to demonstrate the proposed method.

Bayesian selection of misspecified models is overconfident and may cause spurious posterior probabilities for phylogenetic trees.

PubMed

Yang, Ziheng; Zhu, Tianqi

2018-02-20

The Bayesian method is noted to produce spuriously high posterior probabilities for phylogenetic trees in analysis of large datasets, but the precise reasons for this overconfidence are unknown. In general, the performance of Bayesian selection of misspecified models is poorly understood, even though this is of great scientific interest since models are never true in real data analysis. Here we characterize the asymptotic behavior of Bayesian model selection and show that when the competing models are equally wrong, Bayesian model selection exhibits surprising and polarized behaviors in large datasets, supporting one model with full force while rejecting the others. If one model is slightly less wrong than the other, the less wrong model will eventually win when the amount of data increases, but the method may become overconfident before it becomes reliable. We suggest that this extreme behavior may be a major factor for the spuriously high posterior probabilities for evolutionary trees. The philosophical implications of our results to the application of Bayesian model selection to evaluate opposing scientific hypotheses are yet to be explored, as are the behaviors of non-Bayesian methods in similar situations.

A mixture model for bovine abortion and foetal survival.

PubMed

Hanson, Timothy; Bedrick, Edward J; Johnson, Wesley O; Thurmond, Mark C

2003-05-30

The effect of spontaneous abortion on the dairy industry is substantial, costing the industry on the order of US dollars 200 million per year in California alone. We analyse data from a cohort study of nine dairy herds in Central California. A key feature of the analysis is the observation that only a relatively small proportion of cows will abort (around 10;15 per cent), so that it is inappropriate to analyse the time-to-abortion (TTA) data as if it were standard censored survival data, with cows that fail to abort by the end of the study treated as censored observations. We thus broaden the scope to consider the analysis of foetal lifetime distribution (FLD) data for the cows, with the dual goals of characterizing the effects of various risk factors on (i). the likelihood of abortion and, conditional on abortion status, on (ii). the risk of early versus late abortion. A single model is developed to accomplish both goals with two sets of specific herd effects modelled as random effects. Because multimodal foetal hazard functions are expected for the TTA data, both a parametric mixture model and a non-parametric model are developed. Furthermore, the two sets of analyses are linked because of anticipated dependence between the random herd effects. All modelling and inferences are accomplished using modern Bayesian methods. Copyright 2003 John Wiley & Sons, Ltd.

Robust, Adaptive Functional Regression in Functional Mixed Model Framework.

PubMed

Zhu, Hongxiao; Brown, Philip J; Morris, Jeffrey S

2011-09-01

Functional data are increasingly encountered in scientific studies, and their high dimensionality and complexity lead to many analytical challenges. Various methods for functional data analysis have been developed, including functional response regression methods that involve regression of a functional response on univariate/multivariate predictors with nonparametrically represented functional coefficients. In existing methods, however, the functional regression can be sensitive to outlying curves and outlying regions of curves, so is not robust. In this paper, we introduce a new Bayesian method, robust functional mixed models (R-FMM), for performing robust functional regression within the general functional mixed model framework, which includes multiple continuous or categorical predictors and random effect functions accommodating potential between-function correlation induced by the experimental design. The underlying model involves a hierarchical scale mixture model for the fixed effects, random effect and residual error functions. These modeling assumptions across curves result in robust nonparametric estimators of the fixed and random effect functions which down-weight outlying curves and regions of curves, and produce statistics that can be used to flag global and local outliers. These assumptions also lead to distributions across wavelet coefficients that have outstanding sparsity and adaptive shrinkage properties, with great flexibility for the data to determine the sparsity and the heaviness of the tails. Together with the down-weighting of outliers, these within-curve properties lead to fixed and random effect function estimates that appear in our simulations to be remarkably adaptive in their ability to remove spurious features yet retain true features of the functions. We have developed general code to implement this fully Bayesian method that is automatic, requiring the user to only provide the functional data and design matrices. It is efficient enough to handle large data sets, and yields posterior samples of all model parameters that can be used to perform desired Bayesian estimation and inference. Although we present details for a specific implementation of the R-FMM using specific distributional choices in the hierarchical model, 1D functions, and wavelet transforms, the method can be applied more generally using other heavy-tailed distributions, higher dimensional functions (e.g. images), and using other invertible transformations as alternatives to wavelets.

Robust, Adaptive Functional Regression in Functional Mixed Model Framework

PubMed Central

Zhu, Hongxiao; Brown, Philip J.; Morris, Jeffrey S.

2012-01-01

Functional data are increasingly encountered in scientific studies, and their high dimensionality and complexity lead to many analytical challenges. Various methods for functional data analysis have been developed, including functional response regression methods that involve regression of a functional response on univariate/multivariate predictors with nonparametrically represented functional coefficients. In existing methods, however, the functional regression can be sensitive to outlying curves and outlying regions of curves, so is not robust. In this paper, we introduce a new Bayesian method, robust functional mixed models (R-FMM), for performing robust functional regression within the general functional mixed model framework, which includes multiple continuous or categorical predictors and random effect functions accommodating potential between-function correlation induced by the experimental design. The underlying model involves a hierarchical scale mixture model for the fixed effects, random effect and residual error functions. These modeling assumptions across curves result in robust nonparametric estimators of the fixed and random effect functions which down-weight outlying curves and regions of curves, and produce statistics that can be used to flag global and local outliers. These assumptions also lead to distributions across wavelet coefficients that have outstanding sparsity and adaptive shrinkage properties, with great flexibility for the data to determine the sparsity and the heaviness of the tails. Together with the down-weighting of outliers, these within-curve properties lead to fixed and random effect function estimates that appear in our simulations to be remarkably adaptive in their ability to remove spurious features yet retain true features of the functions. We have developed general code to implement this fully Bayesian method that is automatic, requiring the user to only provide the functional data and design matrices. It is efficient enough to handle large data sets, and yields posterior samples of all model parameters that can be used to perform desired Bayesian estimation and inference. Although we present details for a specific implementation of the R-FMM using specific distributional choices in the hierarchical model, 1D functions, and wavelet transforms, the method can be applied more generally using other heavy-tailed distributions, higher dimensional functions (e.g. images), and using other invertible transformations as alternatives to wavelets. PMID:22308015

Verification of Bayesian Clustering in Travel Behaviour Research – First Step to Macroanalysis of Travel Behaviour

NASA Astrophysics Data System (ADS)

Satra, P.; Carsky, J.

2018-04-01

Our research is looking at the travel behaviour from a macroscopic view, taking one municipality as a basic unit. The travel behaviour of one municipality as a whole is becoming one piece of a data in the research of travel behaviour of a larger area, perhaps a country. A data pre-processing is used to cluster the municipalities in groups, which show similarities in their travel behaviour. Such groups can be then researched for reasons of their prevailing pattern of travel behaviour without any distortion caused by municipalities with a different pattern. This paper deals with actual settings of the clustering process, which is based on Bayesian statistics, particularly the mixture model. An optimization of the settings parameters based on correlation of pointer model parameters and relative number of data in clusters is helpful, however not fully reliable method. Thus, method for graphic representation of clusters needs to be developed in order to check their quality. A training of the setting parameters in 2D has proven to be a beneficial method, because it allows visual control of the produced clusters. The clustering better be applied on separate groups of municipalities, where competition of only identical transport modes can be found.

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

PubMed

Jones, Matt; Love, Bradley C

2011-08-01

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

BANYAN. XI. The BANYAN Σ Multivariate Bayesian Algorithm to Identify Members of Young Associations with 150 pc

NASA Astrophysics Data System (ADS)

Gagné, Jonathan; Mamajek, Eric E.; Malo, Lison; Riedel, Adric; Rodriguez, David; Lafrenière, David; Faherty, Jacqueline K.; Roy-Loubier, Olivier; Pueyo, Laurent; Robin, Annie C.; Doyon, René

2018-03-01

BANYAN Σ is a new Bayesian algorithm to identify members of young stellar associations within 150 pc of the Sun. It includes 27 young associations with ages in the range ∼1–800 Myr, modeled with multivariate Gaussians in six-dimensional (6D) XYZUVW space. It is the first such multi-association classification tool to include the nearest sub-groups of the Sco-Cen OB star-forming region, the IC 2602, IC 2391, Pleiades and Platais 8 clusters, and the ρ Ophiuchi, Corona Australis, and Taurus star formation regions. A model of field stars is built from a mixture of multivariate Gaussians based on the Besançon Galactic model. The algorithm can derive membership probabilities for objects with only sky coordinates and proper motion, but can also include parallax and radial velocity measurements, as well as spectrophotometric distance constraints from sequences in color–magnitude or spectral type–magnitude diagrams. BANYAN Σ benefits from an analytical solution to the Bayesian marginalization integrals over unknown radial velocities and distances that makes it more accurate and significantly faster than its predecessor BANYAN II. A contamination versus hit rate analysis is presented and demonstrates that BANYAN Σ achieves a better classification performance than other moving group tools available in the literature, especially in terms of cross-contamination between young associations. An updated list of bona fide members in the 27 young associations, augmented by the Gaia-DR1 release, as well as all parameters for the 6D multivariate Gaussian models for each association and the Galactic field neighborhood within 300 pc are presented. This new tool will make it possible to analyze large data sets such as the upcoming Gaia-DR2 to identify new young stars. IDL and Python versions of BANYAN Σ are made available with this publication, and a more limited online web tool is available at http://www.exoplanetes.umontreal.ca/banyan/banyansigma.php.

How the Bayesians Got Their Beliefs (and What Those Beliefs Actually Are): Comment on Bowers and Davis (2012)

ERIC Educational Resources Information Center

Griffiths, Thomas L.; Chater, Nick; Norris, Dennis; Pouget, Alexandre

2012-01-01

Bowers and Davis (2012) criticize Bayesian modelers for telling "just so" stories about cognition and neuroscience. Their criticisms are weakened by not giving an accurate characterization of the motivation behind Bayesian modeling or the ways in which Bayesian models are used and by not evaluating this theoretical framework against specific…

Bayesian Regression with Network Prior: Optimal Bayesian Filtering Perspective

PubMed Central

Qian, Xiaoning; Dougherty, Edward R.

2017-01-01

The recently introduced intrinsically Bayesian robust filter (IBRF) provides fully optimal filtering relative to a prior distribution over an uncertainty class ofjoint random process models, whereas formerly the theory was limited to model-constrained Bayesian robust filters, for which optimization was limited to the filters that are optimal for models in the uncertainty class. This paper extends the IBRF theory to the situation where there are both a prior on the uncertainty class and sample data. The result is optimal Bayesian filtering (OBF), where optimality is relative to the posterior distribution derived from the prior and the data. The IBRF theories for effective characteristics and canonical expansions extend to the OBF setting. A salient focus of the present work is to demonstrate the advantages of Bayesian regression within the OBF setting over the classical Bayesian approach in the context otlinear Gaussian models. PMID:28824268

Modeling Diagnostic Assessments with Bayesian Networks

ERIC Educational Resources Information Center

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…

Comparing spatially varying coefficient models: a case study examining violent crime rates and their relationships to alcohol outlets and illegal drug arrests

NASA Astrophysics Data System (ADS)

Wheeler, David C.; Waller, Lance A.

2009-03-01

In this paper, we compare and contrast a Bayesian spatially varying coefficient process (SVCP) model with a geographically weighted regression (GWR) model for the estimation of the potentially spatially varying regression effects of alcohol outlets and illegal drug activity on violent crime in Houston, Texas. In addition, we focus on the inherent coefficient shrinkage properties of the Bayesian SVCP model as a way to address increased coefficient variance that follows from collinearity in GWR models. We outline the advantages of the Bayesian model in terms of reducing inflated coefficient variance, enhanced model flexibility, and more formal measuring of model uncertainty for prediction. We find spatially varying effects for alcohol outlets and drug violations, but the amount of variation depends on the type of model used. For the Bayesian model, this variation is controllable through the amount of prior influence placed on the variance of the coefficients. For example, the spatial pattern of coefficients is similar for the GWR and Bayesian models when a relatively large prior variance is used in the Bayesian model.

Philosophy and the practice of Bayesian statistics

PubMed Central

Gelman, Andrew; Shalizi, Cosma Rohilla

2015-01-01

A substantial school in the philosophy of science identifies Bayesian inference with inductive inference and even rationality as such, and seems to be strengthened by the rise and practical success of Bayesian statistics. We argue that the most successful forms of Bayesian statistics do not actually support that particular philosophy but rather accord much better with sophisticated forms of hypothetico-deductivism. We examine the actual role played by prior distributions in Bayesian models, and the crucial aspects of model checking and model revision, which fall outside the scope of Bayesian confirmation theory. We draw on the literature on the consistency of Bayesian updating and also on our experience of applied work in social science. Clarity about these matters should benefit not just philosophy of science, but also statistical practice. At best, the inductivist view has encouraged researchers to fit and compare models without checking them; at worst, theorists have actively discouraged practitioners from performing model checking because it does not fit into their framework. PMID:22364575

Philosophy and the practice of Bayesian statistics.

PubMed

Gelman, Andrew; Shalizi, Cosma Rohilla

2013-02-01

A substantial school in the philosophy of science identifies Bayesian inference with inductive inference and even rationality as such, and seems to be strengthened by the rise and practical success of Bayesian statistics. We argue that the most successful forms of Bayesian statistics do not actually support that particular philosophy but rather accord much better with sophisticated forms of hypothetico-deductivism. We examine the actual role played by prior distributions in Bayesian models, and the crucial aspects of model checking and model revision, which fall outside the scope of Bayesian confirmation theory. We draw on the literature on the consistency of Bayesian updating and also on our experience of applied work in social science. Clarity about these matters should benefit not just philosophy of science, but also statistical practice. At best, the inductivist view has encouraged researchers to fit and compare models without checking them; at worst, theorists have actively discouraged practitioners from performing model checking because it does not fit into their framework. © 2012 The British Psychological Society.

Bayesian inference based on dual generalized order statistics from the exponentiated Weibull model

NASA Astrophysics Data System (ADS)

Al Sobhi, Mashail M.

2015-02-01

Bayesian estimation for the two parameters and the reliability function of the exponentiated Weibull model are obtained based on dual generalized order statistics (DGOS). Also, Bayesian prediction bounds for future DGOS from exponentiated Weibull model are obtained. The symmetric and asymmetric loss functions are considered for Bayesian computations. The Markov chain Monte Carlo (MCMC) methods are used for computing the Bayes estimates and prediction bounds. The results have been specialized to the lower record values. Comparisons are made between Bayesian and maximum likelihood estimators via Monte Carlo simulation.

Analysis of the observed and intrinsic durations of Swift/BAT gamma-ray bursts

NASA Astrophysics Data System (ADS)

Tarnopolski, Mariusz

2016-07-01

The duration distribution of 947 GRBs observed by Swift/BAT, as well as its subsample of 347 events with measured redshift, allowing to examine the durations in both the observer and rest frames, are examined. Using a maximum log-likelihood method, mixtures of two and three standard Gaussians are fitted to each sample, and the adequate model is chosen based on the value of the difference in the log-likelihoods, Akaike information criterion and Bayesian information criterion. It is found that a two-Gaussian is a better description than a three-Gaussian, and that the presumed intermediate-duration class is unlikely to be present in the Swift duration data.

Strong consistency of nonparametric Bayes density estimation on compact metric spaces with applications to specific manifolds

PubMed Central

Bhattacharya, Abhishek; Dunson, David B.

2012-01-01

This article considers a broad class of kernel mixture density models on compact metric spaces and manifolds. Following a Bayesian approach with a nonparametric prior on the location mixing distribution, sufficient conditions are obtained on the kernel, prior and the underlying space for strong posterior consistency at any continuous density. The prior is also allowed to depend on the sample size n and sufficient conditions are obtained for weak and strong consistency. These conditions are verified on compact Euclidean spaces using multivariate Gaussian kernels, on the hypersphere using a von Mises-Fisher kernel and on the planar shape space using complex Watson kernels. PMID:22984295

Fundamentals and Recent Developments in Approximate Bayesian Computation

PubMed Central

Lintusaari, Jarno; Gutmann, Michael U.; Dutta, Ritabrata; Kaski, Samuel; Corander, Jukka

2017-01-01

Abstract Bayesian inference plays an important role in phylogenetics, evolutionary biology, and in many other branches of science. It provides a principled framework for dealing with uncertainty and quantifying how it changes in the light of new evidence. For many complex models and inference problems, however, only approximate quantitative answers are obtainable. Approximate Bayesian computation (ABC) refers to a family of algorithms for approximate inference that makes a minimal set of assumptions by only requiring that sampling from a model is possible. We explain here the fundamentals of ABC, review the classical algorithms, and highlight recent developments. [ABC; approximate Bayesian computation; Bayesian inference; likelihood-free inference; phylogenetics; simulator-based models; stochastic simulation models; tree-based models.] PMID:28175922

Essays on inference in economics, competition, and the rate of profit

NASA Astrophysics Data System (ADS)

Scharfenaker, Ellis S.

This dissertation is comprised of three papers that demonstrate the role of Bayesian methods of inference and Shannon's information theory in classical political economy. The first chapter explores the empirical distribution of profit rate data from North American firms from 1962-2012. This chapter address the fact that existing methods for sample selection from noisy profit rate data in the industrial organization field of economics tends to be conditional on a covariate's value that risks discarding information. Conditioning sample selection instead on the profit rate data's structure by means of a two component (signal and noise) Bayesian mixture model we find the the profit rate sample to be time stationary Laplace distributed, corroborating earlier estimates of cross section distributions. The second chapter compares alternative probabilistic approaches to discrete (quantal) choice analysis and examines the various ways in which they overlap. In particular, the work on individual choice behavior by Duncan Luce and the extension of this work to quantal response problems by game theoreticians is shown to be related both to the rational inattention work of Christopher Sims through Shannon's information theory as well as to the maximum entropy principle of inference proposed physicist Edwin T. Jaynes. In the third chapter I propose a model of ``classically" competitive firms facing informational entropy constraints in their decisions to potentially enter or exit markets based on profit rate differentials. The result is a three parameter logit quantal response distribution for firm entry and exit decisions. Bayesian methods are used for inference into the the distribution of entry and exit decisions conditional on profit rate deviations and firm level data from Compustat is used to test these predictions.

Efficient fuzzy Bayesian inference algorithms for incorporating expert knowledge in parameter estimation

NASA Astrophysics Data System (ADS)

Rajabi, Mohammad Mahdi; Ataie-Ashtiani, Behzad

2016-05-01

Bayesian inference has traditionally been conceived as the proper framework for the formal incorporation of expert knowledge in parameter estimation of groundwater models. However, conventional Bayesian inference is incapable of taking into account the imprecision essentially embedded in expert provided information. In order to solve this problem, a number of extensions to conventional Bayesian inference have been introduced in recent years. One of these extensions is 'fuzzy Bayesian inference' which is the result of integrating fuzzy techniques into Bayesian statistics. Fuzzy Bayesian inference has a number of desirable features which makes it an attractive approach for incorporating expert knowledge in the parameter estimation process of groundwater models: (1) it is well adapted to the nature of expert provided information, (2) it allows to distinguishably model both uncertainty and imprecision, and (3) it presents a framework for fusing expert provided information regarding the various inputs of the Bayesian inference algorithm. However an important obstacle in employing fuzzy Bayesian inference in groundwater numerical modeling applications is the computational burden, as the required number of numerical model simulations often becomes extremely exhaustive and often computationally infeasible. In this paper, a novel approach of accelerating the fuzzy Bayesian inference algorithm is proposed which is based on using approximate posterior distributions derived from surrogate modeling, as a screening tool in the computations. The proposed approach is first applied to a synthetic test case of seawater intrusion (SWI) in a coastal aquifer. It is shown that for this synthetic test case, the proposed approach decreases the number of required numerical simulations by an order of magnitude. Then the proposed approach is applied to a real-world test case involving three-dimensional numerical modeling of SWI in Kish Island, located in the Persian Gulf. An expert elicitation methodology is developed and applied to the real-world test case in order to provide a road map for the use of fuzzy Bayesian inference in groundwater modeling applications.

Strelka: accurate somatic small-variant calling from sequenced tumor-normal sample pairs.

PubMed

Saunders, Christopher T; Wong, Wendy S W; Swamy, Sajani; Becq, Jennifer; Murray, Lisa J; Cheetham, R Keira

2012-07-15

Whole genome and exome sequencing of matched tumor-normal sample pairs is becoming routine in cancer research. The consequent increased demand for somatic variant analysis of paired samples requires methods specialized to model this problem so as to sensitively call variants at any practical level of tumor impurity. We describe Strelka, a method for somatic SNV and small indel detection from sequencing data of matched tumor-normal samples. The method uses a novel Bayesian approach which represents continuous allele frequencies for both tumor and normal samples, while leveraging the expected genotype structure of the normal. This is achieved by representing the normal sample as a mixture of germline variation with noise, and representing the tumor sample as a mixture of the normal sample with somatic variation. A natural consequence of the model structure is that sensitivity can be maintained at high tumor impurity without requiring purity estimates. We demonstrate that the method has superior accuracy and sensitivity on impure samples compared with approaches based on either diploid genotype likelihoods or general allele-frequency tests. The Strelka workflow source code is available at ftp://strelka@ftp.illumina.com/. csaunders@illumina.com

TMA Navigator: network inference, patient stratification and survival analysis with tissue microarray data

PubMed Central

Lubbock, Alexander L. R.; Katz, Elad; Harrison, David J.; Overton, Ian M.

2013-01-01

Tissue microarrays (TMAs) allow multiplexed analysis of tissue samples and are frequently used to estimate biomarker protein expression in tumour biopsies. TMA Navigator (www.tmanavigator.org) is an open access web application for analysis of TMA data and related information, accommodating categorical, semi-continuous and continuous expression scores. Non-biological variation, or batch effects, can hinder data analysis and may be mitigated using the ComBat algorithm, which is incorporated with enhancements for automated application to TMA data. Unsupervised grouping of samples (patients) is provided according to Gaussian mixture modelling of marker scores, with cardinality selected by Bayesian information criterion regularization. Kaplan–Meier survival analysis is available, including comparison of groups identified by mixture modelling using the Mantel-Cox log-rank test. TMA Navigator also supports network inference approaches useful for TMA datasets, which often constitute comparatively few markers. Tissue and cell-type specific networks derived from TMA expression data offer insights into the molecular logic underlying pathophenotypes, towards more effective and personalized medicine. Output is interactive, and results may be exported for use with external programs. Private anonymous access is available, and user accounts may be generated for easier data management. PMID:23761446

Bayesian cross-validation for model evaluation and selection, with application to the North American Breeding Bird Survey

USGS Publications Warehouse

Link, William; Sauer, John R.

2016-01-01

The analysis of ecological data has changed in two important ways over the last 15 years. The development and easy availability of Bayesian computational methods has allowed and encouraged the fitting of complex hierarchical models. At the same time, there has been increasing emphasis on acknowledging and accounting for model uncertainty. Unfortunately, the ability to fit complex models has outstripped the development of tools for model selection and model evaluation: familiar model selection tools such as Akaike's information criterion and the deviance information criterion are widely known to be inadequate for hierarchical models. In addition, little attention has been paid to the evaluation of model adequacy in context of hierarchical modeling, i.e., to the evaluation of fit for a single model. In this paper, we describe Bayesian cross-validation, which provides tools for model selection and evaluation. We describe the Bayesian predictive information criterion and a Bayesian approximation to the BPIC known as the Watanabe-Akaike information criterion. We illustrate the use of these tools for model selection, and the use of Bayesian cross-validation as a tool for model evaluation, using three large data sets from the North American Breeding Bird Survey.

Bayesian networks for maritime traffic accident prevention: benefits and challenges.

PubMed

Hänninen, Maria

2014-12-01

Bayesian networks are quantitative modeling tools whose applications to the maritime traffic safety context are becoming more popular. This paper discusses the utilization of Bayesian networks in maritime safety modeling. Based on literature and the author's own experiences, the paper studies what Bayesian networks can offer to maritime accident prevention and safety modeling and discusses a few challenges in their application to this context. It is argued that the capability of representing rather complex, not necessarily causal but uncertain relationships makes Bayesian networks an attractive modeling tool for the maritime safety and accidents. Furthermore, as the maritime accident and safety data is still rather scarce and has some quality problems, the possibility to combine data with expert knowledge and the easy way of updating the model after acquiring more evidence further enhance their feasibility. However, eliciting the probabilities from the maritime experts might be challenging and the model validation can be tricky. It is concluded that with the utilization of several data sources, Bayesian updating, dynamic modeling, and hidden nodes for latent variables, Bayesian networks are rather well-suited tools for the maritime safety management and decision-making. Copyright © 2014 Elsevier Ltd. All rights reserved.

Estimation of Microbial Contamination of Food from Prevalence and Concentration Data: Application to Listeria monocytogenes in Fresh Vegetables▿

PubMed Central

Crépet, Amélie; Albert, Isabelle; Dervin, Catherine; Carlin, Frédéric

2007-01-01

A normal distribution and a mixture model of two normal distributions in a Bayesian approach using prevalence and concentration data were used to establish the distribution of contamination of the food-borne pathogenic bacteria Listeria monocytogenes in unprocessed and minimally processed fresh vegetables. A total of 165 prevalence studies, including 15 studies with concentration data, were taken from the scientific literature and from technical reports and used for statistical analysis. The predicted mean of the normal distribution of the logarithms of viable L. monocytogenes per gram of fresh vegetables was −2.63 log viable L. monocytogenes organisms/g, and its standard deviation was 1.48 log viable L. monocytogenes organisms/g. These values were determined by considering one contaminated sample in prevalence studies in which samples are in fact negative. This deliberate overestimation is necessary to complete calculations. With the mixture model, the predicted mean of the distribution of the logarithm of viable L. monocytogenes per gram of fresh vegetables was −3.38 log viable L. monocytogenes organisms/g and its standard deviation was 1.46 log viable L. monocytogenes organisms/g. The probabilities of fresh unprocessed and minimally processed vegetables being contaminated with concentrations higher than 1, 2, and 3 log viable L. monocytogenes organisms/g were 1.44, 0.63, and 0.17%, respectively. Introducing a sensitivity rate of 80 or 95% in the mixture model had a small effect on the estimation of the contamination. In contrast, introducing a low sensitivity rate (40%) resulted in marked differences, especially for high percentiles. There was a significantly lower estimation of contamination in the papers and reports of 2000 to 2005 than in those of 1988 to 1999 and a lower estimation of contamination of leafy salads than that of sprouts and other vegetables. The interest of the mixture model for the estimation of microbial contamination is discussed. PMID:17098926

Bayesian Framework for Water Quality Model Uncertainty Estimation and Risk Management

EPA Science Inventory

A formal Bayesian methodology is presented for integrated model calibration and risk-based water quality management using Bayesian Monte Carlo simulation and maximum likelihood estimation (BMCML). The primary focus is on lucid integration of model calibration with risk-based wat...

Dynamic foraging of a top predator in a seasonal polar marine environment.

PubMed

Weinstein, Ben G; Friedlaender, Ari S

2017-11-01

The seasonal movement of animals at broad spatial scales provides insight into life-history, ecology and conservation. By combining high-resolution satellite-tagged data with hierarchical Bayesian movement models, we can associate spatial patterns of movement with marine animal behavior. We used a multi-state mixture model to describe humpback whale traveling and area-restricted search states as they forage along the West Antarctic Peninsula. We estimated the change in the geography, composition and characteristics of these behavioral states through time. We show that whales later in the austral fall spent more time in movements associated with foraging, traveled at lower speeds between foraging areas, and shifted their distribution northward and inshore. Seasonal changes in movement are likely due to a combination of sea ice advance and regional shifts in the primary prey source. Our study is a step towards dynamic movement models in the marine environment at broad scales.

Generative Topographic Mapping (GTM): Universal Tool for Data Visualization, Structure-Activity Modeling and Dataset Comparison.

PubMed

Kireeva, N; Baskin, I I; Gaspar, H A; Horvath, D; Marcou, G; Varnek, A

2012-04-01

Here, the utility of Generative Topographic Maps (GTM) for data visualization, structure-activity modeling and database comparison is evaluated, on hand of subsets of the Database of Useful Decoys (DUD). Unlike other popular dimensionality reduction approaches like Principal Component Analysis, Sammon Mapping or Self-Organizing Maps, the great advantage of GTMs is providing data probability distribution functions (PDF), both in the high-dimensional space defined by molecular descriptors and in 2D latent space. PDFs for the molecules of different activity classes were successfully used to build classification models in the framework of the Bayesian approach. Because PDFs are represented by a mixture of Gaussian functions, the Bhattacharyya kernel has been proposed as a measure of the overlap of datasets, which leads to an elegant method of global comparison of chemical libraries. Copyright © 2012 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim.

Design space construction of multiple dose-strength tablets utilizing bayesian estimation based on one set of design-of-experiments.

PubMed

Maeda, Jin; Suzuki, Tatsuya; Takayama, Kozo

2012-01-01

Design spaces for multiple dose strengths of tablets were constructed using a Bayesian estimation method with one set of design of experiments (DoE) of only the highest dose-strength tablet. The lubricant blending process for theophylline tablets with dose strengths of 100, 50, and 25 mg is used as a model manufacturing process in order to construct design spaces. The DoE was conducted using various Froude numbers (X(1)) and blending times (X(2)) for theophylline 100-mg tablet. The response surfaces, design space, and their reliability of the compression rate of the powder mixture (Y(1)), tablet hardness (Y(2)), and dissolution rate (Y(3)) of the 100-mg tablet were calculated using multivariate spline interpolation, a bootstrap resampling technique, and self-organizing map clustering. Three experiments under an optimal condition and two experiments under other conditions were performed using 50- and 25-mg tablets, respectively. The response surfaces of the highest-strength tablet were corrected to those of the lower-strength tablets by Bayesian estimation using the manufacturing data of the lower-strength tablets. Experiments under three additional sets of conditions of lower-strength tablets showed that the corrected design space made it possible to predict the quality of lower-strength tablets more precisely than the design space of the highest-strength tablet. This approach is useful for constructing design spaces of tablets with multiple strengths.

Cyber-T web server: differential analysis of high-throughput data.

PubMed

Kayala, Matthew A; Baldi, Pierre

2012-07-01

The Bayesian regularization method for high-throughput differential analysis, described in Baldi and Long (A Bayesian framework for the analysis of microarray expression data: regularized t-test and statistical inferences of gene changes. Bioinformatics 2001: 17: 509-519) and implemented in the Cyber-T web server, is one of the most widely validated. Cyber-T implements a t-test using a Bayesian framework to compute a regularized variance of the measurements associated with each probe under each condition. This regularized estimate is derived by flexibly combining the empirical measurements with a prior, or background, derived from pooling measurements associated with probes in the same neighborhood. This approach flexibly addresses problems associated with low replication levels and technology biases, not only for DNA microarrays, but also for other technologies, such as protein arrays, quantitative mass spectrometry and next-generation sequencing (RNA-seq). Here we present an update to the Cyber-T web server, incorporating several useful new additions and improvements. Several preprocessing data normalization options including logarithmic and (Variance Stabilizing Normalization) VSN transforms are included. To augment two-sample t-tests, a one-way analysis of variance is implemented. Several methods for multiple tests correction, including standard frequentist methods and a probabilistic mixture model treatment, are available. Diagnostic plots allow visual assessment of the results. The web server provides comprehensive documentation and example data sets. The Cyber-T web server, with R source code and data sets, is publicly available at http://cybert.ics.uci.edu/.

A latent class distance association model for cross-classified data with a categorical response variable.

PubMed

Vera, José Fernando; de Rooij, Mark; Heiser, Willem J

2014-11-01

In this paper we propose a latent class distance association model for clustering in the predictor space of large contingency tables with a categorical response variable. The rows of such a table are characterized as profiles of a set of explanatory variables, while the columns represent a single outcome variable. In many cases such tables are sparse, with many zero entries, which makes traditional models problematic. By clustering the row profiles into a few specific classes and representing these together with the categories of the response variable in a low-dimensional Euclidean space using a distance association model, a parsimonious prediction model can be obtained. A generalized EM algorithm is proposed to estimate the model parameters and the adjusted Bayesian information criterion statistic is employed to test the number of mixture components and the dimensionality of the representation. An empirical example highlighting the advantages of the new approach and comparing it with traditional approaches is presented. © 2014 The British Psychological Society.

Fingerprinting Sources of Suspended Sediment in a Canadian Agricultural Watershed Using the MixSIAR Bayesian Unmixing Model

NASA Astrophysics Data System (ADS)

Smith, J. P.; Owens, P. N.; Gaspar, L.; Lobb, D. A.; Petticrew, E. L.

2015-12-01

An understanding of sediment redistribution processes and the main sediment sources within a watershed is needed to support watershed management strategies. The fingerprinting technique is increasingly being recognized as a method for establishing the source of the sediment transported within watersheds. However, the different behaviour of the various fingerprinting properties has been recognized as a major limitation of the technique, and the uncertainty associated with tracer selection needs to be addressed. There are also questions associated with which modelling approach (frequentist or Bayesian) is the best to unmix complex environmental mixtures, such as river sediment. This study aims to compare and evaluate the differences between fingerprinting predictions provided by a Bayesian unmixing model (MixSIAR) using different groups of tracer properties for use in sediment source identification. We used fallout radionuclides (e.g. 137Cs) and geochemical elements (e.g. As) as conventional fingerprinting properties, and colour parameters as emerging properties; both alone and in combination. These fingerprinting properties are being used (i.e. Koiter et al., 2013; Barthod et al., 2015) to determine the proportional contributions of fine sediment in the South Tobacco Creek Watershed, an agricultural watershed located in Manitoba, Canada. We show that the unmixing model using a combination of fallout radionuclides and geochemical tracers gave similar results to the model based on colour parameters. Furthermore, we show that a model that combines all tracers (i.e. radionuclide/geochemical and colour) gave similar results, showing that sediment sources change from predominantly topsoil in the upper reaches of the watershed to channel bank and bedrock outcrop material in the lower reaches. Barthod LRM et al. (2015). Selecting color-based tracers and classifying sediment sources in the assessment of sediment dynamics using sediment source fingerprinting. J Environ Qual. Doi:10.2134/jeq2015.01.0043 Koiter AJ et al. (2013). Investigating the role of connectivity and scale in assessing the sources of sediment in an agricultural watershed in the Canadian prairies using sediment source fingerprinting. J Soils Sediments, 13, 1676-1691.

A Comparison of General Diagnostic Models (GDM) and Bayesian Networks Using a Middle School Mathematics Test

ERIC Educational Resources Information Center

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…

US Transuranium and Uranium Registries case study on accidental exposure to uranium hexafluoride.

PubMed

Avtandilashvili, Maia; Puncher, Matthew; McComish, Stacey L; Tolmachev, Sergei Y

2015-03-01

The United States Transuranium and Uranium Registries' (USTUR) whole-body donor (Case 1031) was exposed to an acute inhalation of uranium hexafluoride (UF6) produced from an explosion at a uranium processing plant 65 years prior to his death. The USTUR measurements of tissue samples collected at the autopsy indicated long-term retention of inhaled slightly enriched uranium material (0.85% (235)U) in the deep lungs and thoracic lymph nodes. In the present study, the authors combined the tissue measurement results with historical bioassay data, and analysed them with International Commission on Radiological Protection (ICRP) respiratory tract models and the ICRP Publication 69 systemic model for uranium using maximum likelihood and Bayesian statistical methods. The purpose of the analysis was to estimate intakes and model parameter values that best describe the data, and evaluate their effect on dose assessment. The maximum likelihood analysis, which used the ICRP Publication 66 human respiratory tract model, resulted in a point estimate of 79 mg of uranium for the occupational intake composed of 86% soluble, type F material and 14% insoluble, type S material. For the Bayesian approach, the authors applied the Markov Chain Monte Carlo method, but this time used the revised human respiratory tract model, which is currently being used by ICRP to calculate new dose coefficients for workers. The Bayesian analysis estimated that the mean uranium intake was 160 mg, and calculated the case-specific lung dissolution parameters with their associated uncertainties. The parameters were consistent with the inhaled uranium material being predominantly soluble with a small but significant insoluble component. The 95% posterior range of the rapid dissolution fraction (the fraction of deposited material that is absorbed to blood rapidly) was 0.12 to 0.91 with a median of 0.37. The remaining fraction was absorbed slowly, with a 95% range of 0.000 22 d(-1) to 0.000 36 d(-1) and a median of 0.000 31 d(-1). The effective dose per unit intake calculated using the dissolution parameters derived from the maximum likelihood and the Bayesian analyses was higher than the current ICRP dose coefficient for type F uranium by a factor of 2 or 7, respectively; the higher value of the latter was due to use of the revised respiratory tract model. The dissolution parameter values obtained here may be more appropriate to use for radiation protection purposes when individuals are exposed to a UF6 mixture that contains an insoluble uranium component.

Perceptual decision making: drift-diffusion model is equivalent to a Bayesian model

PubMed Central

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. PMID:24616689

Construction of monitoring model and algorithm design on passenger security during shipping based on improved Bayesian network.

PubMed

Wang, Jiali; Zhang, Qingnian; Ji, Wenfeng

2014-01-01

A large number of data is needed by the computation of the objective Bayesian network, but the data is hard to get in actual computation. The calculation method of Bayesian network was improved in this paper, and the fuzzy-precise Bayesian network was obtained. Then, the fuzzy-precise Bayesian network was used to reason Bayesian network model when the data is limited. The security of passengers during shipping is affected by various factors, and it is hard to predict and control. The index system that has the impact on the passenger safety during shipping was established on basis of the multifield coupling theory in this paper. Meanwhile, the fuzzy-precise Bayesian network was applied to monitor the security of passengers in the shipping process. The model was applied to monitor the passenger safety during shipping of a shipping company in Hainan, and the effectiveness of this model was examined. This research work provides guidance for guaranteeing security of passengers during shipping.

Construction of Monitoring Model and Algorithm Design on Passenger Security during Shipping Based on Improved Bayesian Network

PubMed Central

Wang, Jiali; Zhang, Qingnian; Ji, Wenfeng

2014-01-01

A large number of data is needed by the computation of the objective Bayesian network, but the data is hard to get in actual computation. The calculation method of Bayesian network was improved in this paper, and the fuzzy-precise Bayesian network was obtained. Then, the fuzzy-precise Bayesian network was used to reason Bayesian network model when the data is limited. The security of passengers during shipping is affected by various factors, and it is hard to predict and control. The index system that has the impact on the passenger safety during shipping was established on basis of the multifield coupling theory in this paper. Meanwhile, the fuzzy-precise Bayesian network was applied to monitor the security of passengers in the shipping process. The model was applied to monitor the passenger safety during shipping of a shipping company in Hainan, and the effectiveness of this model was examined. This research work provides guidance for guaranteeing security of passengers during shipping. PMID:25254227

Hierarchical Bayesian Modeling of Fluid-Induced Seismicity

NASA Astrophysics Data System (ADS)

Broccardo, M.; Mignan, A.; Wiemer, S.; Stojadinovic, B.; Giardini, D.

2017-11-01

In this study, we present a Bayesian hierarchical framework to model fluid-induced seismicity. The framework is based on a nonhomogeneous Poisson process with a fluid-induced seismicity rate proportional to the rate of injected fluid. The fluid-induced seismicity rate model depends upon a set of physically meaningful parameters and has been validated for six fluid-induced case studies. In line with the vision of hierarchical Bayesian modeling, the rate parameters are considered as random variables. We develop both the Bayesian inference and updating rules, which are used to develop a probabilistic forecasting model. We tested the Basel 2006 fluid-induced seismic case study to prove that the hierarchical Bayesian model offers a suitable framework to coherently encode both epistemic uncertainty and aleatory variability. Moreover, it provides a robust and consistent short-term seismic forecasting model suitable for online risk quantification and mitigation.

Estimating virus occurrence using Bayesian modeling in multiple drinking water systems of the United States

USGS Publications Warehouse

Varughese, Eunice A.; Brinkman, Nichole E; Anneken, Emily M; Cashdollar, Jennifer S; Fout, G. Shay; Furlong, Edward T.; Kolpin, Dana W.; Glassmeyer, Susan T.; Keely, Scott P

2017-01-01

incorporated into a Bayesian model to more accurately determine viral load in both source and treated water. Results of the Bayesian model indicated that viruses are present in source water and treated water. By using a Bayesian framework that incorporates inhibition, as well as many other parameters that affect viral detection, this study offers an approach for more accurately estimating the occurrence of viral pathogens in environmental waters.

ADAPTIVE ANNEALED IMPORTANCE SAMPLING FOR MULTIMODAL POSTERIOR EXPLORATION AND MODEL SELECTION WITH APPLICATION TO EXTRASOLAR PLANET DETECTION

DOE Office of Scientific and Technical Information (OSTI.GOV)

Liu, Bin, E-mail: bins@ieee.org

2014-07-01

We describe an algorithm that can adaptively provide mixture summaries of multimodal posterior distributions. The parameter space of the involved posteriors ranges in size from a few dimensions to dozens of dimensions. This work was motivated by an astrophysical problem called extrasolar planet (exoplanet) detection, wherein the computation of stochastic integrals that are required for Bayesian model comparison is challenging. The difficulty comes from the highly nonlinear models that lead to multimodal posterior distributions. We resort to importance sampling (IS) to estimate the integrals, and thus translate the problem to be how to find a parametric approximation of the posterior.more » To capture the multimodal structure in the posterior, we initialize a mixture proposal distribution and then tailor its parameters elaborately to make it resemble the posterior to the greatest extent possible. We use the effective sample size (ESS) calculated based on the IS draws to measure the degree of approximation. The bigger the ESS is, the better the proposal resembles the posterior. A difficulty within this tailoring operation lies in the adjustment of the number of mixing components in the mixture proposal. Brute force methods just preset it as a large constant, which leads to an increase in the required computational resources. We provide an iterative delete/merge/add process, which works in tandem with an expectation-maximization step to tailor such a number online. The efficiency of our proposed method is tested via both simulation studies and real exoplanet data analysis.« less

A local approach for focussed Bayesian fusion

NASA Astrophysics Data System (ADS)

Sander, Jennifer; Heizmann, Michael; Goussev, Igor; Beyerer, Jürgen

2009-04-01

Local Bayesian fusion approaches aim to reduce high storage and computational costs of Bayesian fusion which is separated from fixed modeling assumptions. Using the small world formalism, we argue why this proceeding is conform with Bayesian theory. Then, we concentrate on the realization of local Bayesian fusion by focussing the fusion process solely on local regions that are task relevant with a high probability. The resulting local models correspond then to restricted versions of the original one. In a previous publication, we used bounds for the probability of misleading evidence to show the validity of the pre-evaluation of task specific knowledge and prior information which we perform to build local models. In this paper, we prove the validity of this proceeding using information theoretic arguments. For additional efficiency, local Bayesian fusion can be realized in a distributed manner. Here, several local Bayesian fusion tasks are evaluated and unified after the actual fusion process. For the practical realization of distributed local Bayesian fusion, software agents are predestinated. There is a natural analogy between the resulting agent based architecture and criminal investigations in real life. We show how this analogy can be used to improve the efficiency of distributed local Bayesian fusion additionally. Using a landscape model, we present an experimental study of distributed local Bayesian fusion in the field of reconnaissance, which highlights its high potential.

A bayesian cross-validation approach to evaluate genetic baselines and forecast the necessary number of informative single nucleotide polymorphisms

USDA-ARS?s Scientific Manuscript database

Mixed stock analysis (MSA) is a powerful tool used in the management and conservation of numerous species. Its function is to estimate the sources of contributions in a mixture of populations of a species, as well as to estimate the probabilities that individuals originated at a source. Considerable...

A Variational Bayes Genomic-Enabled Prediction Model with Genotype × Environment Interaction

PubMed Central

Montesinos-López, Osval A.; Montesinos-López, Abelardo; Crossa, José; Montesinos-López, José Cricelio; Luna-Vázquez, Francisco Javier; Salinas-Ruiz, Josafhat; Herrera-Morales, José R.; Buenrostro-Mariscal, Raymundo

2017-01-01

There are Bayesian and non-Bayesian genomic models that take into account G×E interactions. However, the computational cost of implementing Bayesian models is high, and becomes almost impossible when the number of genotypes, environments, and traits is very large, while, in non-Bayesian models, there are often important and unsolved convergence problems. The variational Bayes method is popular in machine learning, and, by approximating the probability distributions through optimization, it tends to be faster than Markov Chain Monte Carlo methods. For this reason, in this paper, we propose a new genomic variational Bayes version of the Bayesian genomic model with G×E using half-t priors on each standard deviation (SD) term to guarantee highly noninformative and posterior inferences that are not sensitive to the choice of hyper-parameters. We show the complete theoretical derivation of the full conditional and the variational posterior distributions, and their implementations. We used eight experimental genomic maize and wheat data sets to illustrate the new proposed variational Bayes approximation, and compared its predictions and implementation time with a standard Bayesian genomic model with G×E. Results indicated that prediction accuracies are slightly higher in the standard Bayesian model with G×E than in its variational counterpart, but, in terms of computation time, the variational Bayes genomic model with G×E is, in general, 10 times faster than the conventional Bayesian genomic model with G×E. For this reason, the proposed model may be a useful tool for researchers who need to predict and select genotypes in several environments. PMID:28391241

A Variational Bayes Genomic-Enabled Prediction Model with Genotype × Environment Interaction.

PubMed

Montesinos-López, Osval A; Montesinos-López, Abelardo; Crossa, José; Montesinos-López, José Cricelio; Luna-Vázquez, Francisco Javier; Salinas-Ruiz, Josafhat; Herrera-Morales, José R; Buenrostro-Mariscal, Raymundo

2017-06-07

There are Bayesian and non-Bayesian genomic models that take into account G×E interactions. However, the computational cost of implementing Bayesian models is high, and becomes almost impossible when the number of genotypes, environments, and traits is very large, while, in non-Bayesian models, there are often important and unsolved convergence problems. The variational Bayes method is popular in machine learning, and, by approximating the probability distributions through optimization, it tends to be faster than Markov Chain Monte Carlo methods. For this reason, in this paper, we propose a new genomic variational Bayes version of the Bayesian genomic model with G×E using half-t priors on each standard deviation (SD) term to guarantee highly noninformative and posterior inferences that are not sensitive to the choice of hyper-parameters. We show the complete theoretical derivation of the full conditional and the variational posterior distributions, and their implementations. We used eight experimental genomic maize and wheat data sets to illustrate the new proposed variational Bayes approximation, and compared its predictions and implementation time with a standard Bayesian genomic model with G×E. Results indicated that prediction accuracies are slightly higher in the standard Bayesian model with G×E than in its variational counterpart, but, in terms of computation time, the variational Bayes genomic model with G×E is, in general, 10 times faster than the conventional Bayesian genomic model with G×E. For this reason, the proposed model may be a useful tool for researchers who need to predict and select genotypes in several environments. Copyright © 2017 Montesinos-López et al.

Bayesian Models for Astrophysical Data Using R, JAGS, Python, and Stan

NASA Astrophysics Data System (ADS)

Hilbe, Joseph M.; de Souza, Rafael S.; Ishida, Emille E. O.

2017-05-01

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

Exploring factors related to metastasis free survival in breast cancer patients using Bayesian cure models.

PubMed

Jafari-Koshki, Tohid; Mansourian, Marjan; Mokarian, Fariborz

2014-01-01

Breast cancer is a fatal disease and the most frequently diagnosed cancer in women with an increasing pattern worldwide. The burden is mostly attributed to metastatic cancers that occur in one-third of patients and the treatments are palliative. It is of great interest to determine factors affecting time from cancer diagnosis to secondary metastasis. Cure rate models assume a Poisson distribution for the number of unobservable metastatic-component cells that are completely deleted from the non-metastasis patient body but some may remain and result in metastasis. Time to metastasis is defined as a function of the number of these cells and the time for each cell to develop a detectable sign of metastasis. Covariates are introduced to the model via the rate of metastatic-component cells. We used non-mixture cure rate models with Weibull and log-logistic distributions in a Bayesian setting to assess the relationship between metastasis free survival and covariates. The median of metastasis free survival was 76.9 months. Various models showed that from covariates in the study, lymph node involvement ratio and being progesterone receptor positive were significant, with an adverse and a beneficial effect on metastasis free survival, respectively. The estimated fraction of patients cured from metastasis was almost 48%. The Weibull model had a slightly better performance than log-logistic. Cure rate models are popular in survival studies and outperform other models under certain conditions. We explored the prognostic factors of metastatic breast cancer from a different viewpoint. In this study, metastasis sites were analyzed all together. Conducting similar studies in a larger sample of cancer patients as well as evaluating the prognostic value of covariates in metastasis to each site separately are recommended.

Real medical benefit assessed by indirect comparison.

PubMed

Falissard, Bruno; Zylberman, Myriam; Cucherat, Michel; Izard, Valérie; Meyer, François

2009-01-01

Frequently, in data packages submitted for Marketing Approval to the CHMP, there is a lack of relevant head-to-head comparisons of medicinal products that could enable national authorities responsible for the approval of reimbursement to assess the Added Therapeutic Value (ASMR) of new clinical entities or line extensions of existing therapies.Indirect or mixed treatment comparisons (MTC) are methods stemming from the field of meta-analysis that have been designed to tackle this problem. Adjusted indirect comparisons, meta-regressions, mixed models, Bayesian network analyses pool results of randomised controlled trials (RCTs), enabling a quantitative synthesis.The REAL procedure, recently developed by the HAS (French National Authority for Health), is a mixture of an MTC and effect model based on expert opinions. It is intended to translate the efficacy observed in the trials into effectiveness expected in day-to-day clinical practice in France.

Unsupervised Gaussian Mixture-Model With Expectation Maximization for Detecting Glaucomatous Progression in Standard Automated Perimetry Visual Fields.

PubMed

Yousefi, Siamak; Balasubramanian, Madhusudhanan; Goldbaum, Michael H; Medeiros, Felipe A; Zangwill, Linda M; Weinreb, Robert N; Liebmann, Jeffrey M; Girkin, Christopher A; Bowd, Christopher

2016-05-01

To validate Gaussian mixture-model with expectation maximization (GEM) and variational Bayesian independent component analysis mixture-models (VIM) for detecting glaucomatous progression along visual field (VF) defect patterns (GEM-progression of patterns (POP) and VIM-POP). To compare GEM-POP and VIM-POP with other methods. GEM and VIM models separated cross-sectional abnormal VFs from 859 eyes and normal VFs from 1117 eyes into abnormal and normal clusters. Clusters were decomposed into independent axes. The confidence limit (CL) of stability was established for each axis with a set of 84 stable eyes. Sensitivity for detecting progression was assessed in a sample of 83 eyes with known progressive glaucomatous optic neuropathy (PGON). Eyes were classified as progressed if any defect pattern progressed beyond the CL of stability. Performance of GEM-POP and VIM-POP was compared to point-wise linear regression (PLR), permutation analysis of PLR (PoPLR), and linear regression (LR) of mean deviation (MD), and visual field index (VFI). Sensitivity and specificity for detecting glaucomatous VFs were 89.9% and 93.8%, respectively, for GEM and 93.0% and 97.0%, respectively, for VIM. Receiver operating characteristic (ROC) curve areas for classifying progressed eyes were 0.82 for VIM-POP, 0.86 for GEM-POP, 0.81 for PoPLR, 0.69 for LR of MD, and 0.76 for LR of VFI. GEM-POP was significantly more sensitive to PGON than PoPLR and linear regression of MD and VFI in our sample, while providing localized progression information. Detection of glaucomatous progression can be improved by assessing longitudinal changes in localized patterns of glaucomatous defect identified by unsupervised machine learning.

Application of linear mixed-effects model with LASSO to identify metal components associated with cardiac autonomic responses among welders: a repeated measures study

PubMed Central

Zhang, Jinming; Cavallari, Jennifer M; Fang, Shona C; Weisskopf, Marc G; Lin, Xihong; Mittleman, Murray A; Christiani, David C

2017-01-01

Background Environmental and occupational exposure to metals is ubiquitous worldwide, and understanding the hazardous metal components in this complex mixture is essential for environmental and occupational regulations. Objective To identify hazardous components from metal mixtures that are associated with alterations in cardiac autonomic responses. Methods Urinary concentrations of 16 types of metals were examined and ‘acceleration capacity’ (AC) and ‘deceleration capacity’ (DC), indicators of cardiac autonomic effects, were quantified from ECG recordings among 54 welders. We fitted linear mixed-effects models with least absolute shrinkage and selection operator (LASSO) to identify metal components that are associated with AC and DC. The Bayesian Information Criterion was used as the criterion for model selection procedures. Results Mercury and chromium were selected for DC analysis, whereas mercury, chromium and manganese were selected for AC analysis through the LASSO approach. When we fitted the linear mixed-effects models with ‘selected’ metal components only, the effect of mercury remained significant. Every 1 µg/L increase in urinary mercury was associated with −0.58 ms (−1.03, –0.13) changes in DC and 0.67 ms (0.25, 1.10) changes in AC. Conclusion Our study suggests that exposure to several metals is associated with impaired cardiac autonomic functions. Our findings should be replicated in future studies with larger sample sizes. PMID:28663305

Bayesian Analysis of Nonlinear Structural Equation Models with Nonignorable Missing Data

ERIC Educational Resources Information Center

Lee, Sik-Yum

2006-01-01

A Bayesian approach is developed for analyzing nonlinear structural equation models with nonignorable missing data. The nonignorable missingness mechanism is specified by a logistic regression model. A hybrid algorithm that combines the Gibbs sampler and the Metropolis-Hastings algorithm is used to produce the joint Bayesian estimates of…

Dynamic Bayesian Network Modeling of Game Based Diagnostic Assessments. CRESST Report 837

ERIC Educational Resources Information Center

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…

A close examination of double filtering with fold change and t test in microarray analysis

PubMed Central

2009-01-01

Background Many researchers use the double filtering procedure with fold change and t test to identify differentially expressed genes, in the hope that the double filtering will provide extra confidence in the results. Due to its simplicity, the double filtering procedure has been popular with applied researchers despite the development of more sophisticated methods. Results This paper, for the first time to our knowledge, provides theoretical insight on the drawback of the double filtering procedure. We show that fold change assumes all genes to have a common variance while t statistic assumes gene-specific variances. The two statistics are based on contradicting assumptions. Under the assumption that gene variances arise from a mixture of a common variance and gene-specific variances, we develop the theoretically most powerful likelihood ratio test statistic. We further demonstrate that the posterior inference based on a Bayesian mixture model and the widely used significance analysis of microarrays (SAM) statistic are better approximations to the likelihood ratio test than the double filtering procedure. Conclusion We demonstrate through hypothesis testing theory, simulation studies and real data examples, that well constructed shrinkage testing methods, which can be united under the mixture gene variance assumption, can considerably outperform the double filtering procedure. PMID:19995439

Invited commentary: Lost in estimation--searching for alternatives to markov chains to fit complex Bayesian models.

PubMed

Molitor, John

2012-03-01

Bayesian methods have seen an increase in popularity in a wide variety of scientific fields, including epidemiology. One of the main reasons for their widespread application is the power of the Markov chain Monte Carlo (MCMC) techniques generally used to fit these models. As a result, researchers often implicitly associate Bayesian models with MCMC estimation procedures. However, Bayesian models do not always require Markov-chain-based methods for parameter estimation. This is important, as MCMC estimation methods, while generally quite powerful, are complex and computationally expensive and suffer from convergence problems related to the manner in which they generate correlated samples used to estimate probability distributions for parameters of interest. In this issue of the Journal, Cole et al. (Am J Epidemiol. 2012;175(5):368-375) present an interesting paper that discusses non-Markov-chain-based approaches to fitting Bayesian models. These methods, though limited, can overcome some of the problems associated with MCMC techniques and promise to provide simpler approaches to fitting Bayesian models. Applied researchers will find these estimation approaches intuitively appealing and will gain a deeper understanding of Bayesian models through their use. However, readers should be aware that other non-Markov-chain-based methods are currently in active development and have been widely published in other fields.

The Bayesian reader: explaining word recognition as an optimal Bayesian decision process.

PubMed

Norris, Dennis

2006-04-01

This article presents a theory of visual word recognition that assumes that, in the tasks of word identification, lexical decision, and semantic categorization, human readers behave as optimal Bayesian decision makers. This leads to the development of a computational model of word recognition, the Bayesian reader. The Bayesian reader successfully simulates some of the most significant data on human reading. The model accounts for the nature of the function relating word frequency to reaction time and identification threshold, the effects of neighborhood density and its interaction with frequency, and the variation in the pattern of neighborhood density effects seen in different experimental tasks. Both the general behavior of the model and the way the model predicts different patterns of results in different tasks follow entirely from the assumption that human readers approximate optimal Bayesian decision makers. ((c) 2006 APA, all rights reserved).

Bayesian inference for psychology, part IV: parameter estimation and Bayes factors.

PubMed

Rouder, Jeffrey N; Haaf, Julia M; Vandekerckhove, Joachim

2018-02-01

In the psychological literature, there are two seemingly different approaches to inference: that from estimation of posterior intervals and that from Bayes factors. We provide an overview of each method and show that a salient difference is the choice of models. The two approaches as commonly practiced can be unified with a certain model specification, now popular in the statistics literature, called spike-and-slab priors. A spike-and-slab prior is a mixture of a null model, the spike, with an effect model, the slab. The estimate of the effect size here is a function of the Bayes factor, showing that estimation and model comparison can be unified. The salient difference is that common Bayes factor approaches provide for privileged consideration of theoretically useful parameter values, such as the value corresponding to the null hypothesis, while estimation approaches do not. Both approaches, either privileging the null or not, are useful depending on the goals of the analyst.

Bayesian flood forecasting methods: A review

NASA Astrophysics Data System (ADS)

Han, Shasha; Coulibaly, Paulin

2017-08-01

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

Bayesian modeling of flexible cognitive control

PubMed Central

Jiang, Jiefeng; Heller, Katherine; Egner, Tobias

2014-01-01

“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. PMID:24929218

Bayesian generalized linear mixed modeling of Tuberculosis using informative priors.

PubMed

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 there is no solid external information about the distribution of the parameter of interest. The main aim of this study is to profile people living with TB in South Africa. In this paper, identical regression models are fitted for classical and Bayesian approach both with non-informative and informative prior, using South Africa General Household Survey (GHS) data for the year 2014. For the Bayesian model with informative prior, South Africa General Household Survey dataset for the year 2011 to 2013 are used to set up priors for the model 2014.

Bayesian statistics in medicine: a 25 year review.

PubMed

Ashby, Deborah

2006-11-15

This review examines the state of Bayesian thinking as Statistics in Medicine was launched in 1982, reflecting particularly on its applicability and uses in medical research. It then looks at each subsequent five-year epoch, with a focus on papers appearing in Statistics in Medicine, putting these in the context of major developments in Bayesian thinking and computation with reference to important books, landmark meetings and seminal papers. It charts the growth of Bayesian statistics as it is applied to medicine and makes predictions for the future. From sparse beginnings, where Bayesian statistics was barely mentioned, Bayesian statistics has now permeated all the major areas of medical statistics, including clinical trials, epidemiology, meta-analyses and evidence synthesis, spatial modelling, longitudinal modelling, survival modelling, molecular genetics and decision-making in respect of new technologies.

Too Cool for Stellar Rules: A Bayesian Exploration of Trends in Ultracool Magnetism

NASA Astrophysics Data System (ADS)

Cruz, Kelle L.; Schwab, Ellianna; Williams, Peter K. G.; Hogg, David W.; Rodriguez, David R.; BDNYC

2017-01-01

Ultracool dwarfs, the lowest mass red dwarfs and brown dwarfs (spectral types M7-Y9), are fully convective objects with electrically neutral atmospheres due to their extremely cool temperatures (500-3000 K). Radio observations of ultracool dwarfs indicate the presence of magnetic field strengths on the order of ~kG, however the dynamo driving these fields is not fully understood. To better understand ultracool dwarf magnetic behavior, we analyze photometric radio detections of 196 dwarfs (spectral types M7-T8), observed in the 4.5-8.5 GHz range on the Karl G. Jansky Very Large Array (VLA) and the Australia Telescope Compact Array (ATCA). The measurements in our sample are mostly upper limits, along with a small percentage of confirmed detections. The detections have both large uncertainties and high intrinsic scatter. Using Bayesian analysis to fully take advantage of the information available in these inherently uncertain measurements, we search for trends in radio luminosity as a function of several fundamental parameters: spectral type, effective temperature, and rotation rate. In this poster, we present the preliminary results of our efforts to investigate the possibility of subpopulations with different magnetic characteristics using Gaussian mixture models.

A Sampling-Based Bayesian Approach for Cooperative Multiagent Online Search With Resource Constraints.

PubMed

Xiao, Hu; Cui, Rongxin; Xu, Demin

2018-06-01

This paper presents a cooperative multiagent search algorithm to solve the problem of searching for a target on a 2-D plane under multiple constraints. A Bayesian framework is used to update the local probability density functions (PDFs) of the target when the agents obtain observation information. To obtain the global PDF used for decision making, a sampling-based logarithmic opinion pool algorithm is proposed to fuse the local PDFs, and a particle sampling approach is used to represent the continuous PDF. Then the Gaussian mixture model (GMM) is applied to reconstitute the global PDF from the particles, and a weighted expectation maximization algorithm is presented to estimate the parameters of the GMM. Furthermore, we propose an optimization objective which aims to guide agents to find the target with less resource consumptions, and to keep the resource consumption of each agent balanced simultaneously. To this end, a utility function-based optimization problem is put forward, and it is solved by a gradient-based approach. Several contrastive simulations demonstrate that compared with other existing approaches, the proposed one uses less overall resources and shows a better performance of balancing the resource consumption.

Bayesian Parameter Inference and Model Selection by Population Annealing in Systems Biology

PubMed Central

Murakami, Yohei

2014-01-01

Parameter inference and model selection are very important for mathematical modeling in systems biology. Bayesian statistics can be used to conduct both parameter inference and model selection. Especially, the framework named approximate Bayesian computation is often used for parameter inference and model selection in systems biology. However, Monte Carlo methods needs to be used to compute Bayesian posterior distributions. In addition, the posterior distributions of parameters are sometimes almost uniform or very similar to their prior distributions. In such cases, it is difficult to choose one specific value of parameter with high credibility as the representative value of the distribution. To overcome the problems, we introduced one of the population Monte Carlo algorithms, population annealing. Although population annealing is usually used in statistical mechanics, we showed that population annealing can be used to compute Bayesian posterior distributions in the approximate Bayesian computation framework. To deal with un-identifiability of the representative values of parameters, we proposed to run the simulations with the parameter ensemble sampled from the posterior distribution, named “posterior parameter ensemble”. We showed that population annealing is an efficient and convenient algorithm to generate posterior parameter ensemble. We also showed that the simulations with the posterior parameter ensemble can, not only reproduce the data used for parameter inference, but also capture and predict the data which was not used for parameter inference. Lastly, we introduced the marginal likelihood in the approximate Bayesian computation framework for Bayesian model selection. We showed that population annealing enables us to compute the marginal likelihood in the approximate Bayesian computation framework and conduct model selection depending on the Bayes factor. PMID:25089832

Robust Bayesian hypocentre and uncertainty region estimation: the effect of heavy-tailed distributions and prior information in cases with poor, inconsistent and insufficient arrival times

NASA Astrophysics Data System (ADS)

Martinsson, J.

2013-03-01

We propose methods for robust Bayesian inference of the hypocentre in presence of poor, inconsistent and insufficient phase arrival times. The objectives are to increase the robustness, the accuracy and the precision by introducing heavy-tailed distributions and an informative prior distribution of the seismicity. The effects of the proposed distributions are studied under real measurement conditions in two underground mine networks and validated using 53 blasts with known hypocentres. To increase the robustness against poor, inconsistent or insufficient arrivals, a Gaussian Mixture Model is used as a hypocentre prior distribution to describe the seismically active areas, where the parameters are estimated based on previously located events in the region. The prior is truncated to constrain the solution to valid geometries, for example below the ground surface, excluding known cavities, voids and fractured zones. To reduce the sensitivity to outliers, different heavy-tailed distributions are evaluated to model the likelihood distribution of the arrivals given the hypocentre and the origin time. Among these distributions, the multivariate t-distribution is shown to produce the overall best performance, where the tail-mass adapts to the observed data. Hypocentre and uncertainty region estimates are based on simulations from the posterior distribution using Markov Chain Monte Carlo techniques. Velocity graphs (equivalent to traveltime graphs) are estimated using blasts from known locations, and applied to reduce the main uncertainties and thereby the final estimation error. To focus on the behaviour and the performance of the proposed distributions, a basic single-event Bayesian procedure is considered in this study for clarity. Estimation results are shown with different distributions, with and without prior distribution of seismicity, with wrong prior distribution, with and without error compensation, with and without error description, with insufficient arrival times and in presence of significant outliers. A particular focus is on visual results and comparisons to give a better understanding of the Bayesian advantage and to show the effects of heavy-tailed distributions and informative prior information on real data.

Bayesian analysis of the kinetics of quantal transmitter secretion at the neuromuscular junction.

PubMed

Saveliev, Anatoly; Khuzakhmetova, Venera; Samigullin, Dmitry; Skorinkin, Andrey; Kovyazina, Irina; Nikolsky, Eugeny; Bukharaeva, Ellya

2015-10-01

The timing of transmitter release from nerve endings is considered nowadays as one of the factors determining the plasticity and efficacy of synaptic transmission. In the neuromuscular junction, the moments of release of individual acetylcholine quanta are related to the synaptic delays of uniquantal endplate currents recorded under conditions of lowered extracellular calcium. Using Bayesian modelling, we performed a statistical analysis of synaptic delays in mouse neuromuscular junction with different patterns of rhythmic nerve stimulation and when the entry of calcium ions into the nerve terminal was modified. We have obtained a statistical model of the release timing which is represented as the summation of two independent statistical distributions. The first of these is the exponentially modified Gaussian distribution. The mixture of normal and exponential components in this distribution can be interpreted as a two-stage mechanism of early and late periods of phasic synchronous secretion. The parameters of this distribution depend on both the stimulation frequency of the motor nerve and the calcium ions' entry conditions. The second distribution was modelled as quasi-uniform, with parameters independent of nerve stimulation frequency and calcium entry. Two different probability density functions for the distribution of synaptic delays suggest at least two independent processes controlling the time course of secretion, one of them potentially involving two stages. The relative contribution of these processes to the total number of mediator quanta released depends differently on the motor nerve stimulation pattern and on calcium ion entry into nerve endings.

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

PubMed

Houseman, E Andres; Virji, M Abbas

2017-08-01

Direct reading instruments are valuable tools for measuring exposure as they provide real-time measurements for rapid decision making. However, their use is limited to general survey applications in part due to issues related to their performance. Moreover, statistical analysis of real-time data is complicated by autocorrelation among successive measurements, non-stationary time series, and the presence of left-censoring due to limit-of-detection (LOD). A Bayesian framework is proposed that accounts for non-stationary autocorrelation and LOD issues in exposure time-series data in order to model workplace factors that affect exposure and estimate summary statistics for tasks or other covariates of interest. A spline-based approach is used to model non-stationary autocorrelation with relatively few assumptions about autocorrelation structure. Left-censoring is addressed by integrating over the left tail of the distribution. The model is fit using Markov-Chain Monte Carlo within a Bayesian paradigm. The method can flexibly account for hierarchical relationships, random effects and fixed effects of covariates. The method is implemented using the rjags package in R, and is illustrated by applying it to real-time exposure data. Estimates for task means and covariates from the Bayesian model are compared to those from conventional frequentist models including linear regression, mixed-effects, and time-series models with different autocorrelation structures. Simulations studies are also conducted to evaluate method performance. Simulation studies with percent of measurements below the LOD ranging from 0 to 50% showed lowest root mean squared errors for task means and the least biased standard deviations from the Bayesian model compared to the frequentist models across all levels of LOD. In the application, task means from the Bayesian model were similar to means from the frequentist models, while the standard deviations were different. Parameter estimates for covariates were significant in some frequentist models, but in the Bayesian model their credible intervals contained zero; such discrepancies were observed in multiple datasets. Variance components from the Bayesian model reflected substantial autocorrelation, consistent with the frequentist models, except for the auto-regressive moving average model. Plots of means from the Bayesian model showed good fit to the observed data. The proposed Bayesian model provides an approach for modeling non-stationary autocorrelation in a hierarchical modeling framework to estimate task means, standard deviations, quantiles, and parameter estimates for covariates that are less biased and have better performance characteristics than some of the contemporary methods. Published by Oxford University Press on behalf of the British Occupational Hygiene Society 2017.

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

DTIC Science & Technology

2017-09-01

efficacy of statistical post-processing methods downstream of these dynamical model components with a hierarchical multivariate Bayesian approach to...Bayesian hierarchical modeling, Markov chain Monte Carlo methods , Metropolis algorithm, machine learning, atmospheric prediction 15. NUMBER OF PAGES...scale processes. However, this dissertation explores the efficacy of statistical post-processing methods downstream of these dynamical model components

Bayesian Learning and the Psychology of Rule Induction

ERIC Educational Resources Information Center

Endress, Ansgar D.

2013-01-01

In recent years, Bayesian learning models have been applied to an increasing variety of domains. While such models have been criticized on theoretical grounds, the underlying assumptions and predictions are rarely made concrete and tested experimentally. Here, I use Frank and Tenenbaum's (2011) Bayesian model of rule-learning as a case study to…

Properties of the Bayesian Knowledge Tracing Model

ERIC Educational Resources Information Center

van de Sande, Brett

2013-01-01

Bayesian Knowledge Tracing is used very widely to model student learning. It comes in two different forms: The first form is the Bayesian Knowledge Tracing "hidden Markov model" which predicts the probability of correct application of a skill as a function of the number of previous opportunities to apply that skill and the model…

Bayesian Analysis of Longitudinal Data Using Growth Curve Models

ERIC Educational Resources Information Center

Zhang, Zhiyong; Hamagami, Fumiaki; Wang, Lijuan Lijuan; Nesselroade, John R.; Grimm, Kevin J.

2007-01-01

Bayesian methods for analyzing longitudinal data in social and behavioral research are recommended for their ability to incorporate prior information in estimating simple and complex models. We first summarize the basics of Bayesian methods before presenting an empirical example in which we fit a latent basis growth curve model to achievement data…

Testing students' e-learning via Facebook through Bayesian structural equation modeling.

PubMed

Salarzadeh Jenatabadi, Hashem; Moghavvemi, Sedigheh; Wan Mohamed Radzi, Che Wan Jasimah Bt; Babashamsi, Parastoo; Arashi, Mohammad

2017-01-01

Learning is an intentional activity, with several factors affecting students' intention to use new learning technology. Researchers have investigated technology acceptance in different contexts by developing various theories/models and testing them by a number of means. Although most theories/models developed have been examined through regression or structural equation modeling, Bayesian analysis offers more accurate data analysis results. To address this gap, the unified theory of acceptance and technology use in the context of e-learning via Facebook are re-examined in this study using Bayesian analysis. The data (S1 Data) were collected from 170 students enrolled in a business statistics course at University of Malaya, Malaysia, and tested with the maximum likelihood and Bayesian approaches. The difference between the two methods' results indicates that performance expectancy and hedonic motivation are the strongest factors influencing the intention to use e-learning via Facebook. The Bayesian estimation model exhibited better data fit than the maximum likelihood estimator model. The results of the Bayesian and maximum likelihood estimator approaches are compared and the reasons for the result discrepancy are deliberated.

Testing students’ e-learning via Facebook through Bayesian structural equation modeling

PubMed Central

Moghavvemi, Sedigheh; Wan Mohamed Radzi, Che Wan Jasimah Bt; Babashamsi, Parastoo; Arashi, Mohammad

2017-01-01

Learning is an intentional activity, with several factors affecting students’ intention to use new learning technology. Researchers have investigated technology acceptance in different contexts by developing various theories/models and testing them by a number of means. Although most theories/models developed have been examined through regression or structural equation modeling, Bayesian analysis offers more accurate data analysis results. To address this gap, the unified theory of acceptance and technology use in the context of e-learning via Facebook are re-examined in this study using Bayesian analysis. The data (S1 Data) were collected from 170 students enrolled in a business statistics course at University of Malaya, Malaysia, and tested with the maximum likelihood and Bayesian approaches. The difference between the two methods’ results indicates that performance expectancy and hedonic motivation are the strongest factors influencing the intention to use e-learning via Facebook. The Bayesian estimation model exhibited better data fit than the maximum likelihood estimator model. The results of the Bayesian and maximum likelihood estimator approaches are compared and the reasons for the result discrepancy are deliberated. PMID:28886019

When mechanism matters: Bayesian forecasting using models of ecological diffusion

USGS Publications Warehouse

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.

A New Model for Acquiescence at the Interface of Psychometrics and Cognitive Psychology.

PubMed

Plieninger, Hansjörg; Heck, Daniel W

2018-05-29

When measuring psychological traits, one has to consider that respondents often show content-unrelated response behavior in answering questionnaires. To disentangle the target trait and two such response styles, extreme responding and midpoint responding, Böckenholt ( 2012a ) developed an item response model based on a latent processing tree structure. We propose a theoretically motivated extension of this model to also measure acquiescence, the tendency to agree with both regular and reversed items. Substantively, our approach builds on multinomial processing tree (MPT) models that are used in cognitive psychology to disentangle qualitatively distinct processes. Accordingly, the new model for response styles assumes a mixture distribution of affirmative responses, which are either determined by the underlying target trait or by acquiescence. In order to estimate the model parameters, we rely on Bayesian hierarchical estimation of MPT models. In simulations, we show that the model provides unbiased estimates of response styles and the target trait, and we compare the new model and Böckenholt's model in a recovery study. An empirical example from personality psychology is used for illustrative purposes.

Bayesian naturalness, simplicity, and testability applied to the B ‑ L MSSM GUT

NASA Astrophysics Data System (ADS)

Fundira, Panashe; Purves, Austin

2018-04-01

Recent years have seen increased use of Bayesian model comparison to quantify notions such as naturalness, simplicity, and testability, especially in the area of supersymmetric model building. After demonstrating that Bayesian model comparison can resolve a paradox that has been raised in the literature concerning the naturalness of the proton mass, we apply Bayesian model comparison to GUTs, an area to which it has not been applied before. We find that the GUTs are substantially favored over the nonunifying puzzle model. Of the GUTs we consider, the B ‑ L MSSM GUT is the most favored, but the MSSM GUT is almost equally favored.

Comparison Between Linear and Non-parametric Regression Models for Genome-Enabled Prediction in Wheat

PubMed Central

Pérez-Rodríguez, Paulino; Gianola, Daniel; González-Camacho, Juan Manuel; Crossa, José; Manès, Yann; Dreisigacker, Susanne

2012-01-01

In genome-enabled prediction, parametric, semi-parametric, and non-parametric regression models have been used. This study assessed the predictive ability of linear and non-linear models using dense molecular markers. The linear models were linear on marker effects and included the Bayesian LASSO, Bayesian ridge regression, Bayes A, and Bayes B. The non-linear models (this refers to non-linearity on markers) were reproducing kernel Hilbert space (RKHS) regression, Bayesian regularized neural networks (BRNN), and radial basis function neural networks (RBFNN). These statistical models were compared using 306 elite wheat lines from CIMMYT genotyped with 1717 diversity array technology (DArT) markers and two traits, days to heading (DTH) and grain yield (GY), measured in each of 12 environments. It was found that the three non-linear models had better overall prediction accuracy than the linear regression specification. Results showed a consistent superiority of RKHS and RBFNN over the Bayesian LASSO, Bayesian ridge regression, Bayes A, and Bayes B models. PMID:23275882

Comparison between linear and non-parametric regression models for genome-enabled prediction in wheat.

PubMed

Pérez-Rodríguez, Paulino; Gianola, Daniel; González-Camacho, Juan Manuel; Crossa, José; Manès, Yann; Dreisigacker, Susanne

2012-12-01

In genome-enabled prediction, parametric, semi-parametric, and non-parametric regression models have been used. This study assessed the predictive ability of linear and non-linear models using dense molecular markers. The linear models were linear on marker effects and included the Bayesian LASSO, Bayesian ridge regression, Bayes A, and Bayes B. The non-linear models (this refers to non-linearity on markers) were reproducing kernel Hilbert space (RKHS) regression, Bayesian regularized neural networks (BRNN), and radial basis function neural networks (RBFNN). These statistical models were compared using 306 elite wheat lines from CIMMYT genotyped with 1717 diversity array technology (DArT) markers and two traits, days to heading (DTH) and grain yield (GY), measured in each of 12 environments. It was found that the three non-linear models had better overall prediction accuracy than the linear regression specification. Results showed a consistent superiority of RKHS and RBFNN over the Bayesian LASSO, Bayesian ridge regression, Bayes A, and Bayes B models.

Fast genomic predictions via Bayesian G-BLUP and multilocus models of threshold traits including censored Gaussian data.

PubMed

Kärkkäinen, Hanni P; Sillanpää, Mikko J

2013-09-04

Because of the increased availability of genome-wide sets of molecular markers along with reduced cost of genotyping large samples of individuals, genomic estimated breeding values have become an essential resource in plant and animal breeding. Bayesian methods for breeding value estimation have proven to be accurate and efficient; however, the ever-increasing data sets are placing heavy demands on the parameter estimation algorithms. Although a commendable number of fast estimation algorithms are available for Bayesian models of continuous Gaussian traits, there is a shortage for corresponding models of discrete or censored phenotypes. In this work, we consider a threshold approach of binary, ordinal, and censored Gaussian observations for Bayesian multilocus association models and Bayesian genomic best linear unbiased prediction and present a high-speed generalized expectation maximization algorithm for parameter estimation under these models. We demonstrate our method with simulated and real data. Our example analyses suggest that the use of the extra information present in an ordered categorical or censored Gaussian data set, instead of dichotomizing the data into case-control observations, increases the accuracy of genomic breeding values predicted by Bayesian multilocus association models or by Bayesian genomic best linear unbiased prediction. Furthermore, the example analyses indicate that the correct threshold model is more accurate than the directly used Gaussian model with a censored Gaussian data, while with a binary or an ordinal data the superiority of the threshold model could not be confirmed.

Fast Genomic Predictions via Bayesian G-BLUP and Multilocus Models of Threshold Traits Including Censored Gaussian Data

PubMed Central

Kärkkäinen, Hanni P.; Sillanpää, Mikko J.

2013-01-01

Because of the increased availability of genome-wide sets of molecular markers along with reduced cost of genotyping large samples of individuals, genomic estimated breeding values have become an essential resource in plant and animal breeding. Bayesian methods for breeding value estimation have proven to be accurate and efficient; however, the ever-increasing data sets are placing heavy demands on the parameter estimation algorithms. Although a commendable number of fast estimation algorithms are available for Bayesian models of continuous Gaussian traits, there is a shortage for corresponding models of discrete or censored phenotypes. In this work, we consider a threshold approach of binary, ordinal, and censored Gaussian observations for Bayesian multilocus association models and Bayesian genomic best linear unbiased prediction and present a high-speed generalized expectation maximization algorithm for parameter estimation under these models. We demonstrate our method with simulated and real data. Our example analyses suggest that the use of the extra information present in an ordered categorical or censored Gaussian data set, instead of dichotomizing the data into case-control observations, increases the accuracy of genomic breeding values predicted by Bayesian multilocus association models or by Bayesian genomic best linear unbiased prediction. Furthermore, the example analyses indicate that the correct threshold model is more accurate than the directly used Gaussian model with a censored Gaussian data, while with a binary or an ordinal data the superiority of the threshold model could not be confirmed. PMID:23821618

APPLICATION OF BAYESIAN MONTE CARLO ANALYSIS TO A LAGRANGIAN PHOTOCHEMICAL AIR QUALITY MODEL. (R824792)

EPA Science Inventory

Uncertainties in ozone concentrations predicted with a Lagrangian photochemical air quality model have been estimated using Bayesian Monte Carlo (BMC) analysis. Bayesian Monte Carlo analysis provides a means of combining subjective "prior" uncertainty estimates developed ...

A SEMIPARAMETRIC BAYESIAN MODEL FOR CIRCULAR-LINEAR REGRESSION

EPA Science Inventory

We present a Bayesian approach to regress a circular variable on a linear predictor. The regression coefficients are assumed to have a nonparametric distribution with a Dirichlet process prior. The semiparametric Bayesian approach gives added flexibility to the model and is usefu...

A Bayesian alternative for multi-objective ecohydrological model specification

NASA Astrophysics Data System (ADS)

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 distributions in such approaches.

Diagnostic accuracy of a bayesian latent group analysis for the detection of malingering-related poor effort.

PubMed

Ortega, Alonso; Labrenz, Stephan; Markowitsch, Hans J; Piefke, Martina

2013-01-01

In the last decade, different statistical techniques have been introduced to improve assessment of malingering-related poor effort. In this context, we have recently shown preliminary evidence that a Bayesian latent group model may help to optimize classification accuracy using a simulation research design. In the present study, we conducted two analyses. Firstly, we evaluated how accurately this Bayesian approach can distinguish between participants answering in an honest way (honest response group) and participants feigning cognitive impairment (experimental malingering group). Secondly, we tested the accuracy of our model in the differentiation between patients who had real cognitive deficits (cognitively impaired group) and participants who belonged to the experimental malingering group. All Bayesian analyses were conducted using the raw scores of a visual recognition forced-choice task (2AFC), the Test of Memory Malingering (TOMM, Trial 2), and the Word Memory Test (WMT, primary effort subtests). The first analysis showed 100% accuracy for the Bayesian model in distinguishing participants of both groups with all effort measures. The second analysis showed outstanding overall accuracy of the Bayesian model when estimates were obtained from the 2AFC and the TOMM raw scores. Diagnostic accuracy of the Bayesian model diminished when using the WMT total raw scores. Despite, overall diagnostic accuracy can still be considered excellent. The most plausible explanation for this decrement is the low performance in verbal recognition and fluency tasks of some patients of the cognitively impaired group. Additionally, the Bayesian model provides individual estimates, p(zi |D), of examinees' effort levels. In conclusion, both high classification accuracy levels and Bayesian individual estimates of effort may be very useful for clinicians when assessing for effort in medico-legal settings.

Probabilistic Inference: Task Dependency and Individual Differences of Probability Weighting Revealed by Hierarchical Bayesian Modeling

PubMed Central

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. PMID:27303323

Estimating Tree Height-Diameter Models with the Bayesian Method

PubMed Central

Duan, Aiguo; Zhang, Jianguo; Xiang, Congwei

2014-01-01

Six candidate height-diameter models were used to analyze the height-diameter relationships. The common methods for estimating the height-diameter models have taken the classical (frequentist) approach based on the frequency interpretation of probability, for example, the nonlinear least squares method (NLS) and the maximum likelihood method (ML). The Bayesian method has an exclusive advantage compared with classical method that the parameters to be estimated are regarded as random variables. In this study, the classical and Bayesian methods were used to estimate six height-diameter models, respectively. Both the classical method and Bayesian method showed that the Weibull model was the “best” model using data1. In addition, based on the Weibull model, data2 was used for comparing Bayesian method with informative priors with uninformative priors and classical method. The results showed that the improvement in prediction accuracy with Bayesian method led to narrower confidence bands of predicted value in comparison to that for the classical method, and the credible bands of parameters with informative priors were also narrower than uninformative priors and classical method. The estimated posterior distributions for parameters can be set as new priors in estimating the parameters using data2. PMID:24711733

Estimating tree height-diameter models with the Bayesian method.

PubMed

Zhang, Xiongqing; Duan, Aiguo; Zhang, Jianguo; Xiang, Congwei

2014-01-01

Six candidate height-diameter models were used to analyze the height-diameter relationships. The common methods for estimating the height-diameter models have taken the classical (frequentist) approach based on the frequency interpretation of probability, for example, the nonlinear least squares method (NLS) and the maximum likelihood method (ML). The Bayesian method has an exclusive advantage compared with classical method that the parameters to be estimated are regarded as random variables. In this study, the classical and Bayesian methods were used to estimate six height-diameter models, respectively. Both the classical method and Bayesian method showed that the Weibull model was the "best" model using data1. In addition, based on the Weibull model, data2 was used for comparing Bayesian method with informative priors with uninformative priors and classical method. The results showed that the improvement in prediction accuracy with Bayesian method led to narrower confidence bands of predicted value in comparison to that for the classical method, and the credible bands of parameters with informative priors were also narrower than uninformative priors and classical method. The estimated posterior distributions for parameters can be set as new priors in estimating the parameters using data2.

Mapping malaria risk among children in Côte d'Ivoire using Bayesian geo-statistical models.

PubMed

Raso, Giovanna; Schur, Nadine; Utzinger, Jürg; Koudou, Benjamin G; Tchicaya, Emile S; Rohner, Fabian; N'goran, Eliézer K; Silué, Kigbafori D; Matthys, Barbara; Assi, Serge; Tanner, Marcel; Vounatsou, Penelope

2012-05-09

In Côte d'Ivoire, an estimated 767,000 disability-adjusted life years are due to malaria, placing the country at position number 14 with regard to the global burden of malaria. Risk maps are important to guide control interventions, and hence, the aim of this study was to predict the geographical distribution of malaria infection risk in children aged <16 years in Côte d'Ivoire at high spatial resolution. Using different data sources, a systematic review was carried out to compile and geo-reference survey data on Plasmodium spp. infection prevalence in Côte d'Ivoire, focusing on children aged <16 years. The period from 1988 to 2007 was covered. A suite of Bayesian geo-statistical logistic regression models was fitted to analyse malaria risk. Non-spatial models with and without exchangeable random effect parameters were compared to stationary and non-stationary spatial models. Non-stationarity was modelled assuming that the underlying spatial process is a mixture of separate stationary processes in each ecological zone. The best fitting model based on the deviance information criterion was used to predict Plasmodium spp. infection risk for entire Côte d'Ivoire, including uncertainty. Overall, 235 data points at 170 unique survey locations with malaria prevalence data for individuals aged <16 years were extracted. Most data points (n = 182, 77.4%) were collected between 2000 and 2007. A Bayesian non-stationary regression model showed the best fit with annualized rainfall and maximum land surface temperature identified as significant environmental covariates. This model was used to predict malaria infection risk at non-sampled locations. High-risk areas were mainly found in the north-central and western area, while relatively low-risk areas were located in the north at the country border, in the north-east, in the south-east around Abidjan, and in the central-west between two high prevalence areas. The malaria risk map at high spatial resolution gives an important overview of the geographical distribution of the disease in Côte d'Ivoire. It is a useful tool for the national malaria control programme and can be utilized for spatial targeting of control interventions and rational resource allocation.

Mapping malaria risk among children in Côte d’Ivoire using Bayesian geo-statistical models

PubMed Central

2012-01-01

Background In Côte d’Ivoire, an estimated 767,000 disability-adjusted life years are due to malaria, placing the country at position number 14 with regard to the global burden of malaria. Risk maps are important to guide control interventions, and hence, the aim of this study was to predict the geographical distribution of malaria infection risk in children aged <16 years in Côte d’Ivoire at high spatial resolution. Methods Using different data sources, a systematic review was carried out to compile and geo-reference survey data on Plasmodium spp. infection prevalence in Côte d’Ivoire, focusing on children aged <16 years. The period from 1988 to 2007 was covered. A suite of Bayesian geo-statistical logistic regression models was fitted to analyse malaria risk. Non-spatial models with and without exchangeable random effect parameters were compared to stationary and non-stationary spatial models. Non-stationarity was modelled assuming that the underlying spatial process is a mixture of separate stationary processes in each ecological zone. The best fitting model based on the deviance information criterion was used to predict Plasmodium spp. infection risk for entire Côte d’Ivoire, including uncertainty. Results Overall, 235 data points at 170 unique survey locations with malaria prevalence data for individuals aged <16 years were extracted. Most data points (n = 182, 77.4%) were collected between 2000 and 2007. A Bayesian non-stationary regression model showed the best fit with annualized rainfall and maximum land surface temperature identified as significant environmental covariates. This model was used to predict malaria infection risk at non-sampled locations. High-risk areas were mainly found in the north-central and western area, while relatively low-risk areas were located in the north at the country border, in the north-east, in the south-east around Abidjan, and in the central-west between two high prevalence areas. Conclusion The malaria risk map at high spatial resolution gives an important overview of the geographical distribution of the disease in Côte d’Ivoire. It is a useful tool for the national malaria control programme and can be utilized for spatial targeting of control interventions and rational resource allocation. PMID:22571469

Sparse Event Modeling with Hierarchical Bayesian Kernel Methods

DTIC Science & Technology

2016-01-05

SECURITY CLASSIFICATION OF: The research objective of this proposal was to develop a predictive Bayesian kernel approach to model count data based on...several predictive variables. Such an approach, which we refer to as the Poisson Bayesian kernel model , is able to model the rate of occurrence of...which adds specificity to the model and can make nonlinear data more manageable. Early results show that the 1. REPORT DATE (DD-MM-YYYY) 4. TITLE

Spatial clustering of metal and metalloid mixtures in unregulated water sources on the Navajo Nation - Arizona, New Mexico, and Utah, USA.

PubMed

Hoover, Joseph H; Coker, Eric; Barney, Yolanda; Shuey, Chris; Lewis, Johnnye

2018-08-15

Contaminant mixtures are identified regularly in public and private drinking water supplies throughout the United States; however, the complex and often correlated nature of mixtures makes identification of relevant combinations challenging. This study employed a Bayesian clustering method to identify subgroups of water sources with similar metal and metalloid profiles. Additionally, a spatial scan statistic assessed spatial clustering of these subgroups and a human health metric was applied to investigate potential for human toxicity. These methods were applied to a dataset comprised of metal and metalloid measurements from unregulated water sources located on the Navajo Nation, in the southwest United States. Results indicated distinct subgroups of water sources with similar contaminant profiles and that some of these subgroups were spatially clustered. Several profiles had metal and metalloid concentrations that may have potential for human toxicity including arsenic, uranium, lead, manganese, and selenium. This approach may be useful for identifying mixtures in water sources, spatially evaluating the clusters, and help inform toxicological research investigating mixtures. Copyright © 2018 The Authors. Published by Elsevier B.V. All rights reserved.

Bayesian generalized linear mixed modeling of Tuberculosis using informative priors

PubMed Central

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 there is no solid external information about the distribution of the parameter of interest. The main aim of this study is to profile people living with TB in South Africa. In this paper, identical regression models are fitted for classical and Bayesian approach both with non-informative and informative prior, using South Africa General Household Survey (GHS) data for the year 2014. For the Bayesian model with informative prior, South Africa General Household Survey dataset for the year 2011 to 2013 are used to set up priors for the model 2014. PMID:28257437

Unifying error structures in commonly used biotracer mixing models.

PubMed

Stock, Brian C; Semmens, Brice X

2016-10-01

Mixing models are statistical tools that use biotracers to probabilistically estimate the contribution of multiple sources to a mixture. These biotracers may include contaminants, fatty acids, or stable isotopes, the latter of which are widely used in trophic ecology to estimate the mixed diet of consumers. Bayesian implementations of mixing models using stable isotopes (e.g., MixSIR, SIAR) are regularly used by ecologists for this purpose, but basic questions remain about when each is most appropriate. In this study, we describe the structural differences between common mixing model error formulations in terms of their assumptions about the predation process. We then introduce a new parameterization that unifies these mixing model error structures, as well as implicitly estimates the rate at which consumers sample from source populations (i.e., consumption rate). Using simulations and previously published mixing model datasets, we demonstrate that the new error parameterization outperforms existing models and provides an estimate of consumption. Our results suggest that the error structure introduced here will improve future mixing model estimates of animal diet. © 2016 by the Ecological Society of America.

Non-stationary noise estimation using dictionary learning and Gaussian mixture models

NASA Astrophysics Data System (ADS)

Hughes, James M.; Rockmore, Daniel N.; Wang, Yang

2014-02-01

Stationarity of the noise distribution is a common assumption in image processing. This assumption greatly simplifies denoising estimators and other model parameters and consequently assuming stationarity is often a matter of convenience rather than an accurate model of noise characteristics. The problematic nature of this assumption is exacerbated in real-world contexts, where noise is often highly non-stationary and can possess time- and space-varying characteristics. Regardless of model complexity, estimating the parameters of noise dis- tributions in digital images is a difficult task, and estimates are often based on heuristic assumptions. Recently, sparse Bayesian dictionary learning methods were shown to produce accurate estimates of the level of additive white Gaussian noise in images with minimal assumptions. We show that a similar model is capable of accu- rately modeling certain kinds of non-stationary noise processes, allowing for space-varying noise in images to be estimated, detected, and removed. We apply this modeling concept to several types of non-stationary noise and demonstrate the model's effectiveness on real-world problems, including denoising and segmentation of images according to noise characteristics, which has applications in image forensics.

A Fast Surrogate-facilitated Data-driven Bayesian Approach to Uncertainty Quantification of a Regional Groundwater Flow Model with Structural Error

NASA Astrophysics Data System (ADS)

Xu, T.; Valocchi, A. J.; Ye, M.; Liang, F.

2016-12-01

Due to simplification and/or misrepresentation of the real aquifer system, numerical groundwater flow and solute transport models are usually subject to model structural error. During model calibration, the hydrogeological parameters may be overly adjusted to compensate for unknown structural error. This may result in biased predictions when models are used to forecast aquifer response to new forcing. In this study, we extend a fully Bayesian method [Xu and Valocchi, 2015] to calibrate a real-world, regional groundwater flow model. The method uses a data-driven error model to describe model structural error and jointly infers model parameters and structural error. In this study, Bayesian inference is facilitated using high performance computing and fast surrogate models. The surrogate models are constructed using machine learning techniques to emulate the response simulated by the computationally expensive groundwater model. We demonstrate in the real-world case study that explicitly accounting for model structural error yields parameter posterior distributions that are substantially different from those derived by the classical Bayesian calibration that does not account for model structural error. In addition, the Bayesian with error model method gives significantly more accurate prediction along with reasonable credible intervals.

Spatial Guilds in the Serengeti Food Web Revealed by a Bayesian Group Model

PubMed Central

Baskerville, Edward B.; Dobson, Andy P.; Bedford, Trevor; Allesina, Stefano; Anderson, T. Michael; Pascual, Mercedes

2011-01-01

Food webs, networks of feeding relationships in an ecosystem, provide fundamental insights into mechanisms that determine ecosystem stability and persistence. A standard approach in food-web analysis, and network analysis in general, has been to identify compartments, or modules, defined by many links within compartments and few links between them. This approach can identify large habitat boundaries in the network but may fail to identify other important structures. Empirical analyses of food webs have been further limited by low-resolution data for primary producers. In this paper, we present a Bayesian computational method for identifying group structure using a flexible definition that can describe both functional trophic roles and standard compartments. We apply this method to a newly compiled plant-mammal food web from the Serengeti ecosystem that includes high taxonomic resolution at the plant level, allowing a simultaneous examination of the signature of both habitat and trophic roles in network structure. We find that groups at the plant level reflect habitat structure, coupled at higher trophic levels by groups of herbivores, which are in turn coupled by carnivore groups. Thus the group structure of the Serengeti web represents a mixture of trophic guild structure and spatial pattern, in contrast to the standard compartments typically identified. The network topology supports recent ideas on spatial coupling and energy channels in ecosystems that have been proposed as important for persistence. Furthermore, our Bayesian approach provides a powerful, flexible framework for the study of network structure, and we believe it will prove instrumental in a variety of biological contexts. PMID:22219719

The Bayesian Revolution Approaches Psychological Development

ERIC Educational Resources Information Center

Shultz, Thomas R.

2007-01-01

This commentary reviews five articles that apply Bayesian ideas to psychological development, some with psychology experiments, some with computational modeling, and some with both experiments and modeling. The reviewed work extends the current Bayesian revolution into tasks often studied in children, such as causal learning and word learning, and…

Incorporating approximation error in surrogate based Bayesian inversion

NASA Astrophysics Data System (ADS)

Zhang, J.; Zeng, L.; Li, W.; Wu, L.

2015-12-01

There are increasing interests in applying surrogates for inverse Bayesian modeling to reduce repetitive evaluations of original model. In this way, the computational cost is expected to be saved. However, the approximation error of surrogate model is usually overlooked. This is partly because that it is difficult to evaluate the approximation error for many surrogates. Previous studies have shown that, the direct combination of surrogates and Bayesian methods (e.g., Markov Chain Monte Carlo, MCMC) may lead to biased estimations when the surrogate cannot emulate the highly nonlinear original system. This problem can be alleviated by implementing MCMC in a two-stage manner. However, the computational cost is still high since a relatively large number of original model simulations are required. In this study, we illustrate the importance of incorporating approximation error in inverse Bayesian modeling. Gaussian process (GP) is chosen to construct the surrogate for its convenience in approximation error evaluation. Numerical cases of Bayesian experimental design and parameter estimation for contaminant source identification are used to illustrate this idea. It is shown that, once the surrogate approximation error is well incorporated into Bayesian framework, promising results can be obtained even when the surrogate is directly used, and no further original model simulations are required.

Moving in Parallel Toward a Modern Modeling Epistemology: Bayes Factors and Frequentist Modeling Methods.

PubMed

Rodgers, Joseph Lee

2016-01-01

The Bayesian-frequentist debate typically portrays these statistical perspectives as opposing views. However, both Bayesian and frequentist statisticians have expanded their epistemological basis away from a singular focus on the null hypothesis, to a broader perspective involving the development and comparison of competing statistical/mathematical models. For frequentists, statistical developments such as structural equation modeling and multilevel modeling have facilitated this transition. For Bayesians, the Bayes factor has facilitated this transition. The Bayes factor is treated in articles within this issue of Multivariate Behavioral Research. The current presentation provides brief commentary on those articles and more extended discussion of the transition toward a modern modeling epistemology. In certain respects, Bayesians and frequentists share common goals.

A Bayesian Model of the Memory Colour Effect.

PubMed

Witzel, Christoph; Olkkonen, Maria; Gegenfurtner, Karl R

2018-01-01

According to the memory colour effect, the colour of a colour-diagnostic object is not perceived independently of the object itself. Instead, it has been shown through an achromatic adjustment method that colour-diagnostic objects still appear slightly in their typical colour, even when they are colourimetrically grey. Bayesian models provide a promising approach to capture the effect of prior knowledge on colour perception and to link these effects to more general effects of cue integration. Here, we model memory colour effects using prior knowledge about typical colours as priors for the grey adjustments in a Bayesian model. This simple model does not involve any fitting of free parameters. The Bayesian model roughly captured the magnitude of the measured memory colour effect for photographs of objects. To some extent, the model predicted observed differences in memory colour effects across objects. The model could not account for the differences in memory colour effects across different levels of realism in the object images. The Bayesian model provides a particularly simple account of memory colour effects, capturing some of the multiple sources of variation of these effects.

A Bayesian Model of the Memory Colour Effect

PubMed Central

Olkkonen, Maria; Gegenfurtner, Karl R.

2018-01-01

According to the memory colour effect, the colour of a colour-diagnostic object is not perceived independently of the object itself. Instead, it has been shown through an achromatic adjustment method that colour-diagnostic objects still appear slightly in their typical colour, even when they are colourimetrically grey. Bayesian models provide a promising approach to capture the effect of prior knowledge on colour perception and to link these effects to more general effects of cue integration. Here, we model memory colour effects using prior knowledge about typical colours as priors for the grey adjustments in a Bayesian model. This simple model does not involve any fitting of free parameters. The Bayesian model roughly captured the magnitude of the measured memory colour effect for photographs of objects. To some extent, the model predicted observed differences in memory colour effects across objects. The model could not account for the differences in memory colour effects across different levels of realism in the object images. The Bayesian model provides a particularly simple account of memory colour effects, capturing some of the multiple sources of variation of these effects. PMID:29760874

Multinomial mixture model with heterogeneous classification probabilities

USGS Publications Warehouse

Holland, M.D.; Gray, B.R.

2011-01-01

Royle and Link (Ecology 86(9):2505-2512, 2005) proposed an analytical method that allowed estimation of multinomial distribution parameters and classification probabilities from categorical data measured with error. While useful, we demonstrate algebraically and by simulations that this method yields biased multinomial parameter estimates when the probabilities of correct category classifications vary among sampling units. We address this shortcoming by treating these probabilities as logit-normal random variables within a Bayesian framework. We use Markov chain Monte Carlo to compute Bayes estimates from a simulated sample from the posterior distribution. Based on simulations, this elaborated Royle-Link model yields nearly unbiased estimates of multinomial and correct classification probability estimates when classification probabilities are allowed to vary according to the normal distribution on the logit scale or according to the Beta distribution. The method is illustrated using categorical submersed aquatic vegetation data. ?? 2010 Springer Science+Business Media, LLC.

Bayesian Nitrate Source Apportionment to Individual Groundwater Wells in the Central Valley by use of Nitrogen, Oxygen, and Boron Isotopic Tracers

NASA Astrophysics Data System (ADS)

Lockhart, K.; Harter, T.; Grote, M.; Young, M. B.; Eppich, G.; Deinhart, A.; Wimpenny, J.; Yin, Q. Z.

2014-12-01

Groundwater quality is a concern in alluvial aquifers underlying agricultural areas worldwide, an example of which is the San Joaquin Valley, California. Nitrate from land applied fertilizers or from animal waste can leach to groundwater and contaminate drinking water resources. Dairy manure and synthetic fertilizers are the major sources of nitrate in groundwater in the San Joaquin Valley, however, septic waste can be a major source in some areas. As in other such regions around the world, the rural population in the San Joaquin Valley relies almost exclusively on shallow domestic wells (≤150 m deep), of which many have been affected by nitrate. Consumption of water containing nitrate above the drinking water limit has been linked to major health effects including low blood oxygen in infants and certain cancers. Knowledge of the proportion of each of the three main nitrate sources (manure, synthetic fertilizer, and septic waste) contributing to individual well nitrate can aid future regulatory decisions. Nitrogen, oxygen, and boron isotopes can be used as tracers to differentiate between the three main nitrate sources. Mixing models quantify the proportional contributions of sources to a mixture by using the concentration of conservative tracers within each source as a source signature. Deterministic mixing models are common, but do not allow for variability in the tracer source concentration or overlap of tracer concentrations between sources. Bayesian statistics used in conjunction with mixing models can incorporate variability in the source signature. We developed a Bayesian mixing model on a pilot network of 32 private domestic wells in the San Joaquin Valley for which nitrate as well as nitrogen, oxygen, and boron isotopes were measured. Probability distributions for nitrogen, oxygen, and boron isotope source signatures for manure, fertilizer, and septic waste were compiled from the literature and from a previous groundwater monitoring project on several dairies in the San Joaquin Valley. Median percent contribution of nitrate to wells from fertilizer, manure, and septic waste generally match the expected source based on land use patterns, with some exceptions.

Nonnegative Matrix Factorization for identification of unknown number of sources emitting delayed signals

PubMed Central

Iliev, Filip L.; Stanev, Valentin G.; Vesselinov, Velimir V.

2018-01-01

Factor analysis is broadly used as a powerful unsupervised machine learning tool for reconstruction of hidden features in recorded mixtures of signals. In the case of a linear approximation, the mixtures can be decomposed by a variety of model-free Blind Source Separation (BSS) algorithms. Most of the available BSS algorithms consider an instantaneous mixing of signals, while the case when the mixtures are linear combinations of signals with delays is less explored. Especially difficult is the case when the number of sources of the signals with delays is unknown and has to be determined from the data as well. To address this problem, in this paper, we present a new method based on Nonnegative Matrix Factorization (NMF) that is capable of identifying: (a) the unknown number of the sources, (b) the delays and speed of propagation of the signals, and (c) the locations of the sources. Our method can be used to decompose records of mixtures of signals with delays emitted by an unknown number of sources in a nondispersive medium, based only on recorded data. This is the case, for example, when electromagnetic signals from multiple antennas are received asynchronously; or mixtures of acoustic or seismic signals recorded by sensors located at different positions; or when a shift in frequency is induced by the Doppler effect. By applying our method to synthetic datasets, we demonstrate its ability to identify the unknown number of sources as well as the waveforms, the delays, and the strengths of the signals. Using Bayesian analysis, we also evaluate estimation uncertainties and identify the region of likelihood where the positions of the sources can be found. PMID:29518126

Nonnegative Matrix Factorization for identification of unknown number of sources emitting delayed signals.

PubMed

Iliev, Filip L; Stanev, Valentin G; Vesselinov, Velimir V; Alexandrov, Boian S

2018-01-01

Factor analysis is broadly used as a powerful unsupervised machine learning tool for reconstruction of hidden features in recorded mixtures of signals. In the case of a linear approximation, the mixtures can be decomposed by a variety of model-free Blind Source Separation (BSS) algorithms. Most of the available BSS algorithms consider an instantaneous mixing of signals, while the case when the mixtures are linear combinations of signals with delays is less explored. Especially difficult is the case when the number of sources of the signals with delays is unknown and has to be determined from the data as well. To address this problem, in this paper, we present a new method based on Nonnegative Matrix Factorization (NMF) that is capable of identifying: (a) the unknown number of the sources, (b) the delays and speed of propagation of the signals, and (c) the locations of the sources. Our method can be used to decompose records of mixtures of signals with delays emitted by an unknown number of sources in a nondispersive medium, based only on recorded data. This is the case, for example, when electromagnetic signals from multiple antennas are received asynchronously; or mixtures of acoustic or seismic signals recorded by sensors located at different positions; or when a shift in frequency is induced by the Doppler effect. By applying our method to synthetic datasets, we demonstrate its ability to identify the unknown number of sources as well as the waveforms, the delays, and the strengths of the signals. Using Bayesian analysis, we also evaluate estimation uncertainties and identify the region of likelihood where the positions of the sources can be found.

A Copula-Based Conditional Probabilistic Forecast Model for Wind Power Ramps

DOE Office of Scientific and Technical Information (OSTI.GOV)

Hodge, Brian S; Krishnan, Venkat K; Zhang, Jie

Efficient management of wind ramping characteristics can significantly reduce wind integration costs for balancing authorities. By considering the stochastic dependence of wind power ramp (WPR) features, this paper develops a conditional probabilistic wind power ramp forecast (cp-WPRF) model based on Copula theory. The WPRs dataset is constructed by extracting ramps from a large dataset of historical wind power. Each WPR feature (e.g., rate, magnitude, duration, and start-time) is separately forecasted by considering the coupling effects among different ramp features. To accurately model the marginal distributions with a copula, a Gaussian mixture model (GMM) is adopted to characterize the WPR uncertaintymore » and features. The Canonical Maximum Likelihood (CML) method is used to estimate parameters of the multivariable copula. The optimal copula model is chosen based on the Bayesian information criterion (BIC) from each copula family. Finally, the best conditions based cp-WPRF model is determined by predictive interval (PI) based evaluation metrics. Numerical simulations on publicly available wind power data show that the developed copula-based cp-WPRF model can predict WPRs with a high level of reliability and sharpness.« less

Using Bayesian Networks to Improve Knowledge Assessment

ERIC Educational Resources Information Center

Millan, Eva; Descalco, Luis; Castillo, Gladys; Oliveira, Paula; Diogo, Sandra

2013-01-01

In this paper, we describe the integration and evaluation of an existing generic Bayesian student model (GBSM) into an existing computerized testing system within the Mathematics Education Project (PmatE--Projecto Matematica Ensino) of the University of Aveiro. This generic Bayesian student model had been previously evaluated with simulated…

Bayesian Posterior Odds Ratios: Statistical Tools for Collaborative Evaluations

ERIC Educational Resources Information Center

Hicks, Tyler; Rodríguez-Campos, Liliana; Choi, Jeong Hoon

2018-01-01

To begin statistical analysis, Bayesians quantify their confidence in modeling hypotheses with priors. A prior describes the probability of a certain modeling hypothesis apart from the data. Bayesians should be able to defend their choice of prior to a skeptical audience. Collaboration between evaluators and stakeholders could make their choices…

Bayesian correlated clustering to integrate multiple datasets

PubMed Central

Kirk, Paul; Griffin, Jim E.; Savage, Richard S.; Ghahramani, Zoubin; Wild, David L.

2012-01-01

Motivation: The integration of multiple datasets remains a key challenge in systems biology and genomic medicine. Modern high-throughput technologies generate a broad array of different data types, providing distinct—but often complementary—information. We present a Bayesian method for the unsupervised integrative modelling of multiple datasets, which we refer to as MDI (Multiple Dataset Integration). MDI can integrate information from a wide range of different datasets and data types simultaneously (including the ability to model time series data explicitly using Gaussian processes). Each dataset is modelled using a Dirichlet-multinomial allocation (DMA) mixture model, with dependencies between these models captured through parameters that describe the agreement among the datasets. Results: Using a set of six artificially constructed time series datasets, we show that MDI is able to integrate a significant number of datasets simultaneously, and that it successfully captures the underlying structural similarity between the datasets. We also analyse a variety of real Saccharomyces cerevisiae datasets. In the two-dataset case, we show that MDI’s performance is comparable with the present state-of-the-art. We then move beyond the capabilities of current approaches and integrate gene expression, chromatin immunoprecipitation–chip and protein–protein interaction data, to identify a set of protein complexes for which genes are co-regulated during the cell cycle. Comparisons to other unsupervised data integration techniques—as well as to non-integrative approaches—demonstrate that MDI is competitive, while also providing information that would be difficult or impossible to extract using other methods. Availability: A Matlab implementation of MDI is available from http://www2.warwick.ac.uk/fac/sci/systemsbiology/research/software/. Contact: D.L.Wild@warwick.ac.uk Supplementary information: Supplementary data are available at Bioinformatics online. PMID:23047558

Disease Mapping of Zero-excessive Mesothelioma Data in Flanders

PubMed Central

Neyens, Thomas; Lawson, Andrew B.; Kirby, Russell S.; Nuyts, Valerie; Watjou, Kevin; Aregay, Mehreteab; Carroll, Rachel; Nawrot, Tim S.; Faes, Christel

2016-01-01

Purpose To investigate the distribution of mesothelioma in Flanders using Bayesian disease mapping models that account for both an excess of zeros and overdispersion. Methods The numbers of newly diagnosed mesothelioma cases within all Flemish municipalities between 1999 and 2008 were obtained from the Belgian Cancer Registry. To deal with overdispersion, zero-inflation and geographical association, the hurdle combined model was proposed, which has three components: a Bernoulli zero-inflation mixture component to account for excess zeros, a gamma random effect to adjust for overdispersion and a normal conditional autoregressive random effect to attribute spatial association. This model was compared with other existing methods in literature. Results The results indicate that hurdle models with a random effects term accounting for extra-variance in the Bernoulli zero-inflation component fit the data better than hurdle models that do not take overdispersion in the occurrence of zeros into account. Furthermore, traditional models that do not take into account excessive zeros but contain at least one random effects term that models extra-variance in the counts have better fits compared to their hurdle counterparts. In other words, the extra-variability, due to an excess of zeros, can be accommodated by spatially structured and/or unstructured random effects in a Poisson model such that the hurdle mixture model is not necessary. Conclusions Models taking into account zero-inflation do not always provide better fits to data with excessive zeros than less complex models. In this study, a simple conditional autoregressive model identified a cluster in mesothelioma cases near a former asbestos processing plant (Kapelle-op-den-Bos). This observation is likely linked with historical local asbestos exposures. Future research will clarify this. PMID:27908590

Disease mapping of zero-excessive mesothelioma data in Flanders.

PubMed

Neyens, Thomas; Lawson, Andrew B; Kirby, Russell S; Nuyts, Valerie; Watjou, Kevin; Aregay, Mehreteab; Carroll, Rachel; Nawrot, Tim S; Faes, Christel

2017-01-01

To investigate the distribution of mesothelioma in Flanders using Bayesian disease mapping models that account for both an excess of zeros and overdispersion. The numbers of newly diagnosed mesothelioma cases within all Flemish municipalities between 1999 and 2008 were obtained from the Belgian Cancer Registry. To deal with overdispersion, zero inflation, and geographical association, the hurdle combined model was proposed, which has three components: a Bernoulli zero-inflation mixture component to account for excess zeros, a gamma random effect to adjust for overdispersion, and a normal conditional autoregressive random effect to attribute spatial association. This model was compared with other existing methods in literature. The results indicate that hurdle models with a random effects term accounting for extra variance in the Bernoulli zero-inflation component fit the data better than hurdle models that do not take overdispersion in the occurrence of zeros into account. Furthermore, traditional models that do not take into account excessive zeros but contain at least one random effects term that models extra variance in the counts have better fits compared to their hurdle counterparts. In other words, the extra variability, due to an excess of zeros, can be accommodated by spatially structured and/or unstructured random effects in a Poisson model such that the hurdle mixture model is not necessary. Models taking into account zero inflation do not always provide better fits to data with excessive zeros than less complex models. In this study, a simple conditional autoregressive model identified a cluster in mesothelioma cases near a former asbestos processing plant (Kapelle-op-den-Bos). This observation is likely linked with historical local asbestos exposures. Future research will clarify this. Copyright © 2016 Elsevier Inc. All rights reserved.

BCM: toolkit for Bayesian analysis of Computational Models using samplers.

PubMed

Thijssen, Bram; Dijkstra, Tjeerd M H; Heskes, Tom; Wessels, Lodewyk F A

2016-10-21

Computational models in biology are characterized by a large degree of uncertainty. This uncertainty can be analyzed with Bayesian statistics, however, the sampling algorithms that are frequently used for calculating Bayesian statistical estimates are computationally demanding, and each algorithm has unique advantages and disadvantages. It is typically unclear, before starting an analysis, which algorithm will perform well on a given computational model. We present BCM, a toolkit for the Bayesian analysis of Computational Models using samplers. It provides efficient, multithreaded implementations of eleven algorithms for sampling from posterior probability distributions and for calculating marginal likelihoods. BCM includes tools to simplify the process of model specification and scripts for visualizing the results. The flexible architecture allows it to be used on diverse types of biological computational models. In an example inference task using a model of the cell cycle based on ordinary differential equations, BCM is significantly more efficient than existing software packages, allowing more challenging inference problems to be solved. BCM represents an efficient one-stop-shop for computational modelers wishing to use sampler-based Bayesian statistics.

Two Approaches to Calibration in Metrology

DOE Office of Scientific and Technical Information (OSTI.GOV)

Campanelli, Mark

2014-04-01

Inferring mathematical relationships with quantified uncertainty from measurement data is common to computational science and metrology. Sufficient knowledge of measurement process noise enables Bayesian inference. Otherwise, an alternative approach is required, here termed compartmentalized inference, because collection of uncertain data and model inference occur independently. Bayesian parameterized model inference is compared to a Bayesian-compatible compartmentalized approach for ISO-GUM compliant calibration problems in renewable energy metrology. In either approach, model evidence can help reduce model discrepancy.

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

USGS Publications Warehouse

Dorazio, Robert

2016-01-01

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

[Evaluation of estimation of prevalence ratio using bayesian log-binomial regression model].

PubMed

Gao, W L; Lin, H; Liu, X N; Ren, X W; Li, J S; Shen, X P; Zhu, S L

2017-03-10

To evaluate the estimation of prevalence ratio ( PR ) by using bayesian log-binomial regression model and its application, we estimated the PR of medical care-seeking prevalence to caregivers' recognition of risk signs of diarrhea in their infants by using bayesian log-binomial regression model in Openbugs software. The results showed that caregivers' recognition of infant' s risk signs of diarrhea was associated significantly with a 13% increase of medical care-seeking. Meanwhile, we compared the differences in PR 's point estimation and its interval estimation of medical care-seeking prevalence to caregivers' recognition of risk signs of diarrhea and convergence of three models (model 1: not adjusting for the covariates; model 2: adjusting for duration of caregivers' education, model 3: adjusting for distance between village and township and child month-age based on model 2) between bayesian log-binomial regression model and conventional log-binomial regression model. The results showed that all three bayesian log-binomial regression models were convergence and the estimated PRs were 1.130(95 %CI : 1.005-1.265), 1.128(95 %CI : 1.001-1.264) and 1.132(95 %CI : 1.004-1.267), respectively. Conventional log-binomial regression model 1 and model 2 were convergence and their PRs were 1.130(95 % CI : 1.055-1.206) and 1.126(95 % CI : 1.051-1.203), respectively, but the model 3 was misconvergence, so COPY method was used to estimate PR , which was 1.125 (95 %CI : 1.051-1.200). In addition, the point estimation and interval estimation of PRs from three bayesian log-binomial regression models differed slightly from those of PRs from conventional log-binomial regression model, but they had a good consistency in estimating PR . Therefore, bayesian log-binomial regression model can effectively estimate PR with less misconvergence and have more advantages in application compared with conventional log-binomial regression model.

A Preliminary Bayesian Analysis of Incomplete Longitudinal Data from a Small Sample: Methodological Advances in an International Comparative Study of Educational Inequality

ERIC Educational Resources Information Center

Hsieh, Chueh-An; Maier, Kimberly S.

2009-01-01

The capacity of Bayesian methods in estimating complex statistical models is undeniable. Bayesian data analysis is seen as having a range of advantages, such as an intuitive probabilistic interpretation of the parameters of interest, the efficient incorporation of prior information to empirical data analysis, model averaging and model selection.…

Dynamic Bayesian network modeling for longitudinal brain morphometry

PubMed Central

Chen, Rong; Resnick, Susan M; Davatzikos, Christos; Herskovits, Edward H

2011-01-01

Identifying interactions among brain regions from structural magnetic-resonance images presents one of the major challenges in computational neuroanatomy. We propose a Bayesian data-mining approach to the detection of longitudinal morphological changes in the human brain. Our method uses a dynamic Bayesian network to represent evolving inter-regional dependencies. The major advantage of dynamic Bayesian network modeling is that it can represent complicated interactions among temporal processes. We validated our approach by analyzing a simulated atrophy study, and found that this approach requires only a small number of samples to detect the ground-truth temporal model. We further applied dynamic Bayesian network modeling to a longitudinal study of normal aging and mild cognitive impairment — the Baltimore Longitudinal Study of Aging. We found that interactions among regional volume-change rates for the mild cognitive impairment group are different from those for the normal-aging group. PMID:21963916

Variational learning and bits-back coding: an information-theoretic view to Bayesian learning.

PubMed

Honkela, Antti; Valpola, Harri

2004-07-01

The bits-back coding first introduced by Wallace in 1990 and later by Hinton and van Camp in 1993 provides an interesting link between Bayesian learning and information-theoretic minimum-description-length (MDL) learning approaches. The bits-back coding allows interpreting the cost function used in the variational Bayesian method called ensemble learning as a code length in addition to the Bayesian view of misfit of the posterior approximation and a lower bound of model evidence. Combining these two viewpoints provides interesting insights to the learning process and the functions of different parts of the model. In this paper, the problem of variational Bayesian learning of hierarchical latent variable models is used to demonstrate the benefits of the two views. The code-length interpretation provides new views to many parts of the problem such as model comparison and pruning and helps explain many phenomena occurring in learning.

Semiparametric Bayesian classification with longitudinal markers

PubMed Central

De la Cruz-Mesía, Rolando; Quintana, Fernando A.; Müller, Peter

2013-01-01

Summary We analyse data from a study involving 173 pregnant women. The data are observed values of the β human chorionic gonadotropin hormone measured during the first 80 days of gestational age, including from one up to six longitudinal responses for each woman. The main objective in this study is to predict normal versus abnormal pregnancy outcomes from data that are available at the early stages of pregnancy. We achieve the desired classification with a semiparametric hierarchical model. Specifically, we consider a Dirichlet process mixture prior for the distribution of the random effects in each group. The unknown random-effects distributions are allowed to vary across groups but are made dependent by using a design vector to select different features of a single underlying random probability measure. The resulting model is an extension of the dependent Dirichlet process model, with an additional probability model for group classification. The model is shown to perform better than an alternative model which is based on independent Dirichlet processes for the groups. Relevant posterior distributions are summarized by using Markov chain Monte Carlo methods. PMID:24368871

Classifying emotion in Twitter using Bayesian network

NASA Astrophysics Data System (ADS)

Surya Asriadie, Muhammad; Syahrul Mubarok, Mohamad; Adiwijaya

2018-03-01

Language is used to express not only facts, but also emotions. Emotions are noticeable from behavior up to the social media statuses written by a person. Analysis of emotions in a text is done in a variety of media such as Twitter. This paper studies classification of emotions on twitter using Bayesian network because of its ability to model uncertainty and relationships between features. The result is two models based on Bayesian network which are Full Bayesian Network (FBN) and Bayesian Network with Mood Indicator (BNM). FBN is a massive Bayesian network where each word is treated as a node. The study shows the method used to train FBN is not very effective to create the best model and performs worse compared to Naive Bayes. F1-score for FBN is 53.71%, while for Naive Bayes is 54.07%. BNM is proposed as an alternative method which is based on the improvement of Multinomial Naive Bayes and has much lower computational complexity compared to FBN. Even though it’s not better compared to FBN, the resulting model successfully improves the performance of Multinomial Naive Bayes. F1-Score for Multinomial Naive Bayes model is 51.49%, while for BNM is 52.14%.

Additive Genetic Variability and the Bayesian Alphabet

PubMed Central

Gianola, Daniel; de los Campos, Gustavo; Hill, William G.; Manfredi, Eduardo; Fernando, Rohan

2009-01-01

The use of all available molecular markers in statistical models for prediction of quantitative traits has led to what could be termed a genomic-assisted selection paradigm in animal and plant breeding. This article provides a critical review of some theoretical and statistical concepts in the context of genomic-assisted genetic evaluation of animals and crops. First, relationships between the (Bayesian) variance of marker effects in some regression models and additive genetic variance are examined under standard assumptions. Second, the connection between marker genotypes and resemblance between relatives is explored, and linkages between a marker-based model and the infinitesimal model are reviewed. Third, issues associated with the use of Bayesian models for marker-assisted selection, with a focus on the role of the priors, are examined from a theoretical angle. The sensitivity of a Bayesian specification that has been proposed (called “Bayes A”) with respect to priors is illustrated with a simulation. Methods that can solve potential shortcomings of some of these Bayesian regression procedures are discussed briefly. PMID:19620397

Bayesian network modeling applied to coastal geomorphology: lessons learned from a decade of experimentation and application

NASA Astrophysics Data System (ADS)

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 demonstrate how Bayesian networks are used to extract new insights about coastal morphologic behavior, assess impacts to societal and ecological systems, and communicate probabilistic predictions to decision makers.

A Bayesian least squares support vector machines based framework for fault diagnosis and failure prognosis

NASA Astrophysics Data System (ADS)

Khawaja, Taimoor Saleem

A high-belief low-overhead Prognostics and Health Management (PHM) system is desired for online real-time monitoring of complex non-linear systems operating in a complex (possibly non-Gaussian) noise environment. This thesis presents a Bayesian Least Squares Support Vector Machine (LS-SVM) based framework for fault diagnosis and failure prognosis in nonlinear non-Gaussian systems. The methodology assumes the availability of real-time process measurements, definition of a set of fault indicators and the existence of empirical knowledge (or historical data) to characterize both nominal and abnormal operating conditions. An efficient yet powerful Least Squares Support Vector Machine (LS-SVM) algorithm, set within a Bayesian Inference framework, not only allows for the development of real-time algorithms for diagnosis and prognosis but also provides a solid theoretical framework to address key concepts related to classification for diagnosis and regression modeling for prognosis. SVM machines are founded on the principle of Structural Risk Minimization (SRM) which tends to find a good trade-off between low empirical risk and small capacity. The key features in SVM are the use of non-linear kernels, the absence of local minima, the sparseness of the solution and the capacity control obtained by optimizing the margin. The Bayesian Inference framework linked with LS-SVMs allows a probabilistic interpretation of the results for diagnosis and prognosis. Additional levels of inference provide the much coveted features of adaptability and tunability of the modeling parameters. The two main modules considered in this research are fault diagnosis and failure prognosis. With the goal of designing an efficient and reliable fault diagnosis scheme, a novel Anomaly Detector is suggested based on the LS-SVM machines. The proposed scheme uses only baseline data to construct a 1-class LS-SVM machine which, when presented with online data is able to distinguish between normal behavior and any abnormal or novel data during real-time operation. The results of the scheme are interpreted as a posterior probability of health (1 - probability of fault). As shown through two case studies in Chapter 3, the scheme is well suited for diagnosing imminent faults in dynamical non-linear systems. Finally, the failure prognosis scheme is based on an incremental weighted Bayesian LS-SVR machine. It is particularly suited for online deployment given the incremental nature of the algorithm and the quick optimization problem solved in the LS-SVR algorithm. By way of kernelization and a Gaussian Mixture Modeling (GMM) scheme, the algorithm can estimate "possibly" non-Gaussian posterior distributions for complex non-linear systems. An efficient regression scheme associated with the more rigorous core algorithm allows for long-term predictions, fault growth estimation with confidence bounds and remaining useful life (RUL) estimation after a fault is detected. The leading contributions of this thesis are (a) the development of a novel Bayesian Anomaly Detector for efficient and reliable Fault Detection and Identification (FDI) based on Least Squares Support Vector Machines, (b) the development of a data-driven real-time architecture for long-term Failure Prognosis using Least Squares Support Vector Machines, (c) Uncertainty representation and management using Bayesian Inference for posterior distribution estimation and hyper-parameter tuning, and finally (d) the statistical characterization of the performance of diagnosis and prognosis algorithms in order to relate the efficiency and reliability of the proposed schemes.

A comment on priors for Bayesian occupancy models.

PubMed

Northrup, Joseph M; Gerber, Brian D

2018-01-01

Understanding patterns of species occurrence and the processes underlying these patterns is fundamental to the study of ecology. One of the more commonly used approaches to investigate species occurrence patterns is occupancy modeling, which can account for imperfect detection of a species during surveys. In recent years, there has been a proliferation of Bayesian modeling in ecology, which includes fitting Bayesian occupancy models. The Bayesian framework is appealing to ecologists for many reasons, including the ability to incorporate prior information through the specification of prior distributions on parameters. While ecologists almost exclusively intend to choose priors so that they are "uninformative" or "vague", such priors can easily be unintentionally highly informative. Here we report on how the specification of a "vague" normally distributed (i.e., Gaussian) prior on coefficients in Bayesian occupancy models can unintentionally influence parameter estimation. Using both simulated data and empirical examples, we illustrate how this issue likely compromises inference about species-habitat relationships. While the extent to which these informative priors influence inference depends on the data set, researchers fitting Bayesian occupancy models should conduct sensitivity analyses to ensure intended inference, or employ less commonly used priors that are less informative (e.g., logistic or t prior distributions). We provide suggestions for addressing this issue in occupancy studies, and an online tool for exploring this issue under different contexts.

Final Report, DOE Early Career Award: Predictive modeling of complex physical systems: new tools for statistical inference, uncertainty quantification, and experimental design

DOE Office of Scientific and Technical Information (OSTI.GOV)

Marzouk, Youssef

Predictive simulation of complex physical systems increasingly rests on the interplay of experimental observations with computational models. Key inputs, parameters, or structural aspects of models may be incomplete or unknown, and must be developed from indirect and limited observations. At the same time, quantified uncertainties are needed to qualify computational predictions in the support of design and decision-making. In this context, Bayesian statistics provides a foundation for inference from noisy and limited data, but at prohibitive computional expense. This project intends to make rigorous predictive modeling *feasible* in complex physical systems, via accelerated and scalable tools for uncertainty quantification, Bayesianmore » inference, and experimental design. Specific objectives are as follows: 1. Develop adaptive posterior approximations and dimensionality reduction approaches for Bayesian inference in high-dimensional nonlinear systems. 2. Extend accelerated Bayesian methodologies to large-scale {\\em sequential} data assimilation, fully treating nonlinear models and non-Gaussian state and parameter distributions. 3. Devise efficient surrogate-based methods for Bayesian model selection and the learning of model structure. 4. Develop scalable simulation/optimization approaches to nonlinear Bayesian experimental design, for both parameter inference and model selection. 5. Demonstrate these inferential tools on chemical kinetic models in reacting flow, constructing and refining thermochemical and electrochemical models from limited data. Demonstrate Bayesian filtering on canonical stochastic PDEs and in the dynamic estimation of inhomogeneous subsurface properties and flow fields.« less

Bayesian estimation inherent in a Mexican-hat-type neural network

NASA Astrophysics Data System (ADS)

Takiyama, Ken

2016-05-01

Brain functions, such as perception, motor control and learning, and decision making, have been explained based on a Bayesian framework, i.e., to decrease the effects of noise inherent in the human nervous system or external environment, our brain integrates sensory and a priori information in a Bayesian optimal manner. However, it remains unclear how Bayesian computations are implemented in the brain. Herein, I address this issue by analyzing a Mexican-hat-type neural network, which was used as a model of the visual cortex, motor cortex, and prefrontal cortex. I analytically demonstrate that the dynamics of an order parameter in the model corresponds exactly to a variational inference of a linear Gaussian state-space model, a Bayesian estimation, when the strength of recurrent synaptic connectivity is appropriately stronger than that of an external stimulus, a plausible condition in the brain. This exact correspondence can reveal the relationship between the parameters in the Bayesian estimation and those in the neural network, providing insight for understanding brain functions.

SIBIS: a Bayesian model for inconsistent protein sequence estimation.

PubMed

Khenoussi, Walyd; Vanhoutrève, Renaud; Poch, Olivier; Thompson, Julie D

2014-09-01

The prediction of protein coding genes is a major challenge that depends on the quality of genome sequencing, the accuracy of the model used to elucidate the exonic structure of the genes and the complexity of the gene splicing process leading to different protein variants. As a consequence, today's protein databases contain a huge amount of inconsistency, due to both natural variants and sequence prediction errors. We have developed a new method, called SIBIS, to detect such inconsistencies based on the evolutionary information in multiple sequence alignments. A Bayesian framework, combined with Dirichlet mixture models, is used to estimate the probability of observing specific amino acids and to detect inconsistent or erroneous sequence segments. We evaluated the performance of SIBIS on a reference set of protein sequences with experimentally validated errors and showed that the sensitivity is significantly higher than previous methods, with only a small loss of specificity. We also assessed a large set of human sequences from the UniProt database and found evidence of inconsistency in 48% of the previously uncharacterized sequences. We conclude that the integration of quality control methods like SIBIS in automatic analysis pipelines will be critical for the robust inference of structural, functional and phylogenetic information from these sequences. Source code, implemented in C on a linux system, and the datasets of protein sequences are freely available for download at http://www.lbgi.fr/∼julie/SIBIS. © The Author 2014. Published by Oxford University Press. All rights reserved. For Permissions, please e-mail: journals.permissions@oup.com.

Development of an Integrated Team Training Design and Assessment Architecture to Support Adaptability in Healthcare Teams

DTIC Science & Technology

2016-10-01

and implementation of embedded, adaptive feedback and performance assessment. The investigators also initiated work designing a Bayesian Belief ...training; Teamwork; Adaptive performance; Leadership; Simulation; Modeling; Bayesian belief networks (BBN) 16. SECURITY CLASSIFICATION OF: 17. LIMITATION...Trauma teams Team training Teamwork Adaptability Adaptive performance Leadership Simulation Modeling Bayesian belief networks (BBN) 6

A Bayesian Network Approach to Modeling Learning Progressions and Task Performance. CRESST Report 776

ERIC Educational Resources Information Center

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…

Initialization and Restart in Stochastic Local Search: Computing a Most Probable Explanation in Bayesian Networks

NASA Technical Reports Server (NTRS)

Mengshoel, Ole J.; Wilkins, David C.; Roth, Dan

2010-01-01

For hard computational problems, stochastic local search has proven to be a competitive approach to finding optimal or approximately optimal problem solutions. Two key research questions for stochastic local search algorithms are: Which algorithms are effective for initialization? When should the search process be restarted? In the present work we investigate these research questions in the context of approximate computation of most probable explanations (MPEs) in Bayesian networks (BNs). We introduce a novel approach, based on the Viterbi algorithm, to explanation initialization in BNs. While the Viterbi algorithm works on sequences and trees, our approach works on BNs with arbitrary topologies. We also give a novel formalization of stochastic local search, with focus on initialization and restart, using probability theory and mixture models. Experimentally, we apply our methods to the problem of MPE computation, using a stochastic local search algorithm known as Stochastic Greedy Search. By carefully optimizing both initialization and restart, we reduce the MPE search time for application BNs by several orders of magnitude compared to using uniform at random initialization without restart. On several BNs from applications, the performance of Stochastic Greedy Search is competitive with clique tree clustering, a state-of-the-art exact algorithm used for MPE computation in BNs.

Nonparametric Bayesian Modeling for Automated Database Schema Matching

DOE Office of Scientific and Technical Information (OSTI.GOV)

Ferragut, Erik M; Laska, Jason A

2015-01-01

The problem of merging databases arises in many government and commercial applications. Schema matching, a common first step, identifies equivalent fields between databases. We introduce a schema matching framework that builds nonparametric Bayesian models for each field and compares them by computing the probability that a single model could have generated both fields. Our experiments show that our method is more accurate and faster than the existing instance-based matching algorithms in part because of the use of nonparametric Bayesian models.

Development of dynamic Bayesian models for web application test management

NASA Astrophysics Data System (ADS)

Azarnova, T. V.; Polukhin, P. V.; Bondarenko, Yu V.; Kashirina, I. L.

2018-03-01

The mathematical apparatus of dynamic Bayesian networks is an effective and technically proven tool that can be used to model complex stochastic dynamic processes. According to the results of the research, mathematical models and methods of dynamic Bayesian networks provide a high coverage of stochastic tasks associated with error testing in multiuser software products operated in a dynamically changing environment. Formalized representation of the discrete test process as a dynamic Bayesian model allows us to organize the logical connection between individual test assets for multiple time slices. This approach gives an opportunity to present testing as a discrete process with set structural components responsible for the generation of test assets. Dynamic Bayesian network-based models allow us to combine in one management area individual units and testing components with different functionalities and a direct influence on each other in the process of comprehensive testing of various groups of computer bugs. The application of the proposed models provides an opportunity to use a consistent approach to formalize test principles and procedures, methods used to treat situational error signs, and methods used to produce analytical conclusions based on test results.

Trans-dimensional and hierarchical Bayesian approaches toward rigorous estimation of seismic sources and structures in the Northeast Asia

NASA Astrophysics Data System (ADS)

Kim, Seongryong; Tkalčić, Hrvoje; Mustać, Marija; Rhie, Junkee; Ford, Sean

2016-04-01

A framework is presented within which we provide rigorous estimations for seismic sources and structures in the Northeast Asia. We use Bayesian inversion methods, which enable statistical estimations of models and their uncertainties based on data information. Ambiguities in error statistics and model parameterizations are addressed by hierarchical and trans-dimensional (trans-D) techniques, which can be inherently implemented in the Bayesian inversions. Hence reliable estimation of model parameters and their uncertainties is possible, thus avoiding arbitrary regularizations and parameterizations. Hierarchical and trans-D inversions are performed to develop a three-dimensional velocity model using ambient noise data. To further improve the model, we perform joint inversions with receiver function data using a newly developed Bayesian method. For the source estimation, a novel moment tensor inversion method is presented and applied to regional waveform data of the North Korean nuclear explosion tests. By the combination of new Bayesian techniques and the structural model, coupled with meaningful uncertainties related to each of the processes, more quantitative monitoring and discrimination of seismic events is possible.

Bayesian Models Leveraging Bioactivity and Cytotoxicity Information for Drug Discovery

PubMed Central

Ekins, Sean; Reynolds, Robert C.; Kim, Hiyun; Koo, Mi-Sun; Ekonomidis, Marilyn; Talaue, Meliza; Paget, Steve D.; Woolhiser, Lisa K.; Lenaerts, Anne J.; Bunin, Barry A.; Connell, Nancy; Freundlich, Joel S.

2013-01-01

SUMMARY Identification of unique leads represents a significant challenge in drug discovery. This hurdle is magnified in neglected diseases such as tuberculosis. We have leveraged public high-throughput screening (HTS) data, to experimentally validate virtual screening approach employing Bayesian models built with bioactivity information (single-event model) as well as bioactivity and cytotoxicity information (dual-event model). We virtually screen a commercial library and experimentally confirm actives with hit rates exceeding typical HTS results by 1-2 orders of magnitude. The first dual-event Bayesian model identified compounds with antitubercular whole-cell activity and low mammalian cell cytotoxicity from a published set of antimalarials. The most potent hit exhibits the in vitro activity and in vitro/in vivo safety profile of a drug lead. These Bayesian models offer significant economies in time and cost to drug discovery. PMID:23521795

Bayesian data analysis for newcomers.

PubMed

Kruschke, John K; Liddell, Torrin M

2018-02-01

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

A Dirichlet-Multinomial Bayes Classifier for Disease Diagnosis with Microbial Compositions.

PubMed

Gao, Xiang; Lin, Huaiying; Dong, Qunfeng

2017-01-01

Dysbiosis of microbial communities is associated with various human diseases, raising the possibility of using microbial compositions as biomarkers for disease diagnosis. We have developed a Bayes classifier by modeling microbial compositions with Dirichlet-multinomial distributions, which are widely used to model multicategorical count data with extra variation. The parameters of the Dirichlet-multinomial distributions are estimated from training microbiome data sets based on maximum likelihood. The posterior probability of a microbiome sample belonging to a disease or healthy category is calculated based on Bayes' theorem, using the likelihood values computed from the estimated Dirichlet-multinomial distribution, as well as a prior probability estimated from the training microbiome data set or previously published information on disease prevalence. When tested on real-world microbiome data sets, our method, called DMBC (for Dirichlet-multinomial Bayes classifier), shows better classification accuracy than the only existing Bayesian microbiome classifier based on a Dirichlet-multinomial mixture model and the popular random forest method. The advantage of DMBC is its built-in automatic feature selection, capable of identifying a subset of microbial taxa with the best classification accuracy between different classes of samples based on cross-validation. This unique ability enables DMBC to maintain and even improve its accuracy at modeling species-level taxa. The R package for DMBC is freely available at https://github.com/qunfengdong/DMBC. IMPORTANCE By incorporating prior information on disease prevalence, Bayes classifiers have the potential to estimate disease probability better than other common machine-learning methods. Thus, it is important to develop Bayes classifiers specifically tailored for microbiome data. Our method shows higher classification accuracy than the only existing Bayesian classifier and the popular random forest method, and thus provides an alternative option for using microbial compositions for disease diagnosis.

The Spike-and-Slab Lasso Generalized Linear Models for Prediction and Associated Genes Detection.

PubMed

Tang, Zaixiang; Shen, Yueping; Zhang, Xinyan; Yi, Nengjun

2017-01-01

Large-scale "omics" data have been increasingly used as an important resource for prognostic prediction of diseases and detection of associated genes. However, there are considerable challenges in analyzing high-dimensional molecular data, including the large number of potential molecular predictors, limited number of samples, and small effect of each predictor. We propose new Bayesian hierarchical generalized linear models, called spike-and-slab lasso GLMs, for prognostic prediction and detection of associated genes using large-scale molecular data. The proposed model employs a spike-and-slab mixture double-exponential prior for coefficients that can induce weak shrinkage on large coefficients, and strong shrinkage on irrelevant coefficients. We have developed a fast and stable algorithm to fit large-scale hierarchal GLMs by incorporating expectation-maximization (EM) steps into the fast cyclic coordinate descent algorithm. The proposed approach integrates nice features of two popular methods, i.e., penalized lasso and Bayesian spike-and-slab variable selection. The performance of the proposed method is assessed via extensive simulation studies. The results show that the proposed approach can provide not only more accurate estimates of the parameters, but also better prediction. We demonstrate the proposed procedure on two cancer data sets: a well-known breast cancer data set consisting of 295 tumors, and expression data of 4919 genes; and the ovarian cancer data set from TCGA with 362 tumors, and expression data of 5336 genes. Our analyses show that the proposed procedure can generate powerful models for predicting outcomes and detecting associated genes. The methods have been implemented in a freely available R package BhGLM (http://www.ssg.uab.edu/bhglm/). Copyright © 2017 by the Genetics Society of America.

Evaluation of calibration efficacy under different levels of uncertainty

DOE PAGES

Heo, Yeonsook; Graziano, Diane J.; Guzowski, Leah; ...

2014-06-10

This study examines how calibration performs under different levels of uncertainty in model input data. It specifically assesses the efficacy of Bayesian calibration to enhance the reliability of EnergyPlus model predictions. A Bayesian approach can be used to update uncertain values of parameters, given measured energy-use data, and to quantify the associated uncertainty.We assess the efficacy of Bayesian calibration under a controlled virtual-reality setup, which enables rigorous validation of the accuracy of calibration results in terms of both calibrated parameter values and model predictions. Case studies demonstrate the performance of Bayesian calibration of base models developed from audit data withmore » differing levels of detail in building design, usage, and operation.« less

EFFICIENT MODEL-FITTING AND MODEL-COMPARISON FOR HIGH-DIMENSIONAL BAYESIAN GEOSTATISTICAL MODELS. (R826887)

EPA Science Inventory

Geostatistical models are appropriate for spatially distributed data measured at irregularly spaced locations. We propose an efficient Markov chain Monte Carlo (MCMC) algorithm for fitting Bayesian geostatistical models with substantial numbers of unknown parameters to sizable...

Universal Darwinism As a Process of Bayesian Inference.

PubMed

Campbell, John O

2016-01-01

Many of the mathematical frameworks describing natural selection are equivalent to Bayes' Theorem, also known as Bayesian updating. By definition, a process of Bayesian Inference is one which involves a Bayesian update, so we may conclude that these frameworks describe natural selection as a process of Bayesian inference. Thus, natural selection serves as a counter example to a widely-held interpretation that restricts Bayesian Inference to human mental processes (including the endeavors of statisticians). As Bayesian inference can always be cast in terms of (variational) free energy minimization, natural selection can be viewed as comprising two components: a generative model of an "experiment" in the external world environment, and the results of that "experiment" or the "surprise" entailed by predicted and actual outcomes of the "experiment." Minimization of free energy implies that the implicit measure of "surprise" experienced serves to update the generative model in a Bayesian manner. This description closely accords with the mechanisms of generalized Darwinian process proposed both by Dawkins, in terms of replicators and vehicles, and Campbell, in terms of inferential systems. Bayesian inference is an algorithm for the accumulation of evidence-based knowledge. This algorithm is now seen to operate over a wide range of evolutionary processes, including natural selection, the evolution of mental models and cultural evolutionary processes, notably including science itself. The variational principle of free energy minimization may thus serve as a unifying mathematical framework for universal Darwinism, the study of evolutionary processes operating throughout nature.

Universal Darwinism As a Process of Bayesian Inference

PubMed Central

Campbell, John O.

2016-01-01

Many of the mathematical frameworks describing natural selection are equivalent to Bayes' Theorem, also known as Bayesian updating. By definition, a process of Bayesian Inference is one which involves a Bayesian update, so we may conclude that these frameworks describe natural selection as a process of Bayesian inference. Thus, natural selection serves as a counter example to a widely-held interpretation that restricts Bayesian Inference to human mental processes (including the endeavors of statisticians). As Bayesian inference can always be cast in terms of (variational) free energy minimization, natural selection can be viewed as comprising two components: a generative model of an “experiment” in the external world environment, and the results of that “experiment” or the “surprise” entailed by predicted and actual outcomes of the “experiment.” Minimization of free energy implies that the implicit measure of “surprise” experienced serves to update the generative model in a Bayesian manner. This description closely accords with the mechanisms of generalized Darwinian process proposed both by Dawkins, in terms of replicators and vehicles, and Campbell, in terms of inferential systems. Bayesian inference is an algorithm for the accumulation of evidence-based knowledge. This algorithm is now seen to operate over a wide range of evolutionary processes, including natural selection, the evolution of mental models and cultural evolutionary processes, notably including science itself. The variational principle of free energy minimization may thus serve as a unifying mathematical framework for universal Darwinism, the study of evolutionary processes operating throughout nature. PMID:27375438

A Bayesian hierarchical diffusion model decomposition of performance in Approach–Avoidance Tasks

PubMed Central

Krypotos, Angelos-Miltiadis; Beckers, Tom; Kindt, Merel; Wagenmakers, Eric-Jan

2015-01-01

Common methods for analysing response time (RT) tasks, frequently used across different disciplines of psychology, suffer from a number of limitations such as the failure to directly measure the underlying latent processes of interest and the inability to take into account the uncertainty associated with each individual's point estimate of performance. Here, we discuss a Bayesian hierarchical diffusion model and apply it to RT data. This model allows researchers to decompose performance into meaningful psychological processes and to account optimally for individual differences and commonalities, even with relatively sparse data. We highlight the advantages of the Bayesian hierarchical diffusion model decomposition by applying it to performance on Approach–Avoidance Tasks, widely used in the emotion and psychopathology literature. Model fits for two experimental data-sets demonstrate that the model performs well. The Bayesian hierarchical diffusion model overcomes important limitations of current analysis procedures and provides deeper insight in latent psychological processes of interest. PMID:25491372

Multivariate Bayesian modeling of known and unknown causes of events--an application to biosurveillance.

PubMed

Shen, Yanna; Cooper, Gregory F

2012-09-01

This paper investigates Bayesian modeling of known and unknown causes of events in the context of disease-outbreak detection. We introduce a multivariate Bayesian approach that models multiple evidential features of every person in the population. This approach models and detects (1) known diseases (e.g., influenza and anthrax) by using informative prior probabilities and (2) unknown diseases (e.g., a new, highly contagious respiratory virus that has never been seen before) by using relatively non-informative prior probabilities. We report the results of simulation experiments which support that this modeling method can improve the detection of new disease outbreaks in a population. A contribution of this paper is that it introduces a multivariate Bayesian approach for jointly modeling both known and unknown causes of events. Such modeling has general applicability in domains where the space of known causes is incomplete. Copyright © 2010 Elsevier Ireland Ltd. All rights reserved.

Model Comparison of Bayesian Semiparametric and Parametric Structural Equation Models

ERIC Educational Resources Information Center

Song, Xin-Yuan; Xia, Ye-Mao; Pan, Jun-Hao; Lee, Sik-Yum

2011-01-01

Structural equation models have wide applications. One of the most important issues in analyzing structural equation models is model comparison. This article proposes a Bayesian model comparison statistic, namely the "L[subscript nu]"-measure for both semiparametric and parametric structural equation models. For illustration purposes, we consider…

Rigorous Approach in Investigation of Seismic Structure and Source Characteristicsin Northeast Asia: Hierarchical and Trans-dimensional Bayesian Inversion

NASA Astrophysics Data System (ADS)

Mustac, M.; Kim, S.; Tkalcic, H.; Rhie, J.; Chen, Y.; Ford, S. R.; Sebastian, N.

2015-12-01

Conventional approaches to inverse problems suffer from non-linearity and non-uniqueness in estimations of seismic structures and source properties. Estimated results and associated uncertainties are often biased by applied regularizations and additional constraints, which are commonly introduced to solve such problems. Bayesian methods, however, provide statistically meaningful estimations of models and their uncertainties constrained by data information. In addition, hierarchical and trans-dimensional (trans-D) techniques are inherently implemented in the Bayesian framework to account for involved error statistics and model parameterizations, and, in turn, allow more rigorous estimations of the same. Here, we apply Bayesian methods throughout the entire inference process to estimate seismic structures and source properties in Northeast Asia including east China, the Korean peninsula, and the Japanese islands. Ambient noise analysis is first performed to obtain a base three-dimensional (3-D) heterogeneity model using continuous broadband waveforms from more than 300 stations. As for the tomography of surface wave group and phase velocities in the 5-70 s band, we adopt a hierarchical and trans-D Bayesian inversion method using Voronoi partition. The 3-D heterogeneity model is further improved by joint inversions of teleseismic receiver functions and dispersion data using a newly developed high-efficiency Bayesian technique. The obtained model is subsequently used to prepare 3-D structural Green's functions for the source characterization. A hierarchical Bayesian method for point source inversion using regional complete waveform data is applied to selected events from the region. The seismic structure and source characteristics with rigorously estimated uncertainties from the novel Bayesian methods provide enhanced monitoring and discrimination of seismic events in northeast Asia.

Semiparametric Thurstonian Models for Recurrent Choices: A Bayesian Analysis

ERIC Educational Resources Information Center

Ansari, Asim; Iyengar, Raghuram

2006-01-01

We develop semiparametric Bayesian Thurstonian models for analyzing repeated choice decisions involving multinomial, multivariate binary or multivariate ordinal data. Our modeling framework has multiple components that together yield considerable flexibility in modeling preference utilities, cross-sectional heterogeneity and parameter-driven…

Next Steps in Bayesian Structural Equation Models: Comments on, Variations of, and Extensions to Muthen and Asparouhov (2012)

ERIC Educational Resources Information Center

Rindskopf, David

2012-01-01

Muthen and Asparouhov (2012) made a strong case for the advantages of Bayesian methodology in factor analysis and structural equation models. I show additional extensions and adaptations of their methods and show how non-Bayesians can take advantage of many (though not all) of these advantages by using interval restrictions on parameters. By…

Careful with Those Priors: A Note on Bayesian Estimation in Two-Parameter Logistic Item Response Theory Models

ERIC Educational Resources Information Center

Marcoulides, Katerina M.

2018-01-01

This study examined the use of Bayesian analysis methods for the estimation of item parameters in a two-parameter logistic item response theory model. Using simulated data under various design conditions with both informative and non-informative priors, the parameter recovery of Bayesian analysis methods were examined. Overall results showed that…

A Bayesian Approach to Person Fit Analysis in Item Response Theory Models. Research Report.

ERIC Educational Resources Information Center

Glas, Cees A. W.; Meijer, Rob R.

A Bayesian approach to the evaluation of person fit in item response theory (IRT) models is presented. In a posterior predictive check, the observed value on a discrepancy variable is positioned in its posterior distribution. In a Bayesian framework, a Markov Chain Monte Carlo procedure can be used to generate samples of the posterior distribution…

A Tutorial Introduction to Bayesian Models of Cognitive Development

ERIC Educational Resources Information Center

Perfors, Amy; Tenenbaum, Joshua B.; Griffiths, Thomas L.; Xu, Fei

2011-01-01

We present an introduction to Bayesian inference as it is used in probabilistic models of cognitive development. Our goal is to provide an intuitive and accessible guide to the "what", the "how", and the "why" of the Bayesian approach: what sorts of problems and data the framework is most relevant for, and how and why it may be useful for…

Modeling of Academic Achievement of Primary School Students in Ethiopia Using Bayesian Multilevel Approach

ERIC Educational Resources Information Center

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…

A Simulation Study Comparison of Bayesian Estimation with Conventional Methods for Estimating Unknown Change Points

ERIC Educational Resources Information Center

Wang, Lijuan; McArdle, John J.

2008-01-01

The main purpose of this research is to evaluate the performance of a Bayesian approach for estimating unknown change points using Monte Carlo simulations. The univariate and bivariate unknown change point mixed models were presented and the basic idea of the Bayesian approach for estimating the models was discussed. The performance of Bayesian…

Estimation of parameter uncertainty for an activated sludge model using Bayesian inference: a comparison with the frequentist method.

PubMed

Zonta, Zivko J; Flotats, Xavier; Magrí, Albert

2014-08-01

The procedure commonly used for the assessment of the parameters included in activated sludge models (ASMs) relies on the estimation of their optimal value within a confidence region (i.e. frequentist inference). Once optimal values are estimated, parameter uncertainty is computed through the covariance matrix. However, alternative approaches based on the consideration of the model parameters as probability distributions (i.e. Bayesian inference), may be of interest. The aim of this work is to apply (and compare) both Bayesian and frequentist inference methods when assessing uncertainty for an ASM-type model, which considers intracellular storage and biomass growth, simultaneously. Practical identifiability was addressed exclusively considering respirometric profiles based on the oxygen uptake rate and with the aid of probabilistic global sensitivity analysis. Parameter uncertainty was thus estimated according to both the Bayesian and frequentist inferential procedures. Results were compared in order to evidence the strengths and weaknesses of both approaches. Since it was demonstrated that Bayesian inference could be reduced to a frequentist approach under particular hypotheses, the former can be considered as a more generalist methodology. Hence, the use of Bayesian inference is encouraged for tackling inferential issues in ASM environments.

Generation of a mixture model ground-motion prediction equation for Northern Chile

NASA Astrophysics Data System (ADS)

Haendel, A.; Kuehn, N. M.; Scherbaum, F.

2012-12-01

In probabilistic seismic hazard analysis (PSHA) empirically derived ground motion prediction equations (GMPEs) are usually applied to estimate the ground motion at a site of interest as a function of source, path and site related predictor variables. Because GMPEs are derived from limited datasets they are not expected to give entirely accurate estimates or to reflect the whole range of possible future ground motion, thus giving rise to epistemic uncertainty in the hazard estimates. This is especially true for regions without an indigenous GMPE where foreign models have to be applied. The choice of appropriate GMPEs can then dominate the overall uncertainty in hazard assessments. In order to quantify this uncertainty, the set of ground motion models used in a modern PSHA has to capture (in SSHAC language) the center, body, and range of the possible ground motion at the site of interest. This was traditionally done within a logic tree framework in which existing (or only slightly modified) GMPEs occupy the branches of the tree and the branch weights describe the degree-of-belief of the analyst in their applicability. This approach invites the problem to combine GMPEs of very different quality and hence to potentially overestimate epistemic uncertainty. Some recent hazard analysis have therefore resorted to using a small number of high quality GMPEs as backbone models from which the full distribution of GMPEs for the logic tree (to capture the full range of possible ground motion uncertainty) where subsequently generated by scaling (in a general sense). In the present study, a new approach is proposed to determine an optimized backbone model as weighted components of a mixture model. In doing so, each GMPE is assumed to reflect the generation mechanism (e. g. in terms of stress drop, propagation properties, etc.) for at least a fraction of possible ground motions in the area of interest. The combination of different models into a mixture model (which is learned from observed ground motion data in the region of interest) is then transferring information from other regions to the region where the observations have been produced in a data driven way. The backbone model is learned by comparing the model predictions to observations of the target region. For each observation and each model, the likelihood of an observation given a certain GMPE is calculated. Mixture weights can then be assigned using the expectation maximization (EM) algorithm or Bayesian inference. The new method is used to generate a backbone reference model for Northern Chile, an area for which no dedicated GMPE exists. Strong motion recordings from the target area are used to learn the backbone model from a set of 10 GMPEs developed for different subduction zones of the world. The formation of mixture models is done individually for interface and intraslab type events. The ability of the resulting backbone models to describe ground motions in Northern Chile is then compared to the predictive performance of their constituent models.

Bayesian estimation of differential transcript usage from RNA-seq data.

PubMed

Papastamoulis, Panagiotis; Rattray, Magnus

2017-11-27

Next generation sequencing allows the identification of genes consisting of differentially expressed transcripts, a term which usually refers to changes in the overall expression level. A specific type of differential expression is differential transcript usage (DTU) and targets changes in the relative within gene expression of a transcript. The contribution of this paper is to: (a) extend the use of cjBitSeq to the DTU context, a previously introduced Bayesian model which is originally designed for identifying changes in overall expression levels and (b) propose a Bayesian version of DRIMSeq, a frequentist model for inferring DTU. cjBitSeq is a read based model and performs fully Bayesian inference by MCMC sampling on the space of latent state of each transcript per gene. BayesDRIMSeq is a count based model and estimates the Bayes Factor of a DTU model against a null model using Laplace's approximation. The proposed models are benchmarked against the existing ones using a recent independent simulation study as well as a real RNA-seq dataset. Our results suggest that the Bayesian methods exhibit similar performance with DRIMSeq in terms of precision/recall but offer better calibration of False Discovery Rate.

Development of uncertainty-based work injury model using Bayesian structural equation modelling.

PubMed

Chatterjee, Snehamoy

2014-01-01

This paper proposed a Bayesian method-based structural equation model (SEM) of miners' work injury for an underground coal mine in India. The environmental and behavioural variables for work injury were identified and causal relationships were developed. For Bayesian modelling, prior distributions of SEM parameters are necessary to develop the model. In this paper, two approaches were adopted to obtain prior distribution for factor loading parameters and structural parameters of SEM. In the first approach, the prior distributions were considered as a fixed distribution function with specific parameter values, whereas, in the second approach, prior distributions of the parameters were generated from experts' opinions. The posterior distributions of these parameters were obtained by applying Bayesian rule. The Markov Chain Monte Carlo sampling in the form Gibbs sampling was applied for sampling from the posterior distribution. The results revealed that all coefficients of structural and measurement model parameters are statistically significant in experts' opinion-based priors, whereas, two coefficients are not statistically significant when fixed prior-based distributions are applied. The error statistics reveals that Bayesian structural model provides reasonably good fit of work injury with high coefficient of determination (0.91) and less mean squared error as compared to traditional SEM.

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

NASA Astrophysics Data System (ADS)

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

2017-04-01

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

Application of bayesian networks to real-time flood risk estimation

NASA Astrophysics Data System (ADS)

Garrote, L.; Molina, M.; Blasco, G.

2003-04-01

This paper presents the application of a computational paradigm taken from the field of artificial intelligence - the bayesian network - to model the behaviour of hydrologic basins during floods. The final goal of this research is to develop representation techniques for hydrologic simulation models in order to define, develop and validate a mechanism, supported by a software environment, oriented to build decision models for the prediction and management of river floods in real time. The emphasis is placed on providing decision makers with tools to incorporate their knowledge of basin behaviour, usually formulated in terms of rainfall-runoff models, in the process of real-time decision making during floods. A rainfall-runoff model is only a step in the process of decision making. If a reliable rainfall forecast is available and the rainfall-runoff model is well calibrated, decisions can be based mainly on model results. However, in most practical situations, uncertainties in rainfall forecasts or model performance have to be incorporated in the decision process. The computation paradigm adopted for the simulation of hydrologic processes is the bayesian network. A bayesian network is a directed acyclic graph that represents causal influences between linked variables. Under this representation, uncertain qualitative variables are related through causal relations quantified with conditional probabilities. The solution algorithm allows the computation of the expected probability distribution of unknown variables conditioned to the observations. An approach to represent hydrologic processes by bayesian networks with temporal and spatial extensions is presented in this paper, together with a methodology for the development of bayesian models using results produced by deterministic hydrologic simulation models

Model-based Bayesian inference for ROC data analysis

NASA Astrophysics Data System (ADS)

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.

A Kolmogorov-Smirnov test for the molecular clock based on Bayesian ensembles of phylogenies

PubMed Central

Antoneli, Fernando; Passos, Fernando M.; Lopes, Luciano R.

2018-01-01

Divergence date estimates are central to understand evolutionary processes and depend, in the case of molecular phylogenies, on tests of molecular clocks. Here we propose two non-parametric tests of strict and relaxed molecular clocks built upon a framework that uses the empirical cumulative distribution (ECD) of branch lengths obtained from an ensemble of Bayesian trees and well known non-parametric (one-sample and two-sample) Kolmogorov-Smirnov (KS) goodness-of-fit test. In the strict clock case, the method consists in using the one-sample Kolmogorov-Smirnov (KS) test to directly test if the phylogeny is clock-like, in other words, if it follows a Poisson law. The ECD is computed from the discretized branch lengths and the parameter λ of the expected Poisson distribution is calculated as the average branch length over the ensemble of trees. To compensate for the auto-correlation in the ensemble of trees and pseudo-replication we take advantage of thinning and effective sample size, two features provided by Bayesian inference MCMC samplers. Finally, it is observed that tree topologies with very long or very short branches lead to Poisson mixtures and in this case we propose the use of the two-sample KS test with samples from two continuous branch length distributions, one obtained from an ensemble of clock-constrained trees and the other from an ensemble of unconstrained trees. Moreover, in this second form the test can also be applied to test for relaxed clock models. The use of a statistically equivalent ensemble of phylogenies to obtain the branch lengths ECD, instead of one consensus tree, yields considerable reduction of the effects of small sample size and provides a gain of power. PMID:29300759

Reconciling differences in stratospheric ozone composites

NASA Astrophysics Data System (ADS)

Ball, William T.; Alsing, Justin; Mortlock, Daniel J.; Rozanov, Eugene V.; Tummon, Fiona; Haigh, Joanna D.

2017-10-01

Observations of stratospheric ozone from multiple instruments now span three decades; combining these into composite datasets allows long-term ozone trends to be estimated. Recently, several ozone composites have been published, but trends disagree by latitude and altitude, even between composites built upon the same instrument data. We confirm that the main causes of differences in decadal trend estimates lie in (i) steps in the composite time series when the instrument source data changes and (ii) artificial sub-decadal trends in the underlying instrument data. These artefacts introduce features that can alias with regressors in multiple linear regression (MLR) analysis; both can lead to inaccurate trend estimates. Here, we aim to remove these artefacts using Bayesian methods to infer the underlying ozone time series from a set of composites by building a joint-likelihood function using a Gaussian-mixture density to model outliers introduced by data artefacts, together with a data-driven prior on ozone variability that incorporates knowledge of problems during instrument operation. We apply this Bayesian self-calibration approach to stratospheric ozone in 10° bands from 60° S to 60° N and from 46 to 1 hPa (˜ 21-48 km) for 1985-2012. There are two main outcomes: (i) we independently identify and confirm many of the data problems previously identified, but which remain unaccounted for in existing composites; (ii) we construct an ozone composite, with uncertainties, that is free from most of these problems - we call this the BAyeSian Integrated and Consolidated (BASIC) composite. To analyse the new BASIC composite, we use dynamical linear modelling (DLM), which provides a more robust estimate of long-term changes through Bayesian inference than MLR. BASIC and DLM, together, provide a step forward in improving estimates of decadal trends. Our results indicate a significant recovery of ozone since 1998 in the upper stratosphere, of both northern and southern midlatitudes, in all four composites analysed, and particularly in the BASIC composite. The BASIC results also show no hemispheric difference in the recovery at midlatitudes, in contrast to an apparent feature that is present, but not consistent, in the four composites. Our overall conclusion is that it is possible to effectively combine different ozone composites and account for artefacts and drifts, and that this leads to a clear and significant result that upper stratospheric ozone levels have increased since 1998, following an earlier decline.

Bayesian Modeling of a Human MMORPG Player

NASA Astrophysics Data System (ADS)

Synnaeve, Gabriel; Bessière, Pierre

2011-03-01

This paper describes an application of Bayesian programming to the control of an autonomous avatar in a multiplayer role-playing game (the example is based on World of Warcraft). We model a particular task, which consists of choosing what to do and to select which target in a situation where allies and foes are present. We explain the model in Bayesian programming and show how we could learn the conditional probabilities from data gathered during human-played sessions.

A comment on priors for Bayesian occupancy models

PubMed Central

Gerber, Brian D.

2018-01-01

Understanding patterns of species occurrence and the processes underlying these patterns is fundamental to the study of ecology. One of the more commonly used approaches to investigate species occurrence patterns is occupancy modeling, which can account for imperfect detection of a species during surveys. In recent years, there has been a proliferation of Bayesian modeling in ecology, which includes fitting Bayesian occupancy models. The Bayesian framework is appealing to ecologists for many reasons, including the ability to incorporate prior information through the specification of prior distributions on parameters. While ecologists almost exclusively intend to choose priors so that they are “uninformative” or “vague”, such priors can easily be unintentionally highly informative. Here we report on how the specification of a “vague” normally distributed (i.e., Gaussian) prior on coefficients in Bayesian occupancy models can unintentionally influence parameter estimation. Using both simulated data and empirical examples, we illustrate how this issue likely compromises inference about species-habitat relationships. While the extent to which these informative priors influence inference depends on the data set, researchers fitting Bayesian occupancy models should conduct sensitivity analyses to ensure intended inference, or employ less commonly used priors that are less informative (e.g., logistic or t prior distributions). We provide suggestions for addressing this issue in occupancy studies, and an online tool for exploring this issue under different contexts. PMID:29481554

Bayesian Optimization Under Mixed Constraints with A Slack-Variable Augmented Lagrangian

DOE Office of Scientific and Technical Information (OSTI.GOV)

Picheny, Victor; Gramacy, Robert B.; Wild, Stefan M.

An augmented Lagrangian (AL) can convert a constrained optimization problem into a sequence of simpler (e.g., unconstrained) problems, which are then usually solved with local solvers. Recently, surrogate-based Bayesian optimization (BO) sub-solvers have been successfully deployed in the AL framework for a more global search in the presence of inequality constraints; however, a drawback was that expected improvement (EI) evaluations relied on Monte Carlo. Here we introduce an alternative slack variable AL, and show that in this formulation the EI may be evaluated with library routines. The slack variables furthermore facilitate equality as well as inequality constraints, and mixtures thereof.more » We show our new slack “ALBO” compares favorably to the original. Its superiority over conventional alternatives is reinforced on several mixed constraint examples.« less

The Bayesian boom: good thing or bad?

PubMed Central

Hahn, Ulrike

2014-01-01

A series of high-profile critiques of Bayesian models of cognition have recently sparked controversy. These critiques question the contribution of rational, normative considerations in the study of cognition. The present article takes central claims from these critiques and evaluates them in light of specific models. Closer consideration of actual examples of Bayesian treatments of different cognitive phenomena allows one to defuse these critiques showing that they cannot be sustained across the diversity of applications of the Bayesian framework for cognitive modeling. More generally, there is nothing in the Bayesian framework that would inherently give rise to the deficits that these critiques perceive, suggesting they have been framed at the wrong level of generality. At the same time, the examples are used to demonstrate the different ways in which consideration of rationality uniquely benefits both theory and practice in the study of cognition. PMID:25152738

Calibrating Bayesian Network Representations of Social-Behavioral Models

DOE Office of Scientific and Technical Information (OSTI.GOV)

Whitney, Paul D.; Walsh, Stephen J.

2010-04-08

While human behavior has long been studied, recent and ongoing advances in computational modeling present opportunities for recasting research outcomes in human behavior. In this paper we describe how Bayesian networks can represent outcomes of human behavior research. We demonstrate a Bayesian network that represents political radicalization research – and show a corresponding visual representation of aspects of this research outcome. Since Bayesian networks can be quantitatively compared with external observations, the representation can also be used for empirical assessments of the research which the network summarizes. For a political radicalization model based on published research, we show this empiricalmore » comparison with data taken from the Minorities at Risk Organizational Behaviors database.« less

A comprehensive probabilistic analysis model of oil pipelines network based on Bayesian network

NASA Astrophysics Data System (ADS)

Zhang, C.; Qin, T. X.; Jiang, B.; Huang, C.

2018-02-01

Oil pipelines network is one of the most important facilities of energy transportation. But oil pipelines network accident may result in serious disasters. Some analysis models for these accidents have been established mainly based on three methods, including event-tree, accident simulation and Bayesian network. Among these methods, Bayesian network is suitable for probabilistic analysis. But not all the important influencing factors are considered and the deployment rule of the factors has not been established. This paper proposed a probabilistic analysis model of oil pipelines network based on Bayesian network. Most of the important influencing factors, including the key environment condition and emergency response are considered in this model. Moreover, the paper also introduces a deployment rule for these factors. The model can be used in probabilistic analysis and sensitive analysis of oil pipelines network accident.

An evaluation of Bayesian techniques for controlling model complexity and selecting inputs in a neural network for short-term load forecasting.

PubMed

Hippert, Henrique S; Taylor, James W

2010-04-01

Artificial neural networks have frequently been proposed for electricity load forecasting because of their capabilities for the nonlinear modelling of large multivariate data sets. Modelling with neural networks is not an easy task though; two of the main challenges are defining the appropriate level of model complexity, and choosing the input variables. This paper evaluates techniques for automatic neural network modelling within a Bayesian framework, as applied to six samples containing daily load and weather data for four different countries. We analyse input selection as carried out by the Bayesian 'automatic relevance determination', and the usefulness of the Bayesian 'evidence' for the selection of the best structure (in terms of number of neurones), as compared to methods based on cross-validation. Copyright 2009 Elsevier Ltd. All rights reserved.

Bayesian analysis of CCDM models

NASA Astrophysics Data System (ADS)

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.

Refining value-at-risk estimates using a Bayesian Markov-switching GJR-GARCH copula-EVT model.

PubMed

Sampid, Marius Galabe; Hasim, Haslifah M; Dai, Hongsheng

2018-01-01

In this paper, we propose a model for forecasting Value-at-Risk (VaR) using a Bayesian Markov-switching GJR-GARCH(1,1) model with skewed Student's-t innovation, copula functions and extreme value theory. A Bayesian Markov-switching GJR-GARCH(1,1) model that identifies non-constant volatility over time and allows the GARCH parameters to vary over time following a Markov process, is combined with copula functions and EVT to formulate the Bayesian Markov-switching GJR-GARCH(1,1) copula-EVT VaR model, which is then used to forecast the level of risk on financial asset returns. We further propose a new method for threshold selection in EVT analysis, which we term the hybrid method. Empirical and back-testing results show that the proposed VaR models capture VaR reasonably well in periods of calm and in periods of crisis.

Comparing interval estimates for small sample ordinal CFA models

PubMed Central

Natesan, Prathiba

2015-01-01

Robust maximum likelihood (RML) and asymptotically generalized least squares (AGLS) methods have been recommended for fitting ordinal structural equation models. Studies show that some of these methods underestimate standard errors. However, these studies have not investigated the coverage and bias of interval estimates. An estimate with a reasonable standard error could still be severely biased. This can only be known by systematically investigating the interval estimates. The present study compares Bayesian, RML, and AGLS interval estimates of factor correlations in ordinal confirmatory factor analysis models (CFA) for small sample data. Six sample sizes, 3 factor correlations, and 2 factor score distributions (multivariate normal and multivariate mildly skewed) were studied. Two Bayesian prior specifications, informative and relatively less informative were studied. Undercoverage of confidence intervals and underestimation of standard errors was common in non-Bayesian methods. Underestimated standard errors may lead to inflated Type-I error rates. Non-Bayesian intervals were more positive biased than negatively biased, that is, most intervals that did not contain the true value were greater than the true value. Some non-Bayesian methods had non-converging and inadmissible solutions for small samples and non-normal data. Bayesian empirical standard error estimates for informative and relatively less informative priors were closer to the average standard errors of the estimates. The coverage of Bayesian credibility intervals was closer to what was expected with overcoverage in a few cases. Although some Bayesian credibility intervals were wider, they reflected the nature of statistical uncertainty that comes with the data (e.g., small sample). Bayesian point estimates were also more accurate than non-Bayesian estimates. The results illustrate the importance of analyzing coverage and bias of interval estimates, and how ignoring interval estimates can be misleading. Therefore, editors and policymakers should continue to emphasize the inclusion of interval estimates in research. PMID:26579002

Comparing interval estimates for small sample ordinal CFA models.

PubMed

Natesan, Prathiba

2015-01-01

Robust maximum likelihood (RML) and asymptotically generalized least squares (AGLS) methods have been recommended for fitting ordinal structural equation models. Studies show that some of these methods underestimate standard errors. However, these studies have not investigated the coverage and bias of interval estimates. An estimate with a reasonable standard error could still be severely biased. This can only be known by systematically investigating the interval estimates. The present study compares Bayesian, RML, and AGLS interval estimates of factor correlations in ordinal confirmatory factor analysis models (CFA) for small sample data. Six sample sizes, 3 factor correlations, and 2 factor score distributions (multivariate normal and multivariate mildly skewed) were studied. Two Bayesian prior specifications, informative and relatively less informative were studied. Undercoverage of confidence intervals and underestimation of standard errors was common in non-Bayesian methods. Underestimated standard errors may lead to inflated Type-I error rates. Non-Bayesian intervals were more positive biased than negatively biased, that is, most intervals that did not contain the true value were greater than the true value. Some non-Bayesian methods had non-converging and inadmissible solutions for small samples and non-normal data. Bayesian empirical standard error estimates for informative and relatively less informative priors were closer to the average standard errors of the estimates. The coverage of Bayesian credibility intervals was closer to what was expected with overcoverage in a few cases. Although some Bayesian credibility intervals were wider, they reflected the nature of statistical uncertainty that comes with the data (e.g., small sample). Bayesian point estimates were also more accurate than non-Bayesian estimates. The results illustrate the importance of analyzing coverage and bias of interval estimates, and how ignoring interval estimates can be misleading. Therefore, editors and policymakers should continue to emphasize the inclusion of interval estimates in research.

Bayesian demography 250 years after Bayes

PubMed Central

Bijak, Jakub; Bryant, John

2016-01-01

Bayesian statistics offers an alternative to classical (frequentist) statistics. It is distinguished by its use of probability distributions to describe uncertain quantities, which leads to elegant solutions to many difficult statistical problems. Although Bayesian demography, like Bayesian statistics more generally, is around 250 years old, only recently has it begun to flourish. The aim of this paper is to review the achievements of Bayesian demography, address some misconceptions, and make the case for wider use of Bayesian methods in population studies. We focus on three applications: demographic forecasts, limited data, and highly structured or complex models. The key advantages of Bayesian methods are the ability to integrate information from multiple sources and to describe uncertainty coherently. Bayesian methods also allow for including additional (prior) information next to the data sample. As such, Bayesian approaches are complementary to many traditional methods, which can be productively re-expressed in Bayesian terms. PMID:26902889

A Bayesian approach to meta-analysis of plant pathology studies.

PubMed

Mila, A L; Ngugi, H K

2011-01-01

Bayesian statistical methods are used for meta-analysis in many disciplines, including medicine, molecular biology, and engineering, but have not yet been applied for quantitative synthesis of plant pathology studies. In this paper, we illustrate the key concepts of Bayesian statistics and outline the differences between Bayesian and classical (frequentist) methods in the way parameters describing population attributes are considered. We then describe a Bayesian approach to meta-analysis and present a plant pathological example based on studies evaluating the efficacy of plant protection products that induce systemic acquired resistance for the management of fire blight of apple. In a simple random-effects model assuming a normal distribution of effect sizes and no prior information (i.e., a noninformative prior), the results of the Bayesian meta-analysis are similar to those obtained with classical methods. Implementing the same model with a Student's t distribution and a noninformative prior for the effect sizes, instead of a normal distribution, yields similar results for all but acibenzolar-S-methyl (Actigard) which was evaluated only in seven studies in this example. Whereas both the classical (P = 0.28) and the Bayesian analysis with a noninformative prior (95% credibility interval [CRI] for the log response ratio: -0.63 to 0.08) indicate a nonsignificant effect for Actigard, specifying a t distribution resulted in a significant, albeit variable, effect for this product (CRI: -0.73 to -0.10). These results confirm the sensitivity of the analytical outcome (i.e., the posterior distribution) to the choice of prior in Bayesian meta-analyses involving a limited number of studies. We review some pertinent literature on more advanced topics, including modeling of among-study heterogeneity, publication bias, analyses involving a limited number of studies, and methods for dealing with missing data, and show how these issues can be approached in a Bayesian framework. Bayesian meta-analysis can readily include information not easily incorporated in classical methods, and allow for a full evaluation of competing models. Given the power and flexibility of Bayesian methods, we expect them to become widely adopted for meta-analysis of plant pathology studies.

Introduction to Bayesian statistical approaches to compositional analyses of transgenic crops 1. Model validation and setting the stage.

PubMed

Harrison, Jay M; Breeze, Matthew L; Harrigan, George G

2011-08-01

Statistical comparisons of compositional data generated on genetically modified (GM) crops and their near-isogenic conventional (non-GM) counterparts typically rely on classical significance testing. This manuscript presents an introduction to Bayesian methods for compositional analysis along with recommendations for model validation. The approach is illustrated using protein and fat data from two herbicide tolerant GM soybeans (MON87708 and MON87708×MON89788) and a conventional comparator grown in the US in 2008 and 2009. Guidelines recommended by the US Food and Drug Administration (FDA) in conducting Bayesian analyses of clinical studies on medical devices were followed. This study is the first Bayesian approach to GM and non-GM compositional comparisons. The evaluation presented here supports a conclusion that a Bayesian approach to analyzing compositional data can provide meaningful and interpretable results. We further describe the importance of method validation and approaches to model checking if Bayesian approaches to compositional data analysis are to be considered viable by scientists involved in GM research and regulation. Copyright © 2011 Elsevier Inc. All rights reserved.

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

NASA Astrophysics Data System (ADS)

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

2018-02-01

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

Predicting the Future as Bayesian Inference: People Combine Prior Knowledge with Observations when Estimating Duration and Extent

ERIC Educational Resources Information Center

Griffiths, Thomas L.; Tenenbaum, Joshua B.

2011-01-01

Predicting the future is a basic problem that people have to solve every day and a component of planning, decision making, memory, and causal reasoning. In this article, we present 5 experiments testing a Bayesian model of predicting the duration or extent of phenomena from their current state. This Bayesian model indicates how people should…

Variations on Bayesian Prediction and Inference

DTIC Science & Technology

2016-05-09

inference 2.2.1 Background There are a number of statistical inference problems that are not generally formulated via a full probability model...problem of inference about an unknown parameter, the Bayesian approach requires a full probability 1. REPORT DATE (DD-MM-YYYY) 4. TITLE AND...the problem of inference about an unknown parameter, the Bayesian approach requires a full probability model/likelihood which can be an obstacle

Posterior Predictive Model Checking in Bayesian Networks

ERIC Educational Resources Information Center

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…

Metrics for evaluating performance and uncertainty of Bayesian network models

Treesearch

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...

Technical note: Bayesian calibration of dynamic ruminant nutrition models.

PubMed

Reed, K F; Arhonditsis, G B; France, J; Kebreab, E

2016-08-01

Mechanistic models of ruminant digestion and metabolism have advanced our understanding of the processes underlying ruminant animal physiology. Deterministic modeling practices ignore the inherent variation within and among individual animals and thus have no way to assess how sources of error influence model outputs. We introduce Bayesian calibration of mathematical models to address the need for robust mechanistic modeling tools that can accommodate error analysis by remaining within the bounds of data-based parameter estimation. For the purpose of prediction, the Bayesian approach generates a posterior predictive distribution that represents the current estimate of the value of the response variable, taking into account both the uncertainty about the parameters and model residual variability. Predictions are expressed as probability distributions, thereby conveying significantly more information than point estimates in regard to uncertainty. Our study illustrates some of the technical advantages of Bayesian calibration and discusses the future perspectives in the context of animal nutrition modeling. Copyright © 2016 American Dairy Science Association. Published by Elsevier Inc. All rights reserved.

Bayesian logistic regression approaches to predict incorrect DRG assignment.

PubMed

Suleiman, Mani; Demirhan, Haydar; Boyd, Leanne; Girosi, Federico; Aksakalli, Vural

2018-05-07

Episodes of care involving similar diagnoses and treatments and requiring similar levels of resource utilisation are grouped to the same Diagnosis-Related Group (DRG). In jurisdictions which implement DRG based payment systems, DRGs are a major determinant of funding for inpatient care. Hence, service providers often dedicate auditing staff to the task of checking that episodes have been coded to the correct DRG. The use of statistical models to estimate an episode's probability of DRG error can significantly improve the efficiency of clinical coding audits. This study implements Bayesian logistic regression models with weakly informative prior distributions to estimate the likelihood that episodes require a DRG revision, comparing these models with each other and to classical maximum likelihood estimates. All Bayesian approaches had more stable model parameters than maximum likelihood. The best performing Bayesian model improved overall classification per- formance by 6% compared to maximum likelihood, with a 34% gain compared to random classification, respectively. We found that the original DRG, coder and the day of coding all have a significant effect on the likelihood of DRG error. Use of Bayesian approaches has improved model parameter stability and classification accuracy. This method has already lead to improved audit efficiency in an operational capacity.

Assessment of parametric uncertainty for groundwater reactive transport modeling,

USGS Publications Warehouse

Shi, Xiaoqing; Ye, Ming; Curtis, Gary P.; Miller, Geoffery L.; Meyer, Philip D.; Kohler, Matthias; Yabusaki, Steve; Wu, Jichun

2014-01-01

The validity of using Gaussian assumptions for model residuals in uncertainty quantification of a groundwater reactive transport model was evaluated in this study. Least squares regression methods explicitly assume Gaussian residuals, and the assumption leads to Gaussian likelihood functions, model parameters, and model predictions. While the Bayesian methods do not explicitly require the Gaussian assumption, Gaussian residuals are widely used. This paper shows that the residuals of the reactive transport model are non-Gaussian, heteroscedastic, and correlated in time; characterizing them requires using a generalized likelihood function such as the formal generalized likelihood function developed by Schoups and Vrugt (2010). For the surface complexation model considered in this study for simulating uranium reactive transport in groundwater, parametric uncertainty is quantified using the least squares regression methods and Bayesian methods with both Gaussian and formal generalized likelihood functions. While the least squares methods and Bayesian methods with Gaussian likelihood function produce similar Gaussian parameter distributions, the parameter distributions of Bayesian uncertainty quantification using the formal generalized likelihood function are non-Gaussian. In addition, predictive performance of formal generalized likelihood function is superior to that of least squares regression and Bayesian methods with Gaussian likelihood function. The Bayesian uncertainty quantification is conducted using the differential evolution adaptive metropolis (DREAM(zs)) algorithm; as a Markov chain Monte Carlo (MCMC) method, it is a robust tool for quantifying uncertainty in groundwater reactive transport models. For the surface complexation model, the regression-based local sensitivity analysis and Morris- and DREAM(ZS)-based global sensitivity analysis yield almost identical ranking of parameter importance. The uncertainty analysis may help select appropriate likelihood functions, improve model calibration, and reduce predictive uncertainty in other groundwater reactive transport and environmental modeling.

Prospective evaluation of a Bayesian model to predict organizational change.

PubMed

Molfenter, Todd; Gustafson, Dave; Kilo, Chuck; Bhattacharya, Abhik; Olsson, Jesper

2005-01-01

This research examines a subjective Bayesian model's ability to predict organizational change outcomes and sustainability of those outcomes for project teams participating in a multi-organizational improvement collaborative.

Bayesian truncation errors in chiral effective field theory: model checking and accounting for correlations

NASA Astrophysics Data System (ADS)

Melendez, Jordan; Wesolowski, Sarah; Furnstahl, Dick

2017-09-01

Chiral effective field theory (EFT) predictions are necessarily truncated at some order in the EFT expansion, which induces an error that must be quantified for robust statistical comparisons to experiment. A Bayesian model yields posterior probability distribution functions for these errors based on expectations of naturalness encoded in Bayesian priors and the observed order-by-order convergence pattern of the EFT. As a general example of a statistical approach to truncation errors, the model was applied to chiral EFT for neutron-proton scattering using various semi-local potentials of Epelbaum, Krebs, and Meißner (EKM). Here we discuss how our model can learn correlation information from the data and how to perform Bayesian model checking to validate that the EFT is working as advertised. Supported in part by NSF PHY-1614460 and DOE NUCLEI SciDAC DE-SC0008533.

A FAST BAYESIAN METHOD FOR UPDATING AND FORECASTING HOURLY OZONE LEVELS

EPA Science Inventory

A Bayesian hierarchical space-time model is proposed by combining information from real-time ambient AIRNow air monitoring data, and output from a computer simulation model known as the Community Multi-scale Air Quality (Eta-CMAQ) forecast model. A model validation analysis shows...

Bayesian methods for characterizing unknown parameters of material models

DOE PAGES

Emery, J. M.; Grigoriu, M. D.; Field Jr., R. V.

2016-02-04

A Bayesian framework is developed for characterizing the unknown parameters of probabilistic models for material properties. In this framework, the unknown parameters are viewed as random and described by their posterior distributions obtained from prior information and measurements of quantities of interest that are observable and depend on the unknown parameters. The proposed Bayesian method is applied to characterize an unknown spatial correlation of the conductivity field in the definition of a stochastic transport equation and to solve this equation by Monte Carlo simulation and stochastic reduced order models (SROMs). As a result, the Bayesian method is also employed tomore » characterize unknown parameters of material properties for laser welds from measurements of peak forces sustained by these welds.« less

Bayesian methods for characterizing unknown parameters of material models

DOE Office of Scientific and Technical Information (OSTI.GOV)

Emery, J. M.; Grigoriu, M. D.; Field Jr., R. V.

A Bayesian framework is developed for characterizing the unknown parameters of probabilistic models for material properties. In this framework, the unknown parameters are viewed as random and described by their posterior distributions obtained from prior information and measurements of quantities of interest that are observable and depend on the unknown parameters. The proposed Bayesian method is applied to characterize an unknown spatial correlation of the conductivity field in the definition of a stochastic transport equation and to solve this equation by Monte Carlo simulation and stochastic reduced order models (SROMs). As a result, the Bayesian method is also employed tomore » characterize unknown parameters of material properties for laser welds from measurements of peak forces sustained by these welds.« less

Bayesian methods in reliability

NASA Astrophysics Data System (ADS)

Sander, P.; Badoux, R.

1991-11-01

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

Bayesian accounts of covert selective attention: A tutorial review.

PubMed

Vincent, Benjamin T

2015-05-01

Decision making and optimal observer models offer an important theoretical approach to the study of covert selective attention. While their probabilistic formulation allows quantitative comparison to human performance, the models can be complex and their insights are not always immediately apparent. Part 1 establishes the theoretical appeal of the Bayesian approach, and introduces the way in which probabilistic approaches can be applied to covert search paradigms. Part 2 presents novel formulations of Bayesian models of 4 important covert attention paradigms, illustrating optimal observer predictions over a range of experimental manipulations. Graphical model notation is used to present models in an accessible way and Supplementary Code is provided to help bridge the gap between model theory and practical implementation. Part 3 reviews a large body of empirical and modelling evidence showing that many experimental phenomena in the domain of covert selective attention are a set of by-products. These effects emerge as the result of observers conducting Bayesian inference with noisy sensory observations, prior expectations, and knowledge of the generative structure of the stimulus environment.

Bayesian Action–Perception Computational Model: Interaction of Production and Recognition of Cursive Letters

PubMed Central

Gilet, Estelle; Diard, Julien; Bessière, Pierre

2011-01-01

In this paper, we study the collaboration of perception and action representations involved in cursive letter recognition and production. We propose a mathematical formulation for the whole perception–action loop, based on probabilistic modeling and Bayesian inference, which we call the Bayesian Action–Perception (BAP) model. Being a model of both perception and action processes, the purpose of this model is to study the interaction of these processes. More precisely, the model includes a feedback loop from motor production, which implements an internal simulation of movement. Motor knowledge can therefore be involved during perception tasks. In this paper, we formally define the BAP model and show how it solves the following six varied cognitive tasks using Bayesian inference: i) letter recognition (purely sensory), ii) writer recognition, iii) letter production (with different effectors), iv) copying of trajectories, v) copying of letters, and vi) letter recognition (with internal simulation of movements). We present computer simulations of each of these cognitive tasks, and discuss experimental predictions and theoretical developments. PMID:21674043

Finding Bayesian Optimal Designs for Nonlinear Models: A Semidefinite Programming-Based Approach.

PubMed

Duarte, Belmiro P M; Wong, Weng Kee

2015-08-01

This paper uses semidefinite programming (SDP) to construct Bayesian optimal design for nonlinear regression models. The setup here extends the formulation of the optimal designs problem as an SDP problem from linear to nonlinear models. Gaussian quadrature formulas (GQF) are used to compute the expectation in the Bayesian design criterion, such as D-, A- or E-optimality. As an illustrative example, we demonstrate the approach using the power-logistic model and compare results in the literature. Additionally, we investigate how the optimal design is impacted by different discretising schemes for the design space, different amounts of uncertainty in the parameter values, different choices of GQF and different prior distributions for the vector of model parameters, including normal priors with and without correlated components. Further applications to find Bayesian D-optimal designs with two regressors for a logistic model and a two-variable generalised linear model with a gamma distributed response are discussed, and some limitations of our approach are noted.

Finding Bayesian Optimal Designs for Nonlinear Models: A Semidefinite Programming-Based Approach

PubMed Central

Duarte, Belmiro P. M.; Wong, Weng Kee

2014-01-01

Summary This paper uses semidefinite programming (SDP) to construct Bayesian optimal design for nonlinear regression models. The setup here extends the formulation of the optimal designs problem as an SDP problem from linear to nonlinear models. Gaussian quadrature formulas (GQF) are used to compute the expectation in the Bayesian design criterion, such as D-, A- or E-optimality. As an illustrative example, we demonstrate the approach using the power-logistic model and compare results in the literature. Additionally, we investigate how the optimal design is impacted by different discretising schemes for the design space, different amounts of uncertainty in the parameter values, different choices of GQF and different prior distributions for the vector of model parameters, including normal priors with and without correlated components. Further applications to find Bayesian D-optimal designs with two regressors for a logistic model and a two-variable generalised linear model with a gamma distributed response are discussed, and some limitations of our approach are noted. PMID:26512159

A systematic review of Bayesian articles in psychology: The last 25 years.

PubMed

van de Schoot, Rens; Winter, Sonja D; Ryan, Oisín; Zondervan-Zwijnenburg, Mariëlle; Depaoli, Sarah

2017-06-01

Although the statistical tools most often used by researchers in the field of psychology over the last 25 years are based on frequentist statistics, it is often claimed that the alternative Bayesian approach to statistics is gaining in popularity. In the current article, we investigated this claim by performing the very first systematic review of Bayesian psychological articles published between 1990 and 2015 (n = 1,579). We aim to provide a thorough presentation of the role Bayesian statistics plays in psychology. This historical assessment allows us to identify trends and see how Bayesian methods have been integrated into psychological research in the context of different statistical frameworks (e.g., hypothesis testing, cognitive models, IRT, SEM, etc.). We also describe take-home messages and provide "big-picture" recommendations to the field as Bayesian statistics becomes more popular. Our review indicated that Bayesian statistics is used in a variety of contexts across subfields of psychology and related disciplines. There are many different reasons why one might choose to use Bayes (e.g., the use of priors, estimating otherwise intractable models, modeling uncertainty, etc.). We found in this review that the use of Bayes has increased and broadened in the sense that this methodology can be used in a flexible manner to tackle many different forms of questions. We hope this presentation opens the door for a larger discussion regarding the current state of Bayesian statistics, as well as future trends. (PsycINFO Database Record (c) 2017 APA, all rights reserved).

A Gibbs sampler for Bayesian analysis of site-occupancy data

USGS Publications Warehouse

Dorazio, Robert M.; Rodriguez, Daniel Taylor

2012-01-01

1. A Bayesian analysis of site-occupancy data containing covariates of species occurrence and species detection probabilities is usually completed using Markov chain Monte Carlo methods in conjunction with software programs that can implement those methods for any statistical model, not just site-occupancy models. Although these software programs are quite flexible, considerable experience is often required to specify a model and to initialize the Markov chain so that summaries of the posterior distribution can be estimated efficiently and accurately. 2. As an alternative to these programs, we develop a Gibbs sampler for Bayesian analysis of site-occupancy data that include covariates of species occurrence and species detection probabilities. This Gibbs sampler is based on a class of site-occupancy models in which probabilities of species occurrence and detection are specified as probit-regression functions of site- and survey-specific covariate measurements. 3. To illustrate the Gibbs sampler, we analyse site-occupancy data of the blue hawker, Aeshna cyanea (Odonata, Aeshnidae), a common dragonfly species in Switzerland. Our analysis includes a comparison of results based on Bayesian and classical (non-Bayesian) methods of inference. We also provide code (based on the R software program) for conducting Bayesian and classical analyses of site-occupancy data.

Analysis of the Westland Data Set

NASA Technical Reports Server (NTRS)

Wen, Fang; Willett, Peter; Deb, Somnath

2001-01-01

The "Westland" set of empirical accelerometer helicopter data with seeded and labeled faults is analyzed with the aim of condition monitoring. The autoregressive (AR) coefficients from a simple linear model encapsulate a great deal of information in a relatively few measurements; and it has also been found that augmentation of these by harmonic and other parameters call improve classification significantly. Several techniques have been explored, among these restricted Coulomb energy (RCE) networks, learning vector quantization (LVQ), Gaussian mixture classifiers and decision trees. A problem with these approaches, and in common with many classification paradigms, is that augmentation of the feature dimension can degrade classification ability. Thus, we also introduce the Bayesian data reduction algorithm (BDRA), which imposes a Dirichlet prior oil training data and is thus able to quantify probability of error in all exact manner, such that features may be discarded or coarsened appropriately.

Bayesian decision and mixture models for AE monitoring of steel-concrete composite shear walls

NASA Astrophysics Data System (ADS)

Farhidzadeh, Alireza; Epackachi, Siamak; Salamone, Salvatore; Whittaker, Andrew S.

2015-11-01

This paper presents an approach based on an acoustic emission technique for the health monitoring of steel-concrete (SC) composite shear walls. SC composite walls consist of plain (unreinforced) concrete sandwiched between steel faceplates. Although the use of SC system construction has been studied extensively for nearly 20 years, little-to-no attention has been devoted to the development of structural health monitoring techniques for the inspection of damage of the concrete behind the steel plates. In this work an unsupervised pattern recognition algorithm based on probability theory is proposed to assess the soundness of the concrete infill, and eventually provide a diagnosis of the SC wall’s health. The approach is validated through an experimental study on a large-scale SC shear wall subjected to a displacement controlled reversed cyclic loading.

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

PubMed

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

2018-02-01

We develop Bayesian function-valued trait models that mathematically isolate genetic mechanisms underlying leaf growth trajectories by factoring out genotype-specific differences in photosynthesis. Remote sensing data can be used instead of leaf-level physiological measurements. Characterizing the genetic basis of traits that vary during ontogeny and affect plant performance is a major goal in evolutionary biology and agronomy. Describing genetic programs that specifically regulate morphological traits can be complicated by genotypic differences in physiological traits. We describe the growth trajectories of leaves using novel Bayesian function-valued trait (FVT) modeling approaches in Brassica rapa recombinant inbred lines raised in heterogeneous field settings. While frequentist approaches estimate parameter values by treating each experimental replicate discretely, Bayesian models can utilize information in the global dataset, potentially leading to more robust trait estimation. We illustrate this principle by estimating growth asymptotes in the face of missing data and comparing heritabilities of growth trajectory parameters estimated by Bayesian and frequentist approaches. Using pseudo-Bayes factors, we compare the performance of an initial Bayesian logistic growth model and a model that incorporates carbon assimilation (A max ) as a cofactor, thus statistically accounting for genotypic differences in carbon resources. We further evaluate two remotely sensed spectroradiometric indices, photochemical reflectance (pri2) and MERIS Terrestrial Chlorophyll Index (mtci) as covariates in lieu of A max , because these two indices were genetically correlated with A max across years and treatments yet allow much higher throughput compared to direct leaf-level gas-exchange measurements. For leaf lengths in uncrowded settings, including A max improves model fit over the initial model. The mtci and pri2 indices also outperform direct A max measurements. Of particular importance for evolutionary biologists and plant breeders, hierarchical Bayesian models estimating FVT parameters improve heritabilities compared to frequentist approaches.

Bayesian Estimation of the Logistic Positive Exponent IRT Model

ERIC Educational Resources Information Center

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…

The Misidentified Identifiability Problem of Bayesian Knowledge Tracing

ERIC Educational Resources Information Center

Doroudi, Shayan; Brunskill, Emma

2017-01-01

In this paper, we investigate two purported problems with Bayesian Knowledge Tracing (BKT), a popular statistical model of student learning: "identifiability" and "semantic model degeneracy." In 2007, Beck and Chang stated that BKT is susceptible to an "identifiability problem"--various models with different…

Common quandaries and their practical solutions in Bayesian network modeling

Treesearch

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,...

On the Bayesian Nonparametric Generalization of IRT-Type Models

ERIC Educational Resources Information Center

San Martin, Ernesto; Jara, Alejandro; Rolin, Jean-Marie; Mouchart, Michel

2011-01-01

We study the identification and consistency of Bayesian semiparametric IRT-type models, where the uncertainty on the abilities' distribution is modeled using a prior distribution on the space of probability measures. We show that for the semiparametric Rasch Poisson counts model, simple restrictions ensure the identification of a general…

Selected aspects of prior and likelihood information for a Bayesian classifier in a road safety analysis.

PubMed

Nowakowska, Marzena

2017-04-01

The development of the Bayesian logistic regression model classifying the road accident severity is discussed. The already exploited informative priors (method of moments, maximum likelihood estimation, and two-stage Bayesian updating), along with the original idea of a Boot prior proposal, are investigated when no expert opinion has been available. In addition, two possible approaches to updating the priors, in the form of unbalanced and balanced training data sets, are presented. The obtained logistic Bayesian models are assessed on the basis of a deviance information criterion (DIC), highest probability density (HPD) intervals, and coefficients of variation estimated for the model parameters. The verification of the model accuracy has been based on sensitivity, specificity and the harmonic mean of sensitivity and specificity, all calculated from a test data set. The models obtained from the balanced training data set have a better classification quality than the ones obtained from the unbalanced training data set. The two-stage Bayesian updating prior model and the Boot prior model, both identified with the use of the balanced training data set, outperform the non-informative, method of moments, and maximum likelihood estimation prior models. It is important to note that one should be careful when interpreting the parameters since different priors can lead to different models. Copyright © 2017 Elsevier Ltd. All rights reserved.

Bayesian learning and the psychology of rule induction

PubMed Central

Endress, Ansgar D.

2014-01-01

In recent years, Bayesian learning models have been applied to an increasing variety of domains. While such models have been criticized on theoretical grounds, the underlying assumptions and predictions are rarely made concrete and tested experimentally. Here, I use Frank and Tenenbaum's (2011) Bayesian model of rule-learning as a case study to spell out the underlying assumptions, and to confront them with the empirical results Frank and Tenenbaum (2011) propose to simulate, as well as with novel experiments. While rule-learning is arguably well suited to rational Bayesian approaches, I show that their models are neither psychologically plausible nor ideal observer models. Further, I show that their central assumption is unfounded: humans do not always preferentially learn more specific rules, but, at least in some situations, those rules that happen to be more salient. Even when granting the unsupported assumptions, I show that all of the experiments modeled by Frank and Tenenbaum (2011) either contradict their models, or have a large number of more plausible interpretations. I provide an alternative account of the experimental data based on simple psychological mechanisms, and show that this account both describes the data better, and is easier to falsify. I conclude that, despite the recent surge in Bayesian models of cognitive phenomena, psychological phenomena are best understood by developing and testing psychological theories rather than models that can be fit to virtually any data. PMID:23454791

Advances in Bayesian Modeling in Educational Research

ERIC Educational Resources Information Center

Levy, Roy

2016-01-01

In this article, I provide a conceptually oriented overview of Bayesian approaches to statistical inference and contrast them with frequentist approaches that currently dominate conventional practice in educational research. The features and advantages of Bayesian approaches are illustrated with examples spanning several statistical modeling…

Bayesian Analysis of Multidimensional Item Response Theory Models: A Discussion and Illustration of Three Response Style Models

ERIC Educational Resources Information Center

Leventhal, Brian C.; Stone, Clement A.

2018-01-01

Interest in Bayesian analysis of item response theory (IRT) models has grown tremendously due to the appeal of the paradigm among psychometricians, advantages of these methods when analyzing complex models, and availability of general-purpose software. Possible models include models which reflect multidimensionality due to designed test structure,…

MAFsnp: A Multi-Sample Accurate and Flexible SNP Caller Using Next-Generation Sequencing Data

PubMed Central

Hu, Jiyuan; Li, Tengfei; Xiu, Zidi; Zhang, Hong

2015-01-01

Most existing statistical methods developed for calling single nucleotide polymorphisms (SNPs) using next-generation sequencing (NGS) data are based on Bayesian frameworks, and there does not exist any SNP caller that produces p-values for calling SNPs in a frequentist framework. To fill in this gap, we develop a new method MAFsnp, a Multiple-sample based Accurate and Flexible algorithm for calling SNPs with NGS data. MAFsnp is based on an estimated likelihood ratio test (eLRT) statistic. In practical situation, the involved parameter is very close to the boundary of the parametric space, so the standard large sample property is not suitable to evaluate the finite-sample distribution of the eLRT statistic. Observing that the distribution of the test statistic is a mixture of zero and a continuous part, we propose to model the test statistic with a novel two-parameter mixture distribution. Once the parameters in the mixture distribution are estimated, p-values can be easily calculated for detecting SNPs, and the multiple-testing corrected p-values can be used to control false discovery rate (FDR) at any pre-specified level. With simulated data, MAFsnp is shown to have much better control of FDR than the existing SNP callers. Through the application to two real datasets, MAFsnp is also shown to outperform the existing SNP callers in terms of calling accuracy. An R package “MAFsnp” implementing the new SNP caller is freely available at http://homepage.fudan.edu.cn/zhangh/softwares/. PMID:26309201

Gesture Based Control and EMG Decomposition

NASA Technical Reports Server (NTRS)

Wheeler, Kevin R.; Chang, Mindy H.; Knuth, Kevin H.

2005-01-01

This paper presents two probabilistic developments for use with Electromyograms (EMG). First described is a new-electric interface for virtual device control based on gesture recognition. The second development is a Bayesian method for decomposing EMG into individual motor unit action potentials. This more complex technique will then allow for higher resolution in separating muscle groups for gesture recognition. All examples presented rely upon sampling EMG data from a subject's forearm. The gesture based recognition uses pattern recognition software that has been trained to identify gestures from among a given set of gestures. The pattern recognition software consists of hidden Markov models which are used to recognize the gestures as they are being performed in real-time from moving averages of EMG. Two experiments were conducted to examine the feasibility of this interface technology. The first replicated a virtual joystick interface, and the second replicated a keyboard. Moving averages of EMG do not provide easy distinction between fine muscle groups. To better distinguish between different fine motor skill muscle groups we present a Bayesian algorithm to separate surface EMG into representative motor unit action potentials. The algorithm is based upon differential Variable Component Analysis (dVCA) [l], [2] which was originally developed for Electroencephalograms. The algorithm uses a simple forward model representing a mixture of motor unit action potentials as seen across multiple channels. The parameters of this model are iteratively optimized for each component. Results are presented on both synthetic and experimental EMG data. The synthetic case has additive white noise and is compared with known components. The experimental EMG data was obtained using a custom linear electrode array designed for this study.

MC 2: A Deeper Look at ZwCl 2341.1+0000 with Bayesian Galaxy Clustering and Weak Lensing Analyses

DOE Office of Scientific and Technical Information (OSTI.GOV)

Benson, B.; Wittman, D. M.; Golovich, N.

ZwCl 2341.1+0000, a merging galaxy cluster with disturbed X-ray morphology and widely separated (~3 Mpc) double radio relics, was thought to be an extremely massive (10 - 30 X 10 14M⊙) and complex system with little known about its merger history. We present JVLA 2-4 GHz observations of the cluster, along with new spectroscopy from our Keck/DEIMOS survey, and apply Gaussian Mixture Modeling to the three-dimensional distribution of 227 con rmed cluster galaxies. After adopting the Bayesian Information Criterion to avoid over tting, which we discover can bias total dynamical mass estimates high, we nd that a three-substructure model withmore » a total dynamical mass estimate of 9:39 ± 0:81 X 10 14M⊙ is favored. We also present deep Subaru imaging and perform the rst weak lensing analysis on this system, obtaining a weak lensing mass estimate of 5:57±2:47X10 14M⊙. This is a more robust estimate because it does not depend on the dynamical state of the system, which is disturbed due to the merger. Our results indicate that ZwCl 2341.1+0000 is a multiple merger system comprised of at least three substructures, with the main merger that produced the radio relics occurring near to the plane of the sky, and a younger merger in the North occurring closer to the line of sight. Dynamical modeling of the main merger reproduces observed quantities (relic positions and polarizations, subcluster separation and radial velocity difference), if the merger axis angle of ~10 +34 -6 degrees and the collision speed at pericenter is ~1900 +300 -200 km/s.« less

MC 2: A Deeper Look at ZwCl 2341.1+0000 with Bayesian Galaxy Clustering and Weak Lensing Analyses

DOE PAGES

Benson, B.; Wittman, D. M.; Golovich, N.; ...

2017-05-16

ZwCl 2341.1+0000, a merging galaxy cluster with disturbed X-ray morphology and widely separated (~3 Mpc) double radio relics, was thought to be an extremely massive (10 - 30 X 10 14M⊙) and complex system with little known about its merger history. We present JVLA 2-4 GHz observations of the cluster, along with new spectroscopy from our Keck/DEIMOS survey, and apply Gaussian Mixture Modeling to the three-dimensional distribution of 227 con rmed cluster galaxies. After adopting the Bayesian Information Criterion to avoid over tting, which we discover can bias total dynamical mass estimates high, we nd that a three-substructure model withmore » a total dynamical mass estimate of 9:39 ± 0:81 X 10 14M⊙ is favored. We also present deep Subaru imaging and perform the rst weak lensing analysis on this system, obtaining a weak lensing mass estimate of 5:57±2:47X10 14M⊙. This is a more robust estimate because it does not depend on the dynamical state of the system, which is disturbed due to the merger. Our results indicate that ZwCl 2341.1+0000 is a multiple merger system comprised of at least three substructures, with the main merger that produced the radio relics occurring near to the plane of the sky, and a younger merger in the North occurring closer to the line of sight. Dynamical modeling of the main merger reproduces observed quantities (relic positions and polarizations, subcluster separation and radial velocity difference), if the merger axis angle of ~10 +34 -6 degrees and the collision speed at pericenter is ~1900 +300 -200 km/s.« less

Testing adaptive toolbox models: a Bayesian hierarchical approach.

PubMed

Scheibehenne, Benjamin; Rieskamp, Jörg; 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 framework. How can a toolbox model be quantitatively specified? How can the number of toolbox strategies be limited to prevent uncontrolled strategy sprawl? How can a toolbox model be formally tested against alternative theories? The authors show how these challenges can be met by using Bayesian inference techniques. By means of parameter recovery simulations and the analysis of empirical data across a variety of domains (i.e., judgment and decision making, children's cognitive development, function learning, and perceptual categorization), the authors illustrate how Bayesian inference techniques allow toolbox models to be quantitatively specified, strategy sprawl to be contained, and toolbox models to be rigorously tested against competing theories. The authors demonstrate that their approach applies at the individual level but can also be generalized to the group level with hierarchical Bayesian procedures. The suggested Bayesian inference techniques represent a theoretical and methodological advancement for toolbox theories of cognition and behavior.

Tree Biomass Estimation of Chinese fir (Cunninghamia lanceolata) Based on Bayesian Method

PubMed Central

Zhang, Jianguo

2013-01-01

Chinese fir (Cunninghamia lanceolata (Lamb.) Hook.) is the most important conifer species for timber production with huge distribution area in southern China. Accurate estimation of biomass is required for accounting and monitoring Chinese forest carbon stocking. In the study, allometric equation was used to analyze tree biomass of Chinese fir. The common methods for estimating allometric model have taken the classical approach based on the frequency interpretation of probability. However, many different biotic and abiotic factors introduce variability in Chinese fir biomass model, suggesting that parameters of biomass model are better represented by probability distributions rather than fixed values as classical method. To deal with the problem, Bayesian method was used for estimating Chinese fir biomass model. In the Bayesian framework, two priors were introduced: non-informative priors and informative priors. For informative priors, 32 biomass equations of Chinese fir were collected from published literature in the paper. The parameter distributions from published literature were regarded as prior distributions in Bayesian model for estimating Chinese fir biomass. Therefore, the Bayesian method with informative priors was better than non-informative priors and classical method, which provides a reasonable method for estimating Chinese fir biomass. PMID:24278198

Tree biomass estimation of Chinese fir (Cunninghamia lanceolata) based on Bayesian method.

PubMed

Zhang, Xiongqing; Duan, Aiguo; Zhang, Jianguo

2013-01-01

Chinese fir (Cunninghamia lanceolata (Lamb.) Hook.) is the most important conifer species for timber production with huge distribution area in southern China. Accurate estimation of biomass is required for accounting and monitoring Chinese forest carbon stocking. In the study, allometric equation W = a(D2H)b was used to analyze tree biomass of Chinese fir. The common methods for estimating allometric model have taken the classical approach based on the frequency interpretation of probability. However, many different biotic and abiotic factors introduce variability in Chinese fir biomass model, suggesting that parameters of biomass model are better represented by probability distributions rather than fixed values as classical method. To deal with the problem, Bayesian method was used for estimating Chinese fir biomass model. In the Bayesian framework, two priors were introduced: non-informative priors and informative priors. For informative priors, 32 biomass equations of Chinese fir were collected from published literature in the paper. The parameter distributions from published literature were regarded as prior distributions in Bayesian model for estimating Chinese fir biomass. Therefore, the Bayesian method with informative priors was better than non-informative priors and classical method, which provides a reasonable method for estimating Chinese fir biomass.

Bayesian Methods for the Physical Sciences. Learning from Examples in Astronomy and Physics.

NASA Astrophysics Data System (ADS)

Andreon, Stefano; Weaver, Brian

2015-05-01

Chapter 1: This chapter presents some basic steps for performing a good statistical analysis, all summarized in about one page. Chapter 2: This short chapter introduces the basics of probability theory inan intuitive fashion using simple examples. It also illustrates, again with examples, how to propagate errors and the difference between marginal and profile likelihoods. Chapter 3: This chapter introduces the computational tools and methods that we use for sampling from the posterior distribution. Since all numerical computations, and Bayesian ones are no exception, may end in errors, we also provide a few tips to check that the numerical computation is sampling from the posterior distribution. Chapter 4: Many of the concepts of building, running, and summarizing the resultsof a Bayesian analysis are described with this step-by-step guide using a basic (Gaussian) model. The chapter also introduces examples using Poisson and Binomial likelihoods, and how to combine repeated independent measurements. Chapter 5: All statistical analyses make assumptions, and Bayesian analyses are no exception. This chapter emphasizes that results depend on data and priors (assumptions). We illustrate this concept with examples where the prior plays greatly different roles, from major to negligible. We also provide some advice on how to look for information useful for sculpting the prior. Chapter 6: In this chapter we consider examples for which we want to estimate more than a single parameter. These common problems include estimating location and spread. We also consider examples that require the modeling of two populations (one we are interested in and a nuisance population) or averaging incompatible measurements. We also introduce quite complex examples dealing with upper limits and with a larger-than-expected scatter. Chapter 7: Rarely is a sample randomly selected from the population we wish to study. Often, samples are affected by selection effects, e.g., easier-to-collect events or objects are over-represented in samples and difficult-to-collect are under-represented if not missing altogether. In this chapter we show how to account for non-random data collection to infer the properties of the population from the studied sample. Chapter 8: In this chapter we introduce regression models, i.e., how to fit (regress) one, or more quantities, against each other through a functional relationship and estimate any unknown parameters that dictate this relationship. Questions of interest include: how to deal with samples affected by selection effects? How does a rich data structure influence the fitted parameters? And what about non-linear multiple-predictor fits, upper/lower limits, measurements errors of different amplitudes and an intrinsic variety in the studied populations or an extra source of variability? A number of examples illustrate how to answer these questions and how to predict the value of an unavailable quantity by exploiting the existence of a trend with another, available, quantity. Chapter 9: This chapter provides some advice on how the careful scientist should perform model checking and sensitivity analysis, i.e., how to answer the following questions: is the considered model at odds with the current available data (the fitted data), for example because it is over-simplified compared to some specific complexity pointed out by the data? Furthermore, are the data informative about the quantity being measured or are results sensibly dependent on details of the fitted model? And, finally, what about if assumptions are uncertain? A number of examples illustrate how to answer these questions. Chapter 10: This chapter compares the performance of Bayesian methods against simple, non-Bayesian alternatives, such as maximum likelihood, minimal chi square, ordinary and weighted least square, bivariate correlated errors and intrinsic scatter, and robust estimates of location and scale. Performances are evaluated in terms of quality of the prediction, accuracy of the estimates, and fairness and noisiness of the quoted errors. We also focus on three failures of maximum likelihood methods occurring with small samples, with mixtures, and with regressions with errors in the predictor quantity.

Posterior Predictive Bayesian Phylogenetic Model Selection

PubMed Central

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

The effectiveness of surrogate taxa to conserve freshwater biodiversity

USGS Publications Warehouse

Stewart, David R.; Underwood, Zachary E.; Rahel, Frank J.; Walters, Annika W.

2018-01-01

Establishing protected areas has long been an effective conservation strategy, and is often based on more readily surveyed species. The potential of any freshwater taxa to be a surrogate of other aquatic groups has not been fully explored. We compiled occurrence data on 72 species of freshwater fish, amphibians, mussels, and aquatic reptiles for the Great Plains, Wyoming. We used hierarchical Bayesian multi-species mixture models and MaxEnt models to describe species distributions, and program Zonation to identify conservation priority areas for each aquatic group. The landscape-scale factors that best characterized aquatic species distributions differed among groups. There was low agreement and congruence among taxa-specific conservation priorities (<20%), meaning that no surrogate priority areas would include or protect the best habitats of other aquatic taxa. We found that common, wide-ranging aquatic species were included in taxa-specific priority areas, but rare freshwater species were not included. Thus, the development of conservation priorities based on a single freshwater aquatic group would not protect all species in the other aquatic groups.

Generalized species sampling priors with latent Beta reinforcements

PubMed Central

Airoldi, Edoardo M.; Costa, Thiago; Bassetti, Federico; Leisen, Fabrizio; Guindani, Michele

2014-01-01

Many popular Bayesian nonparametric priors can be characterized in terms of exchangeable species sampling sequences. However, in some applications, exchangeability may not be appropriate. We introduce a novel and probabilistically coherent family of non-exchangeable species sampling sequences characterized by a tractable predictive probability function with weights driven by a sequence of independent Beta random variables. We compare their theoretical clustering properties with those of the Dirichlet Process and the two parameters Poisson-Dirichlet process. The proposed construction provides a complete characterization of the joint process, differently from existing work. We then propose the use of such process as prior distribution in a hierarchical Bayes modeling framework, and we describe a Markov Chain Monte Carlo sampler for posterior inference. We evaluate the performance of the prior and the robustness of the resulting inference in a simulation study, providing a comparison with popular Dirichlet Processes mixtures and Hidden Markov Models. Finally, we develop an application to the detection of chromosomal aberrations in breast cancer by leveraging array CGH data. PMID:25870462

Estimating abundance of an open population with an N-mixture model using auxiliary data on animal movements.

PubMed

Ketz, Alison C; Johnson, Therese L; Monello, Ryan J; Mack, John A; George, Janet L; Kraft, Benjamin R; Wild, Margaret A; Hooten, Mevin B; Hobbs, N Thompson

2018-04-01

Accurate assessment of abundance forms a central challenge in population ecology and wildlife management. Many statistical techniques have been developed to estimate population sizes because populations change over time and space and to correct for the bias resulting from animals that are present in a study area but not observed. The mobility of individuals makes it difficult to design sampling procedures that account for movement into and out of areas with fixed jurisdictional boundaries. Aerial surveys are the gold standard used to obtain data of large mobile species in geographic regions with harsh terrain, but these surveys can be prohibitively expensive and dangerous. Estimating abundance with ground-based census methods have practical advantages, but it can be difficult to simultaneously account for temporary emigration and observer error to avoid biased results. Contemporary research in population ecology increasingly relies on telemetry observations of the states and locations of individuals to gain insight on vital rates, animal movements, and population abundance. Analytical models that use observations of movements to improve estimates of abundance have not been developed. Here we build upon existing multi-state mark-recapture methods using a hierarchical N-mixture model with multiple sources of data, including telemetry data on locations of individuals, to improve estimates of population sizes. We used a state-space approach to model animal movements to approximate the number of marked animals present within the study area at any observation period, thereby accounting for a frequently changing number of marked individuals. We illustrate the approach using data on a population of elk (Cervus elaphus nelsoni) in Northern Colorado, USA. We demonstrate substantial improvement compared to existing abundance estimation methods and corroborate our results from the ground based surveys with estimates from aerial surveys during the same seasons. We develop a hierarchical Bayesian N-mixture model using multiple sources of data on abundance, movement and survival to estimate the population size of a mobile species that uses remote conservation areas. The model improves accuracy of inference relative to previous methods for estimating abundance of open populations. © 2018 by the Ecological Society of America.

Use of limited data to construct Bayesian networks for probabilistic risk assessment.

DOE Office of Scientific and Technical Information (OSTI.GOV)

Groth, Katrina M.; Swiler, Laura Painton

2013-03-01

Probabilistic Risk Assessment (PRA) is a fundamental part of safety/quality assurance for nuclear power and nuclear weapons. Traditional PRA very effectively models complex hardware system risks using binary probabilistic models. However, traditional PRA models are not flexible enough to accommodate non-binary soft-causal factors, such as digital instrumentation&control, passive components, aging, common cause failure, and human errors. Bayesian Networks offer the opportunity to incorporate these risks into the PRA framework. This report describes the results of an early career LDRD project titled %E2%80%9CUse of Limited Data to Construct Bayesian Networks for Probabilistic Risk Assessment%E2%80%9D. The goal of the work was tomore » establish the capability to develop Bayesian Networks from sparse data, and to demonstrate this capability by producing a data-informed Bayesian Network for use in Human Reliability Analysis (HRA) as part of nuclear power plant Probabilistic Risk Assessment (PRA). This report summarizes the research goal and major products of the research.« less

Application of a predictive Bayesian model to environmental accounting.

PubMed

Anex, R P; Englehardt, J D

2001-03-30

Environmental accounting techniques are intended to capture important environmental costs and benefits that are often overlooked in standard accounting practices. Environmental accounting methods themselves often ignore or inadequately represent large but highly uncertain environmental costs and costs conditioned by specific prior events. Use of a predictive Bayesian model is demonstrated for the assessment of such highly uncertain environmental and contingent costs. The predictive Bayesian approach presented generates probability distributions for the quantity of interest (rather than parameters thereof). A spreadsheet implementation of a previously proposed predictive Bayesian model, extended to represent contingent costs, is described and used to evaluate whether a firm should undertake an accelerated phase-out of its PCB containing transformers. Variability and uncertainty (due to lack of information) in transformer accident frequency and severity are assessed simultaneously using a combination of historical accident data, engineering model-based cost estimates, and subjective judgement. Model results are compared using several different risk measures. Use of the model for incorporation of environmental risk management into a company's overall risk management strategy is discussed.

A Bayesian modification to the Jelinski-Moranda software reliability growth model

NASA Technical Reports Server (NTRS)

Littlewood, B.; Sofer, A.

1983-01-01

The Jelinski-Moranda (JM) model for software reliability was examined. It is suggested that a major reason for the poor results given by this model is the poor performance of the maximum likelihood method (ML) of parameter estimation. A reparameterization and Bayesian analysis, involving a slight modelling change, are proposed. It is shown that this new Bayesian-Jelinski-Moranda model (BJM) is mathematically quite tractable, and several metrics of interest to practitioners are obtained. The BJM and JM models are compared by using several sets of real software failure data collected and in all cases the BJM model gives superior reliability predictions. A change in the assumption which underlay both models to present the debugging process more accurately is discussed.

Bayesian regression models outperform partial least squares methods for predicting milk components and technological properties using infrared spectral data

PubMed Central

Ferragina, A.; de los Campos, G.; Vazquez, A. I.; Cecchinato, A.; Bittante, G.

2017-01-01

The aim of this study was to assess the performance of Bayesian models commonly used for genomic selection to predict “difficult-to-predict” dairy traits, such as milk fatty acid (FA) expressed as percentage of total fatty acids, and technological properties, such as fresh cheese yield and protein recovery, using Fourier-transform infrared (FTIR) spectral data. Our main hypothesis was that Bayesian models that can estimate shrinkage and perform variable selection may improve our ability to predict FA traits and technological traits above and beyond what can be achieved using the current calibration models (e.g., partial least squares, PLS). To this end, we assessed a series of Bayesian methods and compared their prediction performance with that of PLS. The comparison between models was done using the same sets of data (i.e., same samples, same variability, same spectral treatment) for each trait. Data consisted of 1,264 individual milk samples collected from Brown Swiss cows for which gas chromatographic FA composition, milk coagulation properties, and cheese-yield traits were available. For each sample, 2 spectra in the infrared region from 5,011 to 925 cm−1 were available and averaged before data analysis. Three Bayesian models: Bayesian ridge regression (Bayes RR), Bayes A, and Bayes B, and 2 reference models: PLS and modified PLS (MPLS) procedures, were used to calibrate equations for each of the traits. The Bayesian models used were implemented in the R package BGLR (http://cran.r-project.org/web/packages/BGLR/index.html), whereas the PLS and MPLS were those implemented in the WinISI II software (Infrasoft International LLC, State College, PA). Prediction accuracy was estimated for each trait and model using 25 replicates of a training-testing validation procedure. Compared with PLS, which is currently the most widely used calibration method, MPLS and the 3 Bayesian methods showed significantly greater prediction accuracy. Accuracy increased in moving from calibration to external validation methods, and in moving from PLS and MPLS to Bayesian methods, particularly Bayes A and Bayes B. The maximum R2 value of validation was obtained with Bayes B and Bayes A. For the FA, C10:0 (% of each FA on total FA basis) had the highest R2 (0.75, achieved with Bayes A and Bayes B), and among the technological traits, fresh cheese yield R2 of 0.82 (achieved with Bayes B). These 2 methods have proven to be useful instruments in shrinking and selecting very informative wavelengths and inferring the structure and functions of the analyzed traits. We conclude that Bayesian models are powerful tools for deriving calibration equations, and, importantly, these equations can be easily developed using existing open-source software. As part of our study, we provide scripts based on the open source R software BGLR, which can be used to train customized prediction equations for other traits or populations. PMID:26387015

Basics of Bayesian methods.

PubMed

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.

Climatic Models Ensemble-based Mid-21st Century Runoff Projections: A Bayesian Framework

NASA Astrophysics Data System (ADS)

Achieng, K. O.; Zhu, J.

2017-12-01

There are a number of North American Regional Climate Change Assessment Program (NARCCAP) climatic models that have been used to project surface runoff in the mid-21st century. Statistical model selection techniques are often used to select the model that best fits data. However, model selection techniques often lead to different conclusions. In this study, ten models are averaged in Bayesian paradigm to project runoff. Bayesian Model Averaging (BMA) is used to project and identify effect of model uncertainty on future runoff projections. Baseflow separation - a two-digital filter which is also called Eckhardt filter - is used to separate USGS streamflow (total runoff) into two components: baseflow and surface runoff. We use this surface runoff as the a priori runoff when conducting BMA of runoff simulated from the ten RCM models. The primary objective of this study is to evaluate how well RCM multi-model ensembles simulate surface runoff, in a Bayesian framework. Specifically, we investigate and discuss the following questions: How well do ten RCM models ensemble jointly simulate surface runoff by averaging over all the models using BMA, given a priori surface runoff? What are the effects of model uncertainty on surface runoff simulation?

Sequential Inverse Problems Bayesian Principles and the Logistic Map Example

NASA Astrophysics Data System (ADS)

Duan, Lian; Farmer, Chris L.; Moroz, Irene M.

2010-09-01

Bayesian statistics provides a general framework for solving inverse problems, but is not without interpretation and implementation problems. This paper discusses difficulties arising from the fact that forward models are always in error to some extent. Using a simple example based on the one-dimensional logistic map, we argue that, when implementation problems are minimal, the Bayesian framework is quite adequate. In this paper the Bayesian Filter is shown to be able to recover excellent state estimates in the perfect model scenario (PMS) and to distinguish the PMS from the imperfect model scenario (IMS). Through a quantitative comparison of the way in which the observations are assimilated in both the PMS and the IMS scenarios, we suggest that one can, sometimes, measure the degree of imperfection.

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

PubMed

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.

Number-Knower Levels in Young Children: Insights from Bayesian Modeling

ERIC Educational Resources Information Center

Lee, Michael D.; Sarnecka, Barbara W.

2011-01-01

Lee and Sarnecka (2010) developed a Bayesian model of young children's behavior on the Give-N test of number knowledge. This paper presents two new extensions of the model, and applies the model to new data. In the first extension, the model is used to evaluate competing theories about the conceptual knowledge underlying children's behavior. One,…

Theory-based Bayesian Models of Inductive Inference

DTIC Science & Technology

2010-07-19

Subjective randomness and natural scene statistics. Psychonomic Bulletin & Review . http://cocosci.berkeley.edu/tom/papers/randscenes.pdf Page 1...in press). Exemplar models as a mechanism for performing Bayesian inference. Psychonomic Bulletin & Review . http://cocosci.berkeley.edu/tom

Modeling Error Distributions of Growth Curve Models through Bayesian Methods

ERIC Educational Resources Information Center

Zhang, Zhiyong

2016-01-01

Growth curve models are widely used in social and behavioral sciences. However, typical growth curve models often assume that the errors are normally distributed although non-normal data may be even more common than normal data. In order to avoid possible statistical inference problems in blindly assuming normality, a general Bayesian framework is…

Bayesian Semiparametric Structural Equation Models with Latent Variables

ERIC Educational Resources Information Center

Yang, Mingan; Dunson, David B.

2010-01-01

Structural equation models (SEMs) with latent variables are widely useful for sparse covariance structure modeling and for inferring relationships among latent variables. Bayesian SEMs are appealing in allowing for the incorporation of prior information and in providing exact posterior distributions of unknowns, including the latent variables. In…

Dynamic Bayesian Networks for Student Modeling

ERIC Educational Resources Information Center

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…

Adaptive MCMC in Bayesian phylogenetics: an application to analyzing partitioned data in BEAST.

PubMed

Baele, Guy; Lemey, Philippe; Rambaut, Andrew; Suchard, Marc A

2017-06-15

Advances in sequencing technology continue to deliver increasingly large molecular sequence datasets that are often heavily partitioned in order to accurately model the underlying evolutionary processes. In phylogenetic analyses, partitioning strategies involve estimating conditionally independent models of molecular evolution for different genes and different positions within those genes, requiring a large number of evolutionary parameters that have to be estimated, leading to an increased computational burden for such analyses. The past two decades have also seen the rise of multi-core processors, both in the central processing unit (CPU) and Graphics processing unit processor markets, enabling massively parallel computations that are not yet fully exploited by many software packages for multipartite analyses. We here propose a Markov chain Monte Carlo (MCMC) approach using an adaptive multivariate transition kernel to estimate in parallel a large number of parameters, split across partitioned data, by exploiting multi-core processing. Across several real-world examples, we demonstrate that our approach enables the estimation of these multipartite parameters more efficiently than standard approaches that typically use a mixture of univariate transition kernels. In one case, when estimating the relative rate parameter of the non-coding partition in a heterochronous dataset, MCMC integration efficiency improves by > 14-fold. Our implementation is part of the BEAST code base, a widely used open source software package to perform Bayesian phylogenetic inference. guy.baele@kuleuven.be. Supplementary data are available at Bioinformatics online. © The Author 2017. Published by Oxford University Press. All rights reserved. For Permissions, please e-mail: journals.permissions@oup.com

Using Bayesian analysis in repeated preclinical in vivo studies for a more effective use of animals.

PubMed

Walley, Rosalind; Sherington, John; Rastrick, Joe; Detrait, Eric; Hanon, Etienne; Watt, Gillian

2016-05-01

Whilst innovative Bayesian approaches are increasingly used in clinical studies, in the preclinical area Bayesian methods appear to be rarely used in the reporting of pharmacology data. This is particularly surprising in the context of regularly repeated in vivo studies where there is a considerable amount of data from historical control groups, which has potential value. This paper describes our experience with introducing Bayesian analysis for such studies using a Bayesian meta-analytic predictive approach. This leads naturally either to an informative prior for a control group as part of a full Bayesian analysis of the next study or using a predictive distribution to replace a control group entirely. We use quality control charts to illustrate study-to-study variation to the scientists and describe informative priors in terms of their approximate effective numbers of animals. We describe two case studies of animal models: the lipopolysaccharide-induced cytokine release model used in inflammation and the novel object recognition model used to screen cognitive enhancers, both of which show the advantage of a Bayesian approach over the standard frequentist analysis. We conclude that using Bayesian methods in stable repeated in vivo studies can result in a more effective use of animals, either by reducing the total number of animals used or by increasing the precision of key treatment differences. This will lead to clearer results and supports the "3Rs initiative" to Refine, Reduce and Replace animals in research. Copyright © 2016 John Wiley & Sons, Ltd. Copyright © 2016 John Wiley & Sons, Ltd.

Computational statistics using the Bayesian Inference Engine

NASA Astrophysics Data System (ADS)

Weinberg, Martin D.

2013-09-01

This paper introduces the Bayesian Inference Engine (BIE), a general parallel, optimized software package for parameter inference and model selection. This package is motivated by the analysis needs of modern astronomical surveys and the need to organize and reuse expensive derived data. The BIE is the first platform for computational statistics designed explicitly to enable Bayesian update and model comparison for astronomical problems. Bayesian update is based on the representation of high-dimensional posterior distributions using metric-ball-tree based kernel density estimation. Among its algorithmic offerings, the BIE emphasizes hybrid tempered Markov chain Monte Carlo schemes that robustly sample multimodal posterior distributions in high-dimensional parameter spaces. Moreover, the BIE implements a full persistence or serialization system that stores the full byte-level image of the running inference and previously characterized posterior distributions for later use. Two new algorithms to compute the marginal likelihood from the posterior distribution, developed for and implemented in the BIE, enable model comparison for complex models and data sets. Finally, the BIE was designed to be a collaborative platform for applying Bayesian methodology to astronomy. It includes an extensible object-oriented and easily extended framework that implements every aspect of the Bayesian inference. By providing a variety of statistical algorithms for all phases of the inference problem, a scientist may explore a variety of approaches with a single model and data implementation. Additional technical details and download details are available from http://www.astro.umass.edu/bie. The BIE is distributed under the GNU General Public License.

The effect of using genealogy-based haplotypes for genomic prediction

PubMed Central

2013-01-01

Background Genomic prediction uses two sources of information: linkage disequilibrium between markers and quantitative trait loci, and additive genetic relationships between individuals. One way to increase the accuracy of genomic prediction is to capture more linkage disequilibrium by regression on haplotypes instead of regression on individual markers. The aim of this study was to investigate the accuracy of genomic prediction using haplotypes based on local genealogy information. Methods A total of 4429 Danish Holstein bulls were genotyped with the 50K SNP chip. Haplotypes were constructed using local genealogical trees. Effects of haplotype covariates were estimated with two types of prediction models: (1) assuming that effects had the same distribution for all haplotype covariates, i.e. the GBLUP method and (2) assuming that a large proportion (π) of the haplotype covariates had zero effect, i.e. a Bayesian mixture method. Results About 7.5 times more covariate effects were estimated when fitting haplotypes based on local genealogical trees compared to fitting individuals markers. Genealogy-based haplotype clustering slightly increased the accuracy of genomic prediction and, in some cases, decreased the bias of prediction. With the Bayesian method, accuracy of prediction was less sensitive to parameter π when fitting haplotypes compared to fitting markers. Conclusions Use of haplotypes based on genealogy can slightly increase the accuracy of genomic prediction. Improved methods to cluster the haplotypes constructed from local genealogy could lead to additional gains in accuracy. PMID:23496971

The effect of using genealogy-based haplotypes for genomic prediction.

PubMed

Edriss, Vahid; Fernando, Rohan L; Su, Guosheng; Lund, Mogens S; Guldbrandtsen, Bernt

2013-03-06

Genomic prediction uses two sources of information: linkage disequilibrium between markers and quantitative trait loci, and additive genetic relationships between individuals. One way to increase the accuracy of genomic prediction is to capture more linkage disequilibrium by regression on haplotypes instead of regression on individual markers. The aim of this study was to investigate the accuracy of genomic prediction using haplotypes based on local genealogy information. A total of 4429 Danish Holstein bulls were genotyped with the 50K SNP chip. Haplotypes were constructed using local genealogical trees. Effects of haplotype covariates were estimated with two types of prediction models: (1) assuming that effects had the same distribution for all haplotype covariates, i.e. the GBLUP method and (2) assuming that a large proportion (π) of the haplotype covariates had zero effect, i.e. a Bayesian mixture method. About 7.5 times more covariate effects were estimated when fitting haplotypes based on local genealogical trees compared to fitting individuals markers. Genealogy-based haplotype clustering slightly increased the accuracy of genomic prediction and, in some cases, decreased the bias of prediction. With the Bayesian method, accuracy of prediction was less sensitive to parameter π when fitting haplotypes compared to fitting markers. Use of haplotypes based on genealogy can slightly increase the accuracy of genomic prediction. Improved methods to cluster the haplotypes constructed from local genealogy could lead to additional gains in accuracy.

Parallel Markov chain Monte Carlo - bridging the gap to high-performance Bayesian computation in animal breeding and genetics.

PubMed

Wu, Xiao-Lin; Sun, Chuanyu; Beissinger, Timothy M; Rosa, Guilherme Jm; Weigel, Kent A; Gatti, Natalia de Leon; Gianola, Daniel

2012-09-25

Most Bayesian models for the analysis of complex traits are not analytically tractable and inferences are based on computationally intensive techniques. This is true of Bayesian models for genome-enabled selection, which uses whole-genome molecular data to predict the genetic merit of candidate animals for breeding purposes. In this regard, parallel computing can overcome the bottlenecks that can arise from series computing. Hence, a major goal of the present study is to bridge the gap to high-performance Bayesian computation in the context of animal breeding and genetics. Parallel Monte Carlo Markov chain algorithms and strategies are described in the context of animal breeding and genetics. Parallel Monte Carlo algorithms are introduced as a starting point including their applications to computing single-parameter and certain multiple-parameter models. Then, two basic approaches for parallel Markov chain Monte Carlo are described: one aims at parallelization within a single chain; the other is based on running multiple chains, yet some variants are discussed as well. Features and strategies of the parallel Markov chain Monte Carlo are illustrated using real data, including a large beef cattle dataset with 50K SNP genotypes. Parallel Markov chain Monte Carlo algorithms are useful for computing complex Bayesian models, which does not only lead to a dramatic speedup in computing but can also be used to optimize model parameters in complex Bayesian models. Hence, we anticipate that use of parallel Markov chain Monte Carlo will have a profound impact on revolutionizing the computational tools for genomic selection programs.

Parallel Markov chain Monte Carlo - bridging the gap to high-performance Bayesian computation in animal breeding and genetics

PubMed Central

2012-01-01

Background Most Bayesian models for the analysis of complex traits are not analytically tractable and inferences are based on computationally intensive techniques. This is true of Bayesian models for genome-enabled selection, which uses whole-genome molecular data to predict the genetic merit of candidate animals for breeding purposes. In this regard, parallel computing can overcome the bottlenecks that can arise from series computing. Hence, a major goal of the present study is to bridge the gap to high-performance Bayesian computation in the context of animal breeding and genetics. Results Parallel Monte Carlo Markov chain algorithms and strategies are described in the context of animal breeding and genetics. Parallel Monte Carlo algorithms are introduced as a starting point including their applications to computing single-parameter and certain multiple-parameter models. Then, two basic approaches for parallel Markov chain Monte Carlo are described: one aims at parallelization within a single chain; the other is based on running multiple chains, yet some variants are discussed as well. Features and strategies of the parallel Markov chain Monte Carlo are illustrated using real data, including a large beef cattle dataset with 50K SNP genotypes. Conclusions Parallel Markov chain Monte Carlo algorithms are useful for computing complex Bayesian models, which does not only lead to a dramatic speedup in computing but can also be used to optimize model parameters in complex Bayesian models. Hence, we anticipate that use of parallel Markov chain Monte Carlo will have a profound impact on revolutionizing the computational tools for genomic selection programs. PMID:23009363

Bayesian survival analysis in clinical trials: What methods are used in practice?

PubMed

Brard, Caroline; Le Teuff, Gwénaël; Le Deley, Marie-Cécile; Hampson, Lisa V

2017-02-01

Background Bayesian statistics are an appealing alternative to the traditional frequentist approach to designing, analysing, and reporting of clinical trials, especially in rare diseases. Time-to-event endpoints are widely used in many medical fields. There are additional complexities to designing Bayesian survival trials which arise from the need to specify a model for the survival distribution. The objective of this article was to critically review the use and reporting of Bayesian methods in survival trials. Methods A systematic review of clinical trials using Bayesian survival analyses was performed through PubMed and Web of Science databases. This was complemented by a full text search of the online repositories of pre-selected journals. Cost-effectiveness, dose-finding studies, meta-analyses, and methodological papers using clinical trials were excluded. Results In total, 28 articles met the inclusion criteria, 25 were original reports of clinical trials and 3 were re-analyses of a clinical trial. Most trials were in oncology (n = 25), were randomised controlled (n = 21) phase III trials (n = 13), and half considered a rare disease (n = 13). Bayesian approaches were used for monitoring in 14 trials and for the final analysis only in 14 trials. In the latter case, Bayesian survival analyses were used for the primary analysis in four cases, for the secondary analysis in seven cases, and for the trial re-analysis in three cases. Overall, 12 articles reported fitting Bayesian regression models (semi-parametric, n = 3; parametric, n = 9). Prior distributions were often incompletely reported: 20 articles did not define the prior distribution used for the parameter of interest. Over half of the trials used only non-informative priors for monitoring and the final analysis (n = 12) when it was specified. Indeed, no articles fitting Bayesian regression models placed informative priors on the parameter of interest. The prior for the treatment effect was based on historical data in only four trials. Decision rules were pre-defined in eight cases when trials used Bayesian monitoring, and in only one case when trials adopted a Bayesian approach to the final analysis. Conclusion Few trials implemented a Bayesian survival analysis and few incorporated external data into priors. There is scope to improve the quality of reporting of Bayesian methods in survival trials. Extension of the Consolidated Standards of Reporting Trials statement for reporting Bayesian clinical trials is recommended.

A Bayesian estimation of a stochastic predator-prey model of economic fluctuations

NASA Astrophysics Data System (ADS)

Dibeh, Ghassan; Luchinsky, Dmitry G.; Luchinskaya, Daria D.; Smelyanskiy, Vadim N.

2007-06-01

In this paper, we develop a Bayesian framework for the empirical estimation of the parameters of one of the best known nonlinear models of the business cycle: The Marx-inspired model of a growth cycle introduced by R. M. Goodwin. The model predicts a series of closed cycles representing the dynamics of labor's share and the employment rate in the capitalist economy. The Bayesian framework is used to empirically estimate a modified Goodwin model. The original model is extended in two ways. First, we allow for exogenous periodic variations of the otherwise steady growth rates of the labor force and productivity per worker. Second, we allow for stochastic variations of those parameters. The resultant modified Goodwin model is a stochastic predator-prey model with periodic forcing. The model is then estimated using a newly developed Bayesian estimation method on data sets representing growth cycles in France and Italy during the years 1960-2005. Results show that inference of the parameters of the stochastic Goodwin model can be achieved. The comparison of the dynamics of the Goodwin model with the inferred values of parameters demonstrates quantitative agreement with the growth cycle empirical data.

A Bayesian Approach for Analyzing Longitudinal Structural Equation Models

ERIC Educational Resources Information Center

Song, Xin-Yuan; Lu, Zhao-Hua; Hser, Yih-Ing; Lee, Sik-Yum

2011-01-01

This article considers a Bayesian approach for analyzing a longitudinal 2-level nonlinear structural equation model with covariates, and mixed continuous and ordered categorical variables. The first-level model is formulated for measures taken at each time point nested within individuals for investigating their characteristics that are dynamically…

Model Diagnostics for Bayesian Networks. Research Report. ETS RR-04-17

ERIC Educational Resources Information Center

Sinharay, Sandip

2004-01-01

Assessing fit of psychometric models has always been an issue of enormous interest, but there exists no unanimously agreed upon item fit diagnostic for the models. Bayesian networks, frequently used in educational assessments (see, for example, Mislevy, Almond, Yan, & Steinberg, 2001) primarily for learning about students' knowledge and…

Bayesian Unimodal Density Regression for Causal Inference

ERIC Educational Resources Information Center

Karabatsos, George; Walker, Stephen G.

2011-01-01

Karabatsos and Walker (2011) introduced a new Bayesian nonparametric (BNP) regression model. Through analyses of real and simulated data, they showed that the BNP regression model outperforms other parametric and nonparametric regression models of common use, in terms of predictive accuracy of the outcome (dependent) variable. The other,…

DOE Office of Scientific and Technical Information (OSTI.GOV)

Ng, B

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.

Bayesian Estimation of the DINA Model with Gibbs Sampling

ERIC Educational Resources Information Center

Culpepper, Steven Andrew

2015-01-01

A Bayesian model formulation of the deterministic inputs, noisy "and" gate (DINA) model is presented. Gibbs sampling is employed to simulate from the joint posterior distribution of item guessing and slipping parameters, subject attribute parameters, and latent class probabilities. The procedure extends concepts in Béguin and Glas,…

ABrox-A user-friendly Python module for approximate Bayesian computation with a focus on model comparison.

PubMed

Mertens, Ulf Kai; Voss, Andreas; Radev, Stefan

2018-01-01

We give an overview of the basic principles of approximate Bayesian computation (ABC), a class of stochastic methods that enable flexible and likelihood-free model comparison and parameter estimation. Our new open-source software called ABrox is used to illustrate ABC for model comparison on two prominent statistical tests, the two-sample t-test and the Levene-Test. We further highlight the flexibility of ABC compared to classical Bayesian hypothesis testing by computing an approximate Bayes factor for two multinomial processing tree models. Last but not least, throughout the paper, we introduce ABrox using the accompanied graphical user interface.

Semisupervised learning using Bayesian interpretation: application to LS-SVM.

PubMed

Adankon, Mathias M; Cheriet, Mohamed; Biem, Alain

2011-04-01

Bayesian reasoning provides an ideal basis for representing and manipulating uncertain knowledge, with the result that many interesting algorithms in machine learning are based on Bayesian inference. In this paper, we use the Bayesian approach with one and two levels of inference to model the semisupervised learning problem and give its application to the successful kernel classifier support vector machine (SVM) and its variant least-squares SVM (LS-SVM). Taking advantage of Bayesian interpretation of LS-SVM, we develop a semisupervised learning algorithm for Bayesian LS-SVM using our approach based on two levels of inference. Experimental results on both artificial and real pattern recognition problems show the utility of our method.

Use of Bayesian Inference in Crystallographic Structure Refinement via Full Diffraction Profile Analysis

PubMed Central

Fancher, Chris M.; Han, Zhen; Levin, Igor; Page, Katharine; Reich, Brian J.; Smith, Ralph C.; Wilson, Alyson G.; Jones, Jacob L.

2016-01-01

A Bayesian inference method for refining crystallographic structures is presented. The distribution of model parameters is stochastically sampled using Markov chain Monte Carlo. Posterior probability distributions are constructed for all model parameters to properly quantify uncertainty by appropriately modeling the heteroskedasticity and correlation of the error structure. The proposed method is demonstrated by analyzing a National Institute of Standards and Technology silicon standard reference material. The results obtained by Bayesian inference are compared with those determined by Rietveld refinement. Posterior probability distributions of model parameters provide both estimates and uncertainties. The new method better estimates the true uncertainties in the model as compared to the Rietveld method. PMID:27550221

Using Bayesian belief networks in adaptive management.

Treesearch

J.B. Nyberg; B.G. Marcot; R. Sulyma

2006-01-01

Bayesian belief and decision networks are relatively new modeling methods that are especially well suited to adaptive-management applications, but they appear not to have been widely used in adaptive management to date. Bayesian belief networks (BBNs) can serve many purposes for practioners of adaptive management, from illustrating system relations conceptually to...

Bayesian hierarchical model of ceftriaxone resistance proportions among Salmonella serotype Heidelberg infections.

PubMed

Gu, Weidong; Medalla, Felicita; Hoekstra, Robert M

2018-02-01

The National Antimicrobial Resistance Monitoring System (NARMS) at the Centers for Disease Control and Prevention tracks resistance among Salmonella infections. The annual number of Salmonella isolates of a particular serotype from states may be small, making direct estimation of resistance proportions unreliable. We developed a Bayesian hierarchical model to improve estimation by borrowing strength from relevant sampling units. We illustrate the models with different specifications of spatio-temporal interaction using 2004-2013 NARMS data for ceftriaxone-resistant Salmonella serotype Heidelberg. Our results show that Bayesian estimates of resistance proportions were smoother than observed values, and the difference between predicted and observed proportions was inversely related to the number of submitted isolates. The model with interaction allowed for tracking of annual changes in resistance proportions at the state level. We demonstrated that Bayesian hierarchical models provide a useful tool to examine spatio-temporal patterns of small sample size such as those found in NARMS. Published by Elsevier Ltd.

Bayesian generalized least squares regression with application to log Pearson type 3 regional skew estimation

NASA Astrophysics Data System (ADS)

Reis, D. S.; Stedinger, J. R.; Martins, E. S.

2005-10-01

This paper develops a Bayesian approach to analysis of a generalized least squares (GLS) regression model for regional analyses of hydrologic data. The new approach allows computation of the posterior distributions of the parameters and the model error variance using a quasi-analytic approach. Two regional skew estimation studies illustrate the value of the Bayesian GLS approach for regional statistical analysis of a shape parameter and demonstrate that regional skew models can be relatively precise with effective record lengths in excess of 60 years. With Bayesian GLS the marginal posterior distribution of the model error variance and the corresponding mean and variance of the parameters can be computed directly, thereby providing a simple but important extension of the regional GLS regression procedures popularized by Tasker and Stedinger (1989), which is sensitive to the likely values of the model error variance when it is small relative to the sampling error in the at-site estimator.

Evidential evaluation of DNA profiles using a discrete statistical model implemented in the DNA LiRa software.

PubMed

Puch-Solis, Roberto; Clayton, Tim

2014-07-01

The high sensitivity of the technology for producing profiles means that it has become routine to produce profiles from relatively small quantities of DNA. The profiles obtained from low template DNA (LTDNA) are affected by several phenomena which must be taken into consideration when interpreting and evaluating this evidence. Furthermore, many of the same phenomena affect profiles from higher amounts of DNA (e.g. where complex mixtures has been revealed). In this article we present a statistical model, which forms the basis of software DNA LiRa, and that is able to calculate likelihood ratios where one to four donors are postulated and for any number of replicates. The model can take into account dropin and allelic dropout for different contributors, template degradation and uncertain allele designations. In this statistical model unknown parameters are treated following the Empirical Bayesian paradigm. The performance of LiRa is tested using examples and the outputs are compared with those generated using two other statistical software packages likeLTD and LRmix. The concept of ban efficiency is introduced as a measure for assessing model sensitivity. Copyright © 2014. Published by Elsevier Ireland Ltd.

Cure fraction model with random effects for regional variation in cancer survival.

PubMed

Seppä, Karri; Hakulinen, Timo; Kim, Hyon-Jung; Läärä, Esa

2010-11-30

Assessing regional differences in the survival of cancer patients is important but difficult when separate regions are small or sparsely populated. In this paper, we apply a mixture cure fraction model with random effects to cause-specific survival data of female breast cancer patients collected by the population-based Finnish Cancer Registry. Two sets of random effects were used to capture the regional variation in the cure fraction and in the survival of the non-cured patients, respectively. This hierarchical model was implemented in a Bayesian framework using a Metropolis-within-Gibbs algorithm. To avoid poor mixing of the Markov chain, when the variance of either set of random effects was close to zero, posterior simulations were based on a parameter-expanded model with tailor-made proposal distributions in Metropolis steps. The random effects allowed the fitting of the cure fraction model to the sparse regional data and the estimation of the regional variation in 10-year cause-specific breast cancer survival with a parsimonious number of parameters. Before 1986, the capital of Finland clearly stood out from the rest, but since then all the 21 hospital districts have achieved approximately the same level of survival. Copyright © 2010 John Wiley & Sons, Ltd.

Bayesian estimation of a source term of radiation release with approximately known nuclide ratios

NASA Astrophysics Data System (ADS)

Tichý, Ondřej; Šmídl, Václav; Hofman, Radek

2016-04-01

We are concerned with estimation of a source term in case of an accidental release from a known location, e.g. a power plant. Usually, the source term of an accidental release of radiation comprises of a mixture of nuclide. The gamma dose rate measurements do not provide a direct information on the source term composition. However, physical properties of respective nuclide (deposition properties, decay half-life) can be used when uncertain information on nuclide ratios is available, e.g. from known reactor inventory. The proposed method is based on linear inverse model where the observation vector y arise as a linear combination y = Mx of a source-receptor-sensitivity (SRS) matrix M and the source term x. The task is to estimate the unknown source term x. The problem is ill-conditioned and further regularization is needed to obtain a reasonable solution. In this contribution, we assume that nuclide ratios of the release is known with some degree of uncertainty. This knowledge is used to form the prior covariance matrix of the source term x. Due to uncertainty in the ratios the diagonal elements of the covariance matrix are considered to be unknown. Positivity of the source term estimate is guaranteed by using multivariate truncated Gaussian distribution. Following Bayesian approach, we estimate all parameters of the model from the data so that y, M, and known ratios are the only inputs of the method. Since the inference of the model is intractable, we follow the Variational Bayes method yielding an iterative algorithm for estimation of all model parameters. Performance of the method is studied on simulated 6 hour power plant release where 3 nuclide are released and 2 nuclide ratios are approximately known. The comparison with method with unknown nuclide ratios will be given to prove the usefulness of the proposed approach. This research is supported by EEA/Norwegian Financial Mechanism under project MSMT-28477/2014 Source-Term Determination of Radionuclide Releases by Inverse Atmospheric Dispersion Modelling (STRADI).

Hierarchical Bayesian spatial models for multispecies conservation planning and monitoring

Treesearch

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

2010-01-01

Biologists who develop and apply habitat models are often familiar with the statistical challenges posed by their data’s spatial structure but are unsure of whether the use of complex spatial models will increase the utility of model results in planning. We compared the relative performance of nonspatial and hierarchical Bayesian spatial models for three vertebrate and...

Variational Bayesian identification and prediction of stochastic nonlinear dynamic causal models.

PubMed

Daunizeau, J; Friston, K J; Kiebel, S J

2009-11-01

In this paper, we describe a general variational Bayesian approach for approximate inference on nonlinear stochastic dynamic models. This scheme extends established approximate inference on hidden-states to cover: (i) nonlinear evolution and observation functions, (ii) unknown parameters and (precision) hyperparameters and (iii) model comparison and prediction under uncertainty. Model identification or inversion entails the estimation of the marginal likelihood or evidence of a model. This difficult integration problem can be finessed by optimising a free-energy bound on the evidence using results from variational calculus. This yields a deterministic update scheme that optimises an approximation to the posterior density on the unknown model variables. We derive such a variational Bayesian scheme in the context of nonlinear stochastic dynamic hierarchical models, for both model identification and time-series prediction. The computational complexity of the scheme is comparable to that of an extended Kalman filter, which is critical when inverting high dimensional models or long time-series. Using Monte-Carlo simulations, we assess the estimation efficiency of this variational Bayesian approach using three stochastic variants of chaotic dynamic systems. We also demonstrate the model comparison capabilities of the method, its self-consistency and its predictive power.

Hierarchical Bayesian spatial models for multispecies conservation planning and monitoring.

PubMed

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

2010-12-01

Biologists who develop and apply habitat models are often familiar with the statistical challenges posed by their data's spatial structure but are unsure of whether the use of complex spatial models will increase the utility of model results in planning. We compared the relative performance of nonspatial and hierarchical Bayesian spatial models for three vertebrate and invertebrate taxa of conservation concern (Church's sideband snails [Monadenia churchi], red tree voles [Arborimus longicaudus], and Pacific fishers [Martes pennanti pacifica]) that provide examples of a range of distributional extents and dispersal abilities. We used presence-absence data derived from regional monitoring programs to develop models with both landscape and site-level environmental covariates. We used Markov chain Monte Carlo algorithms and a conditional autoregressive or intrinsic conditional autoregressive model framework to fit spatial models. The fit of Bayesian spatial models was between 35 and 55% better than the fit of nonspatial analogue models. Bayesian spatial models outperformed analogous models developed with maximum entropy (Maxent) methods. Although the best spatial and nonspatial models included similar environmental variables, spatial models provided estimates of residual spatial effects that suggested how ecological processes might structure distribution patterns. Spatial models built from presence-absence data improved fit most for localized endemic species with ranges constrained by poorly known biogeographic factors and for widely distributed species suspected to be strongly affected by unmeasured environmental variables or population processes. By treating spatial effects as a variable of interest rather than a nuisance, hierarchical Bayesian spatial models, especially when they are based on a common broad-scale spatial lattice (here the national Forest Inventory and Analysis grid of 24 km(2) hexagons), can increase the relevance of habitat models to multispecies conservation planning. Journal compilation © 2010 Society for Conservation Biology. No claim to original US government works.

Using Bayesian Stable Isotope Mixing Models to Enhance Marine Ecosystem Models

EPA Science Inventory

The use of stable isotopes in food web studies has proven to be a valuable tool for ecologists. We investigated the use of Bayesian stable isotope mixing models as constraints for an ecosystem model of a temperate seagrass system on the Atlantic coast of France. δ13C and δ15N i...

Effect of Bayesian Student Modeling on Academic Achievement in Foreign Language Teaching (University Level English Preparatory School Example)

ERIC Educational Resources Information Center

Aslan, Burak Galip; Öztürk, Özlem; Inceoglu, Mustafa Murat

2014-01-01

Considering the increasing importance of adaptive approaches in CALL systems, this study implemented a machine learning based student modeling middleware with Bayesian networks. The profiling approach of the student modeling system is based on Felder and Silverman's Learning Styles Model and Felder and Soloman's Index of Learning Styles…

Competing risk models in reliability systems, a weibull distribution model with bayesian analysis approach

NASA Astrophysics Data System (ADS)

Iskandar, Ismed; Satria Gondokaryono, Yudi

2016-02-01

In reliability theory, the most important problem is to determine the reliability of a complex system from the reliability of its components. The weakness of most reliability theories is that the systems are described and explained as simply functioning or failed. In many real situations, the failures may be from many causes depending upon the age and the environment of the system and its components. Another problem in reliability theory is one of estimating the parameters of the assumed failure models. The estimation may be based on data collected over censored or uncensored life tests. In many reliability problems, the failure data are simply quantitatively inadequate, especially in engineering design and maintenance system. The Bayesian analyses are more beneficial than the classical one in such cases. The Bayesian estimation analyses allow us to combine past knowledge or experience in the form of an apriori distribution with life test data to make inferences of the parameter of interest. In this paper, we have investigated the application of the Bayesian estimation analyses to competing risk systems. The cases are limited to the models with independent causes of failure by using the Weibull distribution as our model. A simulation is conducted for this distribution with the objectives of verifying the models and the estimators and investigating the performance of the estimators for varying sample size. The simulation data are analyzed by using Bayesian and the maximum likelihood analyses. The simulation results show that the change of the true of parameter relatively to another will change the value of standard deviation in an opposite direction. For a perfect information on the prior distribution, the estimation methods of the Bayesian analyses are better than those of the maximum likelihood. The sensitivity analyses show some amount of sensitivity over the shifts of the prior locations. They also show the robustness of the Bayesian analysis within the range between the true value and the maximum likelihood estimated value lines.

Bayesian Factor Analysis as a Variable Selection Problem: Alternative Priors and Consequences

PubMed Central

Lu, Zhao-Hua; Chow, Sy-Miin; Loken, Eric

2016-01-01

Factor analysis is a popular statistical technique for multivariate data analysis. Developments in the structural equation modeling framework have enabled the use of hybrid confirmatory/exploratory approaches in which factor loading structures can be explored relatively flexibly within a confirmatory factor analysis (CFA) framework. Recently, a Bayesian structural equation modeling (BSEM) approach (Muthén & Asparouhov, 2012) has been proposed as a way to explore the presence of cross-loadings in CFA models. We show that the issue of determining factor loading patterns may be formulated as a Bayesian variable selection problem in which Muthén and Asparouhov’s approach can be regarded as a BSEM approach with ridge regression prior (BSEM-RP). We propose another Bayesian approach, denoted herein as the Bayesian structural equation modeling with spike and slab prior (BSEM-SSP), which serves as a one-stage alternative to the BSEM-RP. We review the theoretical advantages and disadvantages of both approaches and compare their empirical performance relative to two modification indices-based approaches and exploratory factor analysis with target rotation. A teacher stress scale data set (Byrne, 2012; Pettegrew & Wolf, 1982) is used to demonstrate our approach. PMID:27314566

Bayesian Inference and Online Learning in Poisson Neuronal Networks.

PubMed

Huang, Yanping; Rao, Rajesh P N

2016-08-01

Motivated by the growing evidence for Bayesian computation in the brain, we show how a two-layer recurrent network of Poisson neurons can perform both approximate Bayesian inference and learning for any hidden Markov model. The lower-layer sensory neurons receive noisy measurements of hidden world states. The higher-layer neurons infer a posterior distribution over world states via Bayesian inference from inputs generated by sensory neurons. We demonstrate how such a neuronal network with synaptic plasticity can implement a form of Bayesian inference similar to Monte Carlo methods such as particle filtering. Each spike in a higher-layer neuron represents a sample of a particular hidden world state. The spiking activity across the neural population approximates the posterior distribution over hidden states. In this model, variability in spiking is regarded not as a nuisance but as an integral feature that provides the variability necessary for sampling during inference. We demonstrate how the network can learn the likelihood model, as well as the transition probabilities underlying the dynamics, using a Hebbian learning rule. We present results illustrating the ability of the network to perform inference and learning for arbitrary hidden Markov models.

Impact assessment of extreme storm events using a Bayesian network

USGS Publications Warehouse

den Heijer, C.(Kees); Knipping, Dirk T.J.A.; Plant, Nathaniel G.; van Thiel de Vries, Jaap S. M.; Baart, Fedor; van Gelder, Pieter H. A. J. M.

2012-01-01

This paper describes an investigation on the usefulness of Bayesian Networks in the safety assessment of dune coasts. A network has been created that predicts the erosion volume based on hydraulic boundary conditions and a number of cross-shore profile indicators. Field measurement data along a large part of the Dutch coast has been used to train the network. Corresponding storm impact on the dunes was calculated with an empirical dune erosion model named duros+. Comparison between the Bayesian Network predictions and the original duros+ results, here considered as observations, results in a skill up to 0.88, provided that the training data covers the range of predictions. Hence, the predictions from a deterministic model (duros+) can be captured in a probabilistic model (Bayesian Network) such that both the process knowledge and uncertainties can be included in impact and vulnerability assessments.

BAYESIAN METHODS FOR REGIONAL-SCALE EUTROPHICATION MODELS. (R830887)

EPA Science Inventory

We demonstrate a Bayesian classification and regression tree (CART) approach to link multiple environmental stressors to biological responses and quantify uncertainty in model predictions. Such an approach can: (1) report prediction uncertainty, (2) be consistent with the amou...

Bayesian conditional-independence modeling of the AIDS epidemic in England and Wales

NASA Astrophysics Data System (ADS)

Gilks, Walter R.; De Angelis, Daniela; Day, Nicholas E.

We describe the use of conditional-independence modeling, Bayesian inference and Markov chain Monte Carlo, to model and project the HIV-AIDS epidemic in homosexual/bisexual males in England and Wales. Complexity in this analysis arises through selectively missing data, indirectly observed underlying processes, and measurement error. Our emphasis is on presentation and discussion of the concepts, not on the technicalities of this analysis, which can be found elsewhere [D. De Angelis, W.R. Gilks, N.E. Day, Bayesian projection of the the acquired immune deficiency syndrome epidemic (with discussion), Applied Statistics, in press].

Bayesian estimation of seasonal course of canopy leaf area index from hyperspectral satellite data

NASA Astrophysics Data System (ADS)

Varvia, Petri; Rautiainen, Miina; Seppänen, Aku

2018-03-01

In this paper, Bayesian inversion of a physically-based forest reflectance model is investigated to estimate of boreal forest canopy leaf area index (LAI) from EO-1 Hyperion hyperspectral data. The data consist of multiple forest stands with different species compositions and structures, imaged in three phases of the growing season. The Bayesian estimates of canopy LAI are compared to reference estimates based on a spectral vegetation index. The forest reflectance model contains also other unknown variables in addition to LAI, for example leaf single scattering albedo and understory reflectance. In the Bayesian approach, these variables are estimated simultaneously with LAI. The feasibility and seasonal variation of these estimates is also examined. Credible intervals for the estimates are also calculated and evaluated. The results show that the Bayesian inversion approach is significantly better than using a comparable spectral vegetation index regression.

Using a web-based application to define the accuracy of diagnostic tests when the gold standard is imperfect.

PubMed

Lim, Cherry; Wannapinij, Prapass; White, Lisa; Day, Nicholas P J; Cooper, Ben S; Peacock, Sharon J; Limmathurotsakul, Direk

2013-01-01

Estimates of the sensitivity and specificity for new diagnostic tests based on evaluation against a known gold standard are imprecise when the accuracy of the gold standard is imperfect. Bayesian latent class models (LCMs) can be helpful under these circumstances, but the necessary analysis requires expertise in computational programming. Here, we describe open-access web-based applications that allow non-experts to apply Bayesian LCMs to their own data sets via a user-friendly interface. Applications for Bayesian LCMs were constructed on a web server using R and WinBUGS programs. The models provided (http://mice.tropmedres.ac) include two Bayesian LCMs: the two-tests in two-population model (Hui and Walter model) and the three-tests in one-population model (Walter and Irwig model). Both models are available with simplified and advanced interfaces. In the former, all settings for Bayesian statistics are fixed as defaults. Users input their data set into a table provided on the webpage. Disease prevalence and accuracy of diagnostic tests are then estimated using the Bayesian LCM, and provided on the web page within a few minutes. With the advanced interfaces, experienced researchers can modify all settings in the models as needed. These settings include correlation among diagnostic test results and prior distributions for all unknown parameters. The web pages provide worked examples with both models using the original data sets presented by Hui and Walter in 1980, and by Walter and Irwig in 1988. We also illustrate the utility of the advanced interface using the Walter and Irwig model on a data set from a recent melioidosis study. The results obtained from the web-based applications were comparable to those published previously. The newly developed web-based applications are open-access and provide an important new resource for researchers worldwide to evaluate new diagnostic tests.

Precise Network Modeling of Systems Genetics Data Using the Bayesian Network Webserver.

PubMed

Ziebarth, Jesse D; Cui, Yan

2017-01-01

The Bayesian Network Webserver (BNW, http://compbio.uthsc.edu/BNW ) is an integrated platform for Bayesian network modeling of biological datasets. It provides a web-based network modeling environment that seamlessly integrates advanced algorithms for probabilistic causal modeling and reasoning with Bayesian networks. BNW is designed for precise modeling of relatively small networks that contain less than 20 nodes. The structure learning algorithms used by BNW guarantee the discovery of the best (most probable) network structure given the data. To facilitate network modeling across multiple biological levels, BNW provides a very flexible interface that allows users to assign network nodes into different tiers and define the relationships between and within the tiers. This function is particularly useful for modeling systems genetics datasets that often consist of multiscalar heterogeneous genotype-to-phenotype data. BNW enables users to, within seconds or minutes, go from having a simply formatted input file containing a dataset to using a network model to make predictions about the interactions between variables and the potential effects of experimental interventions. In this chapter, we will introduce the functions of BNW and show how to model systems genetics datasets with BNW.

Fragment virtual screening based on Bayesian categorization for discovering novel VEGFR-2 scaffolds.

PubMed

Zhang, Yanmin; Jiao, Yu; Xiong, Xiao; Liu, Haichun; Ran, Ting; Xu, Jinxing; Lu, Shuai; Xu, Anyang; Pan, Jing; Qiao, Xin; Shi, Zhihao; Lu, Tao; Chen, Yadong

2015-11-01

The discovery of novel scaffolds against a specific target has long been one of the most significant but challengeable goals in discovering lead compounds. A scaffold that binds in important regions of the active pocket is more favorable as a starting point because scaffolds generally possess greater optimization possibilities. However, due to the lack of sufficient chemical space diversity of the databases and the ineffectiveness of the screening methods, it still remains a great challenge to discover novel active scaffolds. Since the strengths and weaknesses of both fragment-based drug design and traditional virtual screening (VS), we proposed a fragment VS concept based on Bayesian categorization for the discovery of novel scaffolds. This work investigated the proposal through an application on VEGFR-2 target. Firstly, scaffold and structural diversity of chemical space for 10 compound databases were explicitly evaluated. Simultaneously, a robust Bayesian classification model was constructed for screening not only compound databases but also their corresponding fragment databases. Although analysis of the scaffold diversity demonstrated a very unevenly distribution of scaffolds over molecules, results showed that our Bayesian model behaved better in screening fragments than molecules. Through a literature retrospective research, several generated fragments with relatively high Bayesian scores indeed exhibit VEGFR-2 biological activity, which strongly proved the effectiveness of fragment VS based on Bayesian categorization models. This investigation of Bayesian-based fragment VS can further emphasize the necessity for enrichment of compound databases employed in lead discovery by amplifying the diversity of databases with novel structures.

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

PubMed

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

2017-12-01

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

Investigating different approaches to develop informative priors in hierarchical Bayesian safety performance functions.

PubMed

Yu, Rongjie; Abdel-Aty, Mohamed

2013-07-01

The Bayesian inference method has been frequently adopted to develop safety performance functions. One advantage of the Bayesian inference is that prior information for the independent variables can be included in the inference procedures. However, there are few studies that discussed how to formulate informative priors for the independent variables and evaluated the effects of incorporating informative priors in developing safety performance functions. This paper addresses this deficiency by introducing four approaches of developing informative priors for the independent variables based on historical data and expert experience. Merits of these informative priors have been tested along with two types of Bayesian hierarchical models (Poisson-gamma and Poisson-lognormal models). Deviance information criterion (DIC), R-square values, and coefficients of variance for the estimations were utilized as evaluation measures to select the best model(s). Comparison across the models indicated that the Poisson-gamma model is superior with a better model fit and it is much more robust with the informative priors. Moreover, the two-stage Bayesian updating informative priors provided the best goodness-of-fit and coefficient estimation accuracies. Furthermore, informative priors for the inverse dispersion parameter have also been introduced and tested. Different types of informative priors' effects on the model estimations and goodness-of-fit have been compared and concluded. Finally, based on the results, recommendations for future research topics and study applications have been made. Copyright © 2013 Elsevier Ltd. All rights reserved.

How to interpret the results of medical time series data analysis: Classical statistical approaches versus dynamic Bayesian network modeling.

PubMed

Onisko, Agnieszka; Druzdzel, Marek J; Austin, R Marshall

2016-01-01

Classical statistics is a well-established approach in the analysis of medical data. While the medical community seems to be familiar with the concept of a statistical analysis and its interpretation, the Bayesian approach, argued by many of its proponents to be superior to the classical frequentist approach, is still not well-recognized in the analysis of medical data. The goal of this study is to encourage data analysts to use the Bayesian approach, such as modeling with graphical probabilistic networks, as an insightful alternative to classical statistical analysis of medical data. This paper offers a comparison of two approaches to analysis of medical time series data: (1) classical statistical approach, such as the Kaplan-Meier estimator and the Cox proportional hazards regression model, and (2) dynamic Bayesian network modeling. Our comparison is based on time series cervical cancer screening data collected at Magee-Womens Hospital, University of Pittsburgh Medical Center over 10 years. The main outcomes of our comparison are cervical cancer risk assessments produced by the three approaches. However, our analysis discusses also several aspects of the comparison, such as modeling assumptions, model building, dealing with incomplete data, individualized risk assessment, results interpretation, and model validation. Our study shows that the Bayesian approach is (1) much more flexible in terms of modeling effort, and (2) it offers an individualized risk assessment, which is more cumbersome for classical statistical approaches.

Bayesian design criteria: computation, comparison, and application to a pharmacokinetic and a pharmacodynamic model.

PubMed

Merlé, Y; Mentré, F

1995-02-01

In this paper 3 criteria to design experiments for Bayesian estimation of the parameters of nonlinear models with respect to their parameters, when a prior distribution is available, are presented: the determinant of the Bayesian information matrix, the determinant of the pre-posterior covariance matrix, and the expected information provided by an experiment. A procedure to simplify the computation of these criteria is proposed in the case of continuous prior distributions and is compared with the criterion obtained from a linearization of the model about the mean of the prior distribution for the parameters. This procedure is applied to two models commonly encountered in the area of pharmacokinetics and pharmacodynamics: the one-compartment open model with bolus intravenous single-dose injection and the Emax model. They both involve two parameters. Additive as well as multiplicative gaussian measurement errors are considered with normal prior distributions. Various combinations of the variances of the prior distribution and of the measurement error are studied. Our attention is restricted to designs with limited numbers of measurements (1 or 2 measurements). This situation often occurs in practice when Bayesian estimation is performed. The optimal Bayesian designs that result vary with the variances of the parameter distribution and with the measurement error. The two-point optimal designs sometimes differ from the D-optimal designs for the mean of the prior distribution and may consist of replicating measurements. For the studied cases, the determinant of the Bayesian information matrix and its linearized form lead to the same optimal designs. In some cases, the pre-posterior covariance matrix can be far from its lower bound, namely, the inverse of the Bayesian information matrix, especially for the Emax model and a multiplicative measurement error. The expected information provided by the experiment and the determinant of the pre-posterior covariance matrix generally lead to the same designs except for the Emax model and the multiplicative measurement error. Results show that these criteria can be easily computed and that they could be incorporated in modules for designing experiments.

Expectation propagation for large scale Bayesian inference of non-linear molecular networks from perturbation data.

PubMed

Narimani, Zahra; Beigy, Hamid; Ahmad, Ashar; Masoudi-Nejad, Ali; Fröhlich, Holger

2017-01-01

Inferring the structure of molecular networks from time series protein or gene expression data provides valuable information about the complex biological processes of the cell. Causal network structure inference has been approached using different methods in the past. Most causal network inference techniques, such as Dynamic Bayesian Networks and ordinary differential equations, are limited by their computational complexity and thus make large scale inference infeasible. This is specifically true if a Bayesian framework is applied in order to deal with the unavoidable uncertainty about the correct model. We devise a novel Bayesian network reverse engineering approach using ordinary differential equations with the ability to include non-linearity. Besides modeling arbitrary, possibly combinatorial and time dependent perturbations with unknown targets, one of our main contributions is the use of Expectation Propagation, an algorithm for approximate Bayesian inference over large scale network structures in short computation time. We further explore the possibility of integrating prior knowledge into network inference. We evaluate the proposed model on DREAM4 and DREAM8 data and find it competitive against several state-of-the-art existing network inference methods.

A probabilistic approach to remote compositional analysis of planetary surfaces

USGS Publications Warehouse

Lapotre, Mathieu G.A.; Ehlmann, Bethany L.; Minson, Sarah E.

2017-01-01

Reflected light from planetary surfaces provides information, including mineral/ice compositions and grain sizes, by study of albedo and absorption features as a function of wavelength. However, deconvolving the compositional signal in spectra is complicated by the nonuniqueness of the inverse problem. Trade-offs between mineral abundances and grain sizes in setting reflectance, instrument noise, and systematic errors in the forward model are potential sources of uncertainty, which are often unquantified. Here we adopt a Bayesian implementation of the Hapke model to determine sets of acceptable-fit mineral assemblages, as opposed to single best fit solutions. We quantify errors and uncertainties in mineral abundances and grain sizes that arise from instrument noise, compositional end members, optical constants, and systematic forward model errors for two suites of ternary mixtures (olivine-enstatite-anorthite and olivine-nontronite-basaltic glass) in a series of six experiments in the visible-shortwave infrared (VSWIR) wavelength range. We show that grain sizes are generally poorly constrained from VSWIR spectroscopy. Abundance and grain size trade-offs lead to typical abundance errors of ≤1 wt % (occasionally up to ~5 wt %), while ~3% noise in the data increases errors by up to ~2 wt %. Systematic errors further increase inaccuracies by a factor of 4. Finally, phases with low spectral contrast or inaccurate optical constants can further increase errors. Overall, typical errors in abundance are <10%, but sometimes significantly increase for specific mixtures, prone to abundance/grain-size trade-offs that lead to high unmixing uncertainties. These results highlight the need for probabilistic approaches to remote determination of planetary surface composition.

Reconstructing Constructivism: Causal Models, Bayesian Learning Mechanisms, and the Theory Theory

ERIC Educational Resources Information Center

Gopnik, Alison; Wellman, Henry M.

2012-01-01

We propose a new version of the "theory theory" grounded in the computational framework of probabilistic causal models and Bayesian learning. Probabilistic models allow a constructivist but rigorous and detailed approach to cognitive development. They also explain the learning of both more specific causal hypotheses and more abstract framework…

A Bayesian Multi-Level Factor Analytic Model of Consumer Price Sensitivities across Categories

ERIC Educational Resources Information Center

Duvvuri, Sri Devi; Gruca, Thomas S.

2010-01-01

Identifying price sensitive consumers is an important problem in marketing. We develop a Bayesian multi-level factor analytic model of the covariation among household-level price sensitivities across product categories that are substitutes. Based on a multivariate probit model of category incidence, this framework also allows the researcher to…

Small Sample Properties of Bayesian Multivariate Autoregressive Time Series Models

ERIC Educational Resources Information Center

Price, Larry R.

2012-01-01

The aim of this study was to compare the small sample (N = 1, 3, 5, 10, 15) performance of a Bayesian multivariate vector autoregressive (BVAR-SEM) time series model relative to frequentist power and parameter estimation bias. A multivariate autoregressive model was developed based on correlated autoregressive time series vectors of varying…

Application of Bayesian Maximum Entropy Filter in parameter calibration of groundwater flow model in PingTung Plain

NASA Astrophysics Data System (ADS)

Cheung, Shao-Yong; Lee, Chieh-Han; Yu, Hwa-Lung

2017-04-01

Due to the limited hydrogeological observation data and high levels of uncertainty within, parameter estimation of the groundwater model has been an important issue. There are many methods of parameter estimation, for example, Kalman filter provides a real-time calibration of parameters through measurement of groundwater monitoring wells, related methods such as Extended Kalman Filter and Ensemble Kalman Filter are widely applied in groundwater research. However, Kalman Filter method is limited to linearity. This study propose a novel method, Bayesian Maximum Entropy Filtering, which provides a method that can considers the uncertainty of data in parameter estimation. With this two methods, we can estimate parameter by given hard data (certain) and soft data (uncertain) in the same time. In this study, we use Python and QGIS in groundwater model (MODFLOW) and development of Extended Kalman Filter and Bayesian Maximum Entropy Filtering in Python in parameter estimation. This method may provide a conventional filtering method and also consider the uncertainty of data. This study was conducted through numerical model experiment to explore, combine Bayesian maximum entropy filter and a hypothesis for the architecture of MODFLOW groundwater model numerical estimation. Through the virtual observation wells to simulate and observe the groundwater model periodically. The result showed that considering the uncertainty of data, the Bayesian maximum entropy filter will provide an ideal result of real-time parameters estimation.

Bayesian-MCMC-based parameter estimation of stealth aircraft RCS models

NASA Astrophysics Data System (ADS)

Xia, Wei; Dai, Xiao-Xia; Feng, Yuan

2015-12-01

When modeling a stealth aircraft with low RCS (Radar Cross Section), conventional parameter estimation methods may cause a deviation from the actual distribution, owing to the fact that the characteristic parameters are estimated via directly calculating the statistics of RCS. The Bayesian-Markov Chain Monte Carlo (Bayesian-MCMC) method is introduced herein to estimate the parameters so as to improve the fitting accuracies of fluctuation models. The parameter estimations of the lognormal and the Legendre polynomial models are reformulated in the Bayesian framework. The MCMC algorithm is then adopted to calculate the parameter estimates. Numerical results show that the distribution curves obtained by the proposed method exhibit improved consistence with the actual ones, compared with those fitted by the conventional method. The fitting accuracy could be improved by no less than 25% for both fluctuation models, which implies that the Bayesian-MCMC method might be a good candidate among the optimal parameter estimation methods for stealth aircraft RCS models. Project supported by the National Natural Science Foundation of China (Grant No. 61101173), the National Basic Research Program of China (Grant No. 613206), the National High Technology Research and Development Program of China (Grant No. 2012AA01A308), the State Scholarship Fund by the China Scholarship Council (CSC), and the Oversea Academic Training Funds, and University of Electronic Science and Technology of China (UESTC).

Bayesian regression models outperform partial least squares methods for predicting milk components and technological properties using infrared spectral data.

PubMed

Ferragina, A; de los Campos, G; Vazquez, A I; Cecchinato, A; Bittante, G

2015-11-01

The aim of this study was to assess the performance of Bayesian models commonly used for genomic selection to predict "difficult-to-predict" dairy traits, such as milk fatty acid (FA) expressed as percentage of total fatty acids, and technological properties, such as fresh cheese yield and protein recovery, using Fourier-transform infrared (FTIR) spectral data. Our main hypothesis was that Bayesian models that can estimate shrinkage and perform variable selection may improve our ability to predict FA traits and technological traits above and beyond what can be achieved using the current calibration models (e.g., partial least squares, PLS). To this end, we assessed a series of Bayesian methods and compared their prediction performance with that of PLS. The comparison between models was done using the same sets of data (i.e., same samples, same variability, same spectral treatment) for each trait. Data consisted of 1,264 individual milk samples collected from Brown Swiss cows for which gas chromatographic FA composition, milk coagulation properties, and cheese-yield traits were available. For each sample, 2 spectra in the infrared region from 5,011 to 925 cm(-1) were available and averaged before data analysis. Three Bayesian models: Bayesian ridge regression (Bayes RR), Bayes A, and Bayes B, and 2 reference models: PLS and modified PLS (MPLS) procedures, were used to calibrate equations for each of the traits. The Bayesian models used were implemented in the R package BGLR (http://cran.r-project.org/web/packages/BGLR/index.html), whereas the PLS and MPLS were those implemented in the WinISI II software (Infrasoft International LLC, State College, PA). Prediction accuracy was estimated for each trait and model using 25 replicates of a training-testing validation procedure. Compared with PLS, which is currently the most widely used calibration method, MPLS and the 3 Bayesian methods showed significantly greater prediction accuracy. Accuracy increased in moving from calibration to external validation methods, and in moving from PLS and MPLS to Bayesian methods, particularly Bayes A and Bayes B. The maximum R(2) value of validation was obtained with Bayes B and Bayes A. For the FA, C10:0 (% of each FA on total FA basis) had the highest R(2) (0.75, achieved with Bayes A and Bayes B), and among the technological traits, fresh cheese yield R(2) of 0.82 (achieved with Bayes B). These 2 methods have proven to be useful instruments in shrinking and selecting very informative wavelengths and inferring the structure and functions of the analyzed traits. We conclude that Bayesian models are powerful tools for deriving calibration equations, and, importantly, these equations can be easily developed using existing open-source software. As part of our study, we provide scripts based on the open source R software BGLR, which can be used to train customized prediction equations for other traits or populations. Copyright © 2015 American Dairy Science Association. Published by Elsevier Inc. All rights reserved.

Bayesian stock assessment of Pacific herring in Prince William Sound, Alaska.

PubMed

Muradian, Melissa L; Branch, Trevor A; Moffitt, Steven D; Hulson, Peter-John F

2017-01-01

The Pacific herring (Clupea pallasii) population in Prince William Sound, Alaska crashed in 1993 and has yet to recover, affecting food web dynamics in the Sound and impacting Alaskan communities. To help researchers design and implement the most effective monitoring, management, and recovery programs, a Bayesian assessment of Prince William Sound herring was developed by reformulating the current model used by the Alaska Department of Fish and Game. The Bayesian model estimated pre-fishery spawning biomass of herring age-3 and older in 2013 to be a median of 19,410 mt (95% credibility interval 12,150-31,740 mt), with a 54% probability that biomass in 2013 was below the management limit used to regulate fisheries in Prince William Sound. The main advantages of the Bayesian model are that it can more objectively weight different datasets and provide estimates of uncertainty for model parameters and outputs, unlike the weighted sum-of-squares used in the original model. In addition, the revised model could be used to manage herring stocks with a decision rule that considers both stock status and the uncertainty in stock status.

Bayesian stock assessment of Pacific herring in Prince William Sound, Alaska

PubMed Central

Moffitt, Steven D.; Hulson, Peter-John F.

2017-01-01

The Pacific herring (Clupea pallasii) population in Prince William Sound, Alaska crashed in 1993 and has yet to recover, affecting food web dynamics in the Sound and impacting Alaskan communities. To help researchers design and implement the most effective monitoring, management, and recovery programs, a Bayesian assessment of Prince William Sound herring was developed by reformulating the current model used by the Alaska Department of Fish and Game. The Bayesian model estimated pre-fishery spawning biomass of herring age-3 and older in 2013 to be a median of 19,410 mt (95% credibility interval 12,150–31,740 mt), with a 54% probability that biomass in 2013 was below the management limit used to regulate fisheries in Prince William Sound. The main advantages of the Bayesian model are that it can more objectively weight different datasets and provide estimates of uncertainty for model parameters and outputs, unlike the weighted sum-of-squares used in the original model. In addition, the revised model could be used to manage herring stocks with a decision rule that considers both stock status and the uncertainty in stock status. PMID:28222151

New prior sampling methods for nested sampling - Development and testing

NASA Astrophysics Data System (ADS)

Stokes, Barrie; Tuyl, Frank; Hudson, Irene

2017-06-01

Nested Sampling is a powerful algorithm for fitting models to data in the Bayesian setting, introduced by Skilling [1]. The nested sampling algorithm proceeds by carrying out a series of compressive steps, involving successively nested iso-likelihood boundaries, starting with the full prior distribution of the problem parameters. The "central problem" of nested sampling is to draw at each step a sample from the prior distribution whose likelihood is greater than the current likelihood threshold, i.e., a sample falling inside the current likelihood-restricted region. For both flat and informative priors this ultimately requires uniform sampling restricted to the likelihood-restricted region. We present two new methods of carrying out this sampling step, and illustrate their use with the lighthouse problem [2], a bivariate likelihood used by Gregory [3] and a trivariate Gaussian mixture likelihood. All the algorithm development and testing reported here has been done with Mathematica® [4].

Mitochondrial phylogenomics of Hemiptera reveals adaptive innovations driving the diversification of true bugs

PubMed Central

Li, Hu; Leavengood, John M.; Chapman, Eric G.; Burkhardt, Daniel; Song, Fan; Jiang, Pei; Liu, Jinpeng; Cai, Wanzhi

2017-01-01

Hemiptera, the largest non-holometabolous order of insects, represents approximately 7% of metazoan diversity. With extraordinary life histories and highly specialized morphological adaptations, hemipterans have exploited diverse habitats and food sources through approximately 300 Myr of evolution. To elucidate the phylogeny and evolutionary history of Hemiptera, we carried out the most comprehensive mitogenomics analysis on the richest taxon sampling to date covering all the suborders and infraorders, including 34 newly sequenced and 94 published mitogenomes. With optimized branch length and sequence heterogeneity, Bayesian analyses using a site-heterogeneous mixture model resolved the higher-level hemipteran phylogeny as (Sternorrhyncha, (Auchenorrhyncha, (Coleorrhyncha, Heteroptera))). Ancestral character state reconstruction and divergence time estimation suggest that the success of true bugs (Heteroptera) is probably due to angiosperm coevolution, but key adaptive innovations (e.g. prognathous mouthpart, predatory behaviour, and haemelytron) facilitated multiple independent shifts among diverse feeding habits and multiple independent colonizations of aquatic habitats. PMID:28878063

Multilevel modeling of single-case data: A comparison of maximum likelihood and Bayesian estimation.

PubMed

Moeyaert, Mariola; Rindskopf, David; Onghena, Patrick; Van den Noortgate, Wim

2017-12-01

The focus of this article is to describe Bayesian estimation, including construction of prior distributions, and to compare parameter recovery under the Bayesian framework (using weakly informative priors) and the maximum likelihood (ML) framework in the context of multilevel modeling of single-case experimental data. Bayesian estimation results were found similar to ML estimation results in terms of the treatment effect estimates, regardless of the functional form and degree of information included in the prior specification in the Bayesian framework. In terms of the variance component estimates, both the ML and Bayesian estimation procedures result in biased and less precise variance estimates when the number of participants is small (i.e., 3). By increasing the number of participants to 5 or 7, the relative bias is close to 5% and more precise estimates are obtained for all approaches, except for the inverse-Wishart prior using the identity matrix. When a more informative prior was added, more precise estimates for the fixed effects and random effects were obtained, even when only 3 participants were included. (PsycINFO Database Record (c) 2017 APA, all rights reserved).

An approach to quantifying the efficiency of a Bayesian filter

USDA-ARS?s Scientific Manuscript database

Data assimilation is defined as the Bayesian conditioning of uncertain model simulations on observations for the purpose of reducing uncertainty about model states. Practical data assimilation applications require that simplifying assumptions be made about the prior and posterior state distributions...

Efficient Probabilistic Diagnostics for Electrical Power Systems

NASA Technical Reports Server (NTRS)

Mengshoel, Ole J.; Chavira, Mark; Cascio, Keith; Poll, Scott; Darwiche, Adnan; Uckun, Serdar

2008-01-01

We consider in this work the probabilistic approach to model-based diagnosis when applied to electrical power systems (EPSs). Our probabilistic approach is formally well-founded, as it based on Bayesian networks and arithmetic circuits. We investigate the diagnostic task known as fault isolation, and pay special attention to meeting two of the main challenges . model development and real-time reasoning . often associated with real-world application of model-based diagnosis technologies. To address the challenge of model development, we develop a systematic approach to representing electrical power systems as Bayesian networks, supported by an easy-to-use speci.cation language. To address the real-time reasoning challenge, we compile Bayesian networks into arithmetic circuits. Arithmetic circuit evaluation supports real-time diagnosis by being predictable and fast. In essence, we introduce a high-level EPS speci.cation language from which Bayesian networks that can diagnose multiple simultaneous failures are auto-generated, and we illustrate the feasibility of using arithmetic circuits, compiled from Bayesian networks, for real-time diagnosis on real-world EPSs of interest to NASA. The experimental system is a real-world EPS, namely the Advanced Diagnostic and Prognostic Testbed (ADAPT) located at the NASA Ames Research Center. In experiments with the ADAPT Bayesian network, which currently contains 503 discrete nodes and 579 edges, we .nd high diagnostic accuracy in scenarios where one to three faults, both in components and sensors, were inserted. The time taken to compute the most probable explanation using arithmetic circuits has a small mean of 0.2625 milliseconds and standard deviation of 0.2028 milliseconds. In experiments with data from ADAPT we also show that arithmetic circuit evaluation substantially outperforms joint tree propagation and variable elimination, two alternative algorithms for diagnosis using Bayesian network inference.

Prediction and assimilation of surf-zone processes using a Bayesian network: Part I: Forward models

USGS Publications Warehouse

Plant, Nathaniel G.; Holland, K. Todd

2011-01-01

Prediction of coastal processes, including waves, currents, and sediment transport, can be obtained from a variety of detailed geophysical-process models with many simulations showing significant skill. This capability supports a wide range of research and applied efforts that can benefit from accurate numerical predictions. However, the predictions are only as accurate as the data used to drive the models and, given the large temporal and spatial variability of the surf zone, inaccuracies in data are unavoidable such that useful predictions require corresponding estimates of uncertainty. We demonstrate how a Bayesian-network model can be used to provide accurate predictions of wave-height evolution in the surf zone given very sparse and/or inaccurate boundary-condition data. The approach is based on a formal treatment of a data-assimilation problem that takes advantage of significant reduction of the dimensionality of the model system. We demonstrate that predictions of a detailed geophysical model of the wave evolution are reproduced accurately using a Bayesian approach. In this surf-zone application, forward prediction skill was 83%, and uncertainties in the model inputs were accurately transferred to uncertainty in output variables. We also demonstrate that if modeling uncertainties were not conveyed to the Bayesian network (i.e., perfect data or model were assumed), then overly optimistic prediction uncertainties were computed. More consistent predictions and uncertainties were obtained by including model-parameter errors as a source of input uncertainty. Improved predictions (skill of 90%) were achieved because the Bayesian network simultaneously estimated optimal parameters while predicting wave heights.

Accuracy of dengue clinical diagnosis with and without NS1 antigen rapid test: Comparison between human and Bayesian network model decision.

PubMed

Sa-Ngamuang, Chaitawat; Haddawy, Peter; Luvira, Viravarn; Piyaphanee, Watcharapong; Iamsirithaworn, Sopon; Lawpoolsri, Saranath

2018-06-18

Differentiating dengue patients from other acute febrile illness patients is a great challenge among physicians. Several dengue diagnosis methods are recommended by WHO. The application of specific laboratory tests is still limited due to high cost, lack of equipment, and uncertain validity. Therefore, clinical diagnosis remains a common practice especially in resource limited settings. Bayesian networks have been shown to be a useful tool for diagnostic decision support. This study aimed to construct Bayesian network models using basic demographic, clinical, and laboratory profiles of acute febrile illness patients to diagnose dengue. Data of 397 acute undifferentiated febrile illness patients who visited the fever clinic of the Bangkok Hospital for Tropical Diseases, Thailand, were used for model construction and validation. The two best final models were selected: one with and one without NS1 rapid test result. The diagnostic accuracy of the models was compared with that of physicians on the same set of patients. The Bayesian network models provided good diagnostic accuracy of dengue infection, with ROC AUC of 0.80 and 0.75 for models with and without NS1 rapid test result, respectively. The models had approximately 80% specificity and 70% sensitivity, similar to the diagnostic accuracy of the hospital's fellows in infectious disease. Including information on NS1 rapid test improved the specificity, but reduced the sensitivity, both in model and physician diagnoses. The Bayesian network model developed in this study could be useful to assist physicians in diagnosing dengue, particularly in regions where experienced physicians and laboratory confirmation tests are limited.

Assimilating multi-source uncertainties of a parsimonious conceptual hydrological model using hierarchical Bayesian modeling

Treesearch

Wei Wu; James Clark; James Vose

2010-01-01

Hierarchical Bayesian (HB) modeling allows for multiple sources of uncertainty by factoring complex relationships into conditional distributions that can be used to draw inference and make predictions. We applied an HB model to estimate the parameters and state variables of a parsimonious hydrological model – GR4J – by coherently assimilating the uncertainties from the...

Incorporation of diet information derived from Bayesian stable isotope mixing models into mass-balanced marine ecosystem models: A case study from the Marennes-Oleron Estuary, France

EPA Science Inventory

We investigated the use of output from Bayesian stable isotope mixing models as constraints for a linear inverse food web model of a temperate intertidal seagrass system in the Marennes-Oléron Bay, France. Linear inverse modeling (LIM) is a technique that estimates a complete net...

Prediction of Individual Serum Infliximab Concentrations in Inflammatory Bowel Disease by a Bayesian Dashboard System.

PubMed

Eser, Alexander; Primas, Christian; Reinisch, Sieglinde; Vogelsang, Harald; Novacek, Gottfried; Mould, Diane R; Reinisch, Walter

2018-01-30

Despite a robust exposure-response relationship of infliximab in inflammatory bowel disease (IBD), attempts to adjust dosing to individually predicted serum concentrations of infliximab (SICs) are lacking. Compared with labor-intensive conventional software for pharmacokinetic (PK) modeling (eg, NONMEM) dashboards are easy-to-use programs incorporating complex Bayesian statistics to determine individual pharmacokinetics. We evaluated various infliximab detection assays and the number of samples needed to precisely forecast individual SICs using a Bayesian dashboard. We assessed long-term infliximab retention in patients being dosed concordantly versus discordantly with Bayesian dashboard recommendations. Three hundred eighty-two serum samples from 117 adult IBD patients on infliximab maintenance therapy were analyzed by 3 commercially available assays. Data from each assay was modeled using NONMEM and a Bayesian dashboard. PK parameter precision and residual variability were assessed. Forecast concentrations from both systems were compared with observed concentrations. Infliximab retention was assessed by prediction for dose intensification via Bayesian dashboard versus real-life practice. Forecast precision of SICs varied between detection assays. At least 3 SICs from a reliable assay are needed for an accurate forecast. The Bayesian dashboard performed similarly to NONMEM to predict SICs. Patients dosed concordantly with Bayesian dashboard recommendations had a significantly longer median drug survival than those dosed discordantly (51.5 versus 4.6 months, P < .0001). The Bayesian dashboard helps to assess the diagnostic performance of infliximab detection assays. Three, not single, SICs provide sufficient information for individualized dose adjustment when incorporated into the Bayesian dashboard. Treatment adjusted to forecasted SICs is associated with longer drug retention of infliximab. © 2018, The American College of Clinical Pharmacology.

The accuracy of Genomic Selection in Norwegian red cattle assessed by cross-validation.

PubMed

Luan, Tu; Woolliams, John A; Lien, Sigbjørn; Kent, Matthew; Svendsen, Morten; Meuwissen, Theo H E

2009-11-01

Genomic Selection (GS) is a newly developed tool for the estimation of breeding values for quantitative traits through the use of dense markers covering the whole genome. For a successful application of GS, accuracy of the prediction of genomewide breeding value (GW-EBV) is a key issue to consider. Here we investigated the accuracy and possible bias of GW-EBV prediction, using real bovine SNP genotyping (18,991 SNPs) and phenotypic data of 500 Norwegian Red bulls. The study was performed on milk yield, fat yield, protein yield, first lactation mastitis traits, and calving ease. Three methods, best linear unbiased prediction (G-BLUP), Bayesian statistics (BayesB), and a mixture model approach (MIXTURE), were used to estimate marker effects, and their accuracy and bias were estimated by using cross-validation. The accuracies of the GW-EBV prediction were found to vary widely between 0.12 and 0.62. G-BLUP gave overall the highest accuracy. We observed a strong relationship between the accuracy of the prediction and the heritability of the trait. GW-EBV prediction for production traits with high heritability achieved higher accuracy and also lower bias than health traits with low heritability. To achieve a similar accuracy for the health traits probably more records will be needed.

Spatial distribution of psychotic disorders in an urban area of France: an ecological study.

PubMed

Pignon, Baptiste; Schürhoff, Franck; Baudin, Grégoire; Ferchiou, Aziz; Richard, Jean-Romain; Saba, Ghassen; Leboyer, Marion; Kirkbride, James B; Szöke, Andrei

2016-05-18

Previous analyses of neighbourhood variations of non-affective psychotic disorders (NAPD) have focused mainly on incidence. However, prevalence studies provide important insights on factors associated with disease evolution as well as for healthcare resource allocation. This study aimed to investigate the distribution of prevalent NAPD cases in an urban area in France. The number of cases in each neighbourhood was modelled as a function of potential confounders and ecological variables, namely: migrant density, economic deprivation and social fragmentation. This was modelled using statistical models of increasing complexity: frequentist models (using Poisson and negative binomial regressions), and several Bayesian models. For each model, assumptions validity were checked and compared as to how this fitted to the data, in order to test for possible spatial variation in prevalence. Data showed significant overdispersion (invalidating the Poisson regression model) and residual autocorrelation (suggesting the need to use Bayesian models). The best Bayesian model was Leroux's model (i.e. a model with both strong correlation between neighbouring areas and weaker correlation between areas further apart), with economic deprivation as an explanatory variable (OR = 1.13, 95% CI [1.02-1.25]). In comparison with frequentist methods, the Bayesian model showed a better fit. The number of cases showed non-random spatial distribution and was linked to economic deprivation.

Model averaging, optimal inference, and habit formation

PubMed Central

FitzGerald, Thomas H. B.; Dolan, Raymond J.; Friston, Karl J.

2014-01-01

Postulating that the brain performs approximate Bayesian inference generates principled and empirically testable models of neuronal function—the subject of much current interest in neuroscience and related disciplines. Current formulations address inference and learning under some assumed and particular model. In reality, organisms are often faced with an additional challenge—that of determining which model or models of their environment are the best for guiding behavior. Bayesian model averaging—which says that an agent should weight the predictions of different models according to their evidence—provides a principled way to solve this problem. Importantly, because model evidence is determined by both the accuracy and complexity of the model, optimal inference requires that these be traded off against one another. This means an agent's behavior should show an equivalent balance. We hypothesize that Bayesian model averaging plays an important role in cognition, given that it is both optimal and realizable within a plausible neuronal architecture. We outline model averaging and how it might be implemented, and then explore a number of implications for brain and behavior. In particular, we propose that model averaging can explain a number of apparently suboptimal phenomena within the framework of approximate (bounded) Bayesian inference, focusing particularly upon the relationship between goal-directed and habitual behavior. PMID:25018724

Using SAS PROC MCMC for Item Response Theory Models

PubMed Central

Samonte, Kelli

2014-01-01

Interest in using Bayesian methods for estimating item response theory models has grown at a remarkable rate in recent years. This attentiveness to Bayesian estimation has also inspired a growth in available software such as WinBUGS, R packages, BMIRT, MPLUS, and SAS PROC MCMC. This article intends to provide an accessible overview of Bayesian methods in the context of item response theory to serve as a useful guide for practitioners in estimating and interpreting item response theory (IRT) models. Included is a description of the estimation procedure used by SAS PROC MCMC. Syntax is provided for estimation of both dichotomous and polytomous IRT models, as well as a discussion on how to extend the syntax to accommodate more complex IRT models. PMID:29795834

Application of Bayesian model averaging to measurements of the primordial power spectrum

NASA Astrophysics Data System (ADS)

Parkinson, David; Liddle, Andrew R.

2010-11-01

Cosmological parameter uncertainties are often stated assuming a particular model, neglecting the model uncertainty, even when Bayesian model selection is unable to identify a conclusive best model. Bayesian model averaging is a method for assessing parameter uncertainties in situations where there is also uncertainty in the underlying model. We apply model averaging to the estimation of the parameters associated with the primordial power spectra of curvature and tensor perturbations. We use CosmoNest and MultiNest to compute the model evidences and posteriors, using cosmic microwave data from WMAP, ACBAR, BOOMERanG, and CBI, plus large-scale structure data from the SDSS DR7. We find that the model-averaged 95% credible interval for the spectral index using all of the data is 0.940

PBPK modeling of the cis- and trans-permethrin isomers and their major urinary metabolites in rats

DOE Office of Scientific and Technical Information (OSTI.GOV)

Willemin, Marie-Emilie; Sorbonne University, Université de Technologie de Compiègne, CNRS, UMR 7338 Biomechanics and Bioengineering, Centre de recherche Royallieu CS 60319,60203 Compiègnee Cedex; Desmots, Sophie

2016-03-01

Permethrin, a pyrethroid insecticide, is suspected to induce neuronal and hormonal disturbances in humans. The widespread exposure of the populations has been confirmed by the detection of the urinary metabolites of permethrin in biomonitoring studies. Permethrin is a chiral molecule presenting two forms, the cis and the trans isomers. Because in vitro studies indicated a metabolic interaction between the trans and cis isomers of permethrin, we adapted and calibrated a PBPK model for trans- and cis-permethrin separately in rats. The model also describes the toxicokinetics of three urinary metabolites, cis- and trans-3-(2,2 dichlorovinyl)-2,2-dimethyl-(1-cyclopropane) carboxylic acid (cis- and trans-DCCA), 3-phenoxybenzoic acidmore » (3-PBA) and 4′OH-phenoxybenzoic acid (4′-OH-PBA). In vivo experiments performed in Sprague–Dawley rats were used to calibrate the PBPK model in a Bayesian framework. The model captured well the toxicokinetics of permethrin isomers and their metabolites including the rapid absorption, the accumulation in fat, the extensive metabolism of the parent compounds, and the rapid elimination of metabolites in urine. Average hepatic clearances in rats were estimated to be 2.4 and 5.7 L/h/kg for cis- and trans-permethrin, respectively. High concentrations of the metabolite 4′-OH-PBA were measured in urine compared to cis- and trans-DCCA and 3-PBA. The confidence in the extended PBPK model was then confirmed by good predictions of published experimental data obtained using the isomers mixture. The extended PBPK model could be extrapolated to humans to predict the internal dose of exposure to permethrin from biomonitoring data in urine. - Highlights: • A PBPK model of isomers of permethrin and its urinary metabolites was developed. • A quantitative link was established for permethrin and its biomarkers of exposure. • The bayesian framework allows getting confidence interval on the estimated parameters. • The PBPK model can be extrapolated to human and used in a reverse dosimetry context.« less