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Bayesian covariance selection in generalized linear mixed models
 Biometrics
, 2006
"... SUMMARY. The generalized linear mixed model (GLMM), which extends the generalized linear model (GLM) to incorporate random effects characterizing heterogeneity among subjects, is widely used in analyzing correlated and longitudinal data. Although there is often interest in identifying the subset of ..."
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Cited by 8 (3 self)
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SUMMARY. The generalized linear mixed model (GLMM), which extends the generalized linear model (GLM) to incorporate random effects characterizing heterogeneity among subjects, is widely used in analyzing correlated and longitudinal data. Although there is often interest in identifying the subset of predictors that have random effects, random effects selection can be challenging, particularly when outcome distributions are nonnormal. This article proposes a fully Bayesian approach to the problem of simultaneous selection of fixed and random effects in GLMMs. Integrating out the random effects induces a covariance structure on the multivariate outcome data, and an important problem which we also consider is that of covariance selection. Our approach relies on variable selectiontype mixture priors for the components in a special LDU decomposition of the random effects covariance. A stochastic search MCMC algorithm is developed, which relies on Gibbs sampling, with Taylor series expansions used to approximate intractable integrals. Simulated data examples are presented for different exponential family distributions, and the approach is applied to discrete survival data from a timetopregnancy study.
The Elicitation of Probabilities A Review of the Statistical Literature
, 2005
"... “We live in an uncertain world, and probability risk assessment deals as directly with that fact as anything we do. Uncertainty arises partly because we are fallible. ..."
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Cited by 3 (0 self)
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“We live in an uncertain world, and probability risk assessment deals as directly with that fact as anything we do. Uncertainty arises partly because we are fallible.
Bayesian Variable Selection and Data Integration for Biological Regulatory Networks
"... • Genes are long sequences of DNA that are transcribed to eventually become a protein • Nearidentical genetic material can lead to many different cell types and species • A critical aspect of cellular function is how genes are regulated and which genes are regulated together Shane T. Jensen 2 March ..."
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Cited by 2 (0 self)
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• Genes are long sequences of DNA that are transcribed to eventually become a protein • Nearidentical genetic material can lead to many different cell types and species • A critical aspect of cellular function is how genes are regulated and which genes are regulated together Shane T. Jensen 2 March 5, 2008Gene Regulatory Networks • Genes are regulated by transcription factor (TF) proteins that bind directly to the DNA sequence near to a gene • The bound protein affects the amount of transcription, thereby affecting the amount of protein produced • The collection of TFs and their target genes is often called the gene regulatory network – Goal is to elucidate regulatory network: which genes are targeted for regulation by a particuler TF?
Specification of prior distributions under model uncertainty
, 2008
"... We consider the specification of prior distributions for Bayesian model comparison, focusing on regressiontype models. We propose a particular joint specification of the prior distribution across models so that sensitivity of posterior model probabilities to the dispersion of prior distributions fo ..."
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We consider the specification of prior distributions for Bayesian model comparison, focusing on regressiontype models. We propose a particular joint specification of the prior distribution across models so that sensitivity of posterior model probabilities to the dispersion of prior distributions for the parameters of individual models (Lindley’s paradox) is diminished. We illustrate the behavior of inferential and predictive posterior quantities in linear and loglinear regressions under our proposed prior densities with a series of simulated and real data examples.
Bayesian Models for Variable Selection that Incorporate Biological Information
"... Variable selection has been the focus of much research in recent years. Bayesian methods have found many successful applications, particularly in situations where the amount of measured variables can be much greater than the number of observations. One such example is the analysis of genomics data. ..."
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Variable selection has been the focus of much research in recent years. Bayesian methods have found many successful applications, particularly in situations where the amount of measured variables can be much greater than the number of observations. One such example is the analysis of genomics data. In this paper we first review Bayesian variable selection methods for linear settings, including regression and classification models. We focus in particular on recent prior constructions that have been used for the analysis of genomic data and briefly describe two novel applications that integrate different sources of biological information into the analysis of experimental data. Next, we address variable selection for a different modeling context, i.e. mixture models. We address both clustering and discriminant analysis settings and conclude with an application to gene expression data for patients affected by leukemia.
Quantifying the Objective Cost of Uncertainty in Complex Dynamical Systems
, 2013
"... Realworld problems often involve complex systems that cannot be perfectly modeled or identified, and many engineering applications aim to design operators that can perform reliably in the presence of such uncertainty. In this paper, we propose a novel Bayesian framework for objectivebased uncertai ..."
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Realworld problems often involve complex systems that cannot be perfectly modeled or identified, and many engineering applications aim to design operators that can perform reliably in the presence of such uncertainty. In this paper, we propose a novel Bayesian framework for objectivebased uncertainty quantification (UQ), which quantifies the uncertainty in a given system based on the expected increase of the operational cost that it induces. This measure of uncertainty, called MOCU (mean objective cost of uncertainty), provides a practical way of quantifying the effect of various types of system uncertainties on the operation of interest. Furthermore, the proposed UQ framework provides a general mathematical basis for designing robust operators, and it can be applied to diverse applications, including robust filtering, classification, and control. We demonstrate the utility and effectiveness of the proposed framework by applying it to the problem of robust structural intervention of gene regulatory networks, an important application in translational genomics. Index Terms Mean objective cost of uncertainty (MOCU), objectivebased uncertainty quantification (UQ), robust operator design, robust network intervention.