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Default Prior Distributions 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 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. Data sets and computer code used in this article are available online.

SUBMITTER: Ghosh J

PROVIDER: S-EPMC3755784 | biostudies-literature | 2009 Jun

REPOSITORIES: biostudies-literature

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Default Prior Distributions and Efficient Posterior Computation in Bayesian Factor Analysis.

Ghosh Joyee J Dunson David B DB

Journal of computational and graphical statistics : a joint publication of American Statistical Association, Institute of Mathematical Statistics, Interface Foundation of North America 20090601 2

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 c ...[more]

PMID: 23997568

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Dataset Information

Default Prior Distributions and Efficient Posterior Computation in Bayesian Factor Analysis.

Publications

Default Prior Distributions and Efficient Posterior Computation in Bayesian Factor Analysis.

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