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15
Default prior distributions and efficient posterior computation in Bayesian factor analysis
 Journal of Computational and Graphical Statistics
, 2009
"... Factor analytic models are widely used in social sciences. These models have also proven useful for sparse modeling of the covariance structure in multidimensional data. Normal prior distributions for factor loadings and inverse gamma prior distributions for residual variances are a popular choice b ..."
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Cited by 28 (6 self)
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Factor analytic models are widely used in social sciences. These models have also proven useful for sparse modeling of the covariance structure in multidimensional data. Normal prior distributions for factor loadings and inverse gamma prior distributions for residual variances are a popular choice because of their conditionally conjugate form. However, such prior distributions require elicitation of many hyperparameters and tend to result in poorly behaved Gibbs samplers. In addition, one must choose an informative specification, as high variance prior distributions face problems due to impropriety of the posterior distribution. This article proposes a default, heavy tailed prior distribution specification, which is induced through parameter expansion while facilitating efficient posterior computation. We also develop an approach to allow uncertainty in the number of factors. The methods are illustrated through simulated examples and epidemiology and toxicology applications.
Default Priors and Efficient Posterior Computation in Bayesian Factor Analysis
"... Abstract. Factor analytic models are widely used in social sciences. These models have also proven useful for sparse modeling of the covariance structure in multidimensional data. Normal priors for factor loadings and inverse gamma priors for residual variances are a popular choice because of their ..."
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Cited by 5 (2 self)
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Abstract. Factor analytic models are widely used in social sciences. These models have also proven useful for sparse modeling of the covariance structure in multidimensional data. Normal priors for factor loadings and inverse gamma priors for residual variances are a popular choice because of their conditionally conjugate form. However, such priors require elicitation of many hyperparameters and tend to result in poorly behaved Gibbs samplers. In addition, one must choose an informative specification, as high variance priors face problems due to impropriety of the posterior. This article proposes a default, heavy tailed prior specification, which is induced through parameter expansion while facilitating efficient posterior computation. We also develop an approach to allow uncertainty in the number of factors. The methods are illustrated through simulated examples and epidemiology and toxicology applications.
Parallel multivariate slice sampling
, 2009
"... Slice sampling provides an easily implemented method for constructing a Markov chain Monte Carlo (MCMC) algorithm. However, slice sampling has two major drawbacks: (i) it requires repeated evaluation of likelihoods for each update, which can make it impractical when evaluations are expensive or as t ..."
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Cited by 5 (0 self)
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Slice sampling provides an easily implemented method for constructing a Markov chain Monte Carlo (MCMC) algorithm. However, slice sampling has two major drawbacks: (i) it requires repeated evaluation of likelihoods for each update, which can make it impractical when evaluations are expensive or as the number of evaluations grows (geometrically) with the dimension of the slice sampler, and (ii) since it can be challenging to construct multivariate updates, the updates are typically univariate, which often results in slow mixing samplers. We propose an approach to multivariate slice sampling that naturally lends itself to a parallel implementation. Our approach takes advantage of recent advances in computer architectures, for instance, the newest generation of graphics cards can execute roughly 30, 000 threads simultaneously. We demonstrate that it is possible to construct a multivariate slice sampler that has good mixing properties and is efficient in terms of computing time. The contributions of this article are therefore twofold. We study approaches for constructing a multivariate slice sampler, and we show how parallel computing can be useful for making MCMC algorithms computationally efficient. We study various implementations of our algorithm in the context of real and simulated data. 1
Identification and quantification of metabolites in (1)H NMR spectra by Bayesian model selection. Bioinformatics
"... Motivation: Nuclear Magnetic Resonance (NMR) spectroscopy is widely used for highthroughput characterization of metabolites in complex biological mixtures. However, accurate interpretation of the spectra in terms of identities and abundances of metabolites can be challenging, in particular in crowd ..."
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Motivation: Nuclear Magnetic Resonance (NMR) spectroscopy is widely used for highthroughput characterization of metabolites in complex biological mixtures. However, accurate interpretation of the spectra in terms of identities and abundances of metabolites can be challenging, in particular in crowded regions with heavy peak overlap. Although a number of computational approaches for this task have recently been proposed, they are not entirely satisfactory in either accuracy or extent of automation. Results: We introduce a probabilistic approach Bayesian Quantification (BQuant), for fully automated databasebased identification and quantification of metabolites in local regions of 1H NMR spectra. The approach represents the spectra as mixtures of reference profiles from a database, and infers the identities and the abundances of metabolites by Bayesian model selection. We show using a simulated dataset, a spikein experiment, and a metabolomic investigation of plasma samples that BQuant outperforms the available automated alternatives in accuracy for both identification and quantification. Availability: The R package BQuant is available at:
Consistent highdimensional Bayesian variable selection via penalized credible regions
, 2012
"... Consistent highdimensional Bayesian variable selection via penalized credible regions For highdimensional data, particularly when the number of predictors greatly exceeds the sample size, selection of relevant predictors for regression is a challenging problem. Methods such as sure screening, for ..."
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Consistent highdimensional Bayesian variable selection via penalized credible regions For highdimensional data, particularly when the number of predictors greatly exceeds the sample size, selection of relevant predictors for regression is a challenging problem. Methods such as sure screening, forward selection, or penalized regressions are commonly used. Bayesian variable selection methods place prior distributions on the parameters along with a prior over model space, or equivalently, a mixture prior on the parameters having mass at zero. Since exhaustive enumeration is not feasible, posterior model probabilities are often obtained via long MCMC runs. The chosen model can depend heavily on various choices for priors and also posterior thresholds. Alternatively, we propose a conjugate prior only on the full model parameters and use sparse solutions within posterior credible regions to perform selection. These posterior credible regions often have closedform representations, and it is shown that these sparse solutions can be computed via existing algorithms. The approach is shown to outperform common methods in the highdimensional setting, particularly under correlation. By searching for a sparse solution within a joint credible region, consistent model selection is established. Furthermore, it is shown that, under certain conditions, the use of marginal credible intervals can give consistent selection up to the case where the dimension grows exponentially in the sample size. The proposed approach successfully accomplishes variable selection in the highdimensional setting, while avoiding pitfalls that plague typical Bayesian variable selection methods.
Momentbased method for random effects selection in linear mixed models. Stat Sin 2012;22:1539–62
"... Abstract: The selection of random effects in linear mixed models is an important yet challenging problem in practice. We propose a robust and unified framework for automatically selecting random effects and estimating covariance components in linear mixed models. A momentbased loss function is fir ..."
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Abstract: The selection of random effects in linear mixed models is an important yet challenging problem in practice. We propose a robust and unified framework for automatically selecting random effects and estimating covariance components in linear mixed models. A momentbased loss function is first constructed for estimating the covariance matrix of random effects. Two types of shrinkage penalties, a hard thresholding operator and a new sandwichtype softthresholding penalty, are then imposed for sparse estimation and random effects selection. Compared with existing approaches, the new procedure does not require any distributional assumption on the random effects and error terms. We establish the asymptotic properties of the resulting estimator in terms of its consistency in both random effects selection and variance component estimation. Optimization strategies are suggested to tackle the computational challenges involved in estimating the sparse variancecovariance matrix. Furthermore, we extend the procedure to incorporate the selection of fixed effects as well. Numerical results show the promising performance of the new approach in selecting both random and fixed effects, and consequently, improving the efficiency of estimating model parameters. Finally, we apply the approach to a data set from the Amsterdam Growth and Health study.
CRITERIA FOR GENERALIZED LINEAR MODEL SELECTION BASED ON KULLBACK’S SYMMETRIC DIVERGENCE
, 2011
"... Criteria for generalized linear model selection based on Kullback's symmetric divergence ..."
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Criteria for generalized linear model selection based on Kullback's symmetric divergence
BAYESIAN METHODS TO IMPUTE MISSING COVARIATES FOR CAUSAL INFERENCE AND MODEL SELECTION
, 2008
"... This thesis presents new approaches to deal with missing covariate data in two situations; matching in observational studies and model selection for generalized linear models. In observational studies, inferences about treatment effects are often affected by confounding covariates. Analysts can redu ..."
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This thesis presents new approaches to deal with missing covariate data in two situations; matching in observational studies and model selection for generalized linear models. In observational studies, inferences about treatment effects are often affected by confounding covariates. Analysts can reduce bias due to differences in control and treated units ’ observed covariates using propensity score matching, which results in a matched control group with similar characteristics to the treated group. Propensity scores are typically estimated from the data using a logistic regression. When covariates are partially observed, missing values can be filled in using multiple imputation. Analysts can estimate propensity scores from the imputed data sets to find a matched control set. Typically, in observational studies, covariates are spread thinly over a large space. It is not always clear what an appropriate imputation model for the missing data should be. Implausible imputations can influence the matches selected and hence the estimate of the treatment effect. In propensity score matching, units tend to be selected from among those lying in the treated units ’ covariate space.
Bayesian Variable Selection for Latent Class Models
, 2010
"... In this article we develop a latent class model with class probabilities that depend on subjectspecific covariates. One of our major goals is to identify important predictors of latent classes. We consider methodology that allows estimation of latent classes while allowing for variable selection un ..."
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In this article we develop a latent class model with class probabilities that depend on subjectspecific covariates. One of our major goals is to identify important predictors of latent classes. We consider methodology that allows estimation of latent classes while allowing for variable selection uncertainty. We propose a Bayesian variable selection approach and implement a stochastic search Gibbs sampler for posterior computation to obtain model averaged estimates of quantities of interest such as marginal inclusion probabilities of predictors. Our methods are illustrated through simulation studies and application to data on weight gain during pregnancy, where it is of interest to identify important predictors of latent weight gain classes.