Efficient Factor-Analytic Priors for Correlation Matrices

• Activity Number: 298
• Type: Contributed
• Date/Time: Tuesday, August 2, 2011 : 8:30 AM to 10:20 AM
• Sponsor: Section on Bayesian Statistical Science
• Author(s): Jared Murray*+ and Lawrence Carin and David Dunson and Joe Lucas
• Companies: Duke University and Duke University and Duke University and Duke Institute for Genome Sciences and Policy
• Keywords: Bayesian ; Factor analysis ; Correlation matrix ; Parameter expansion ; Data augmentation

Abstract

We introduce a new class of computationally efficient priors for correlation matrices via parameter expansion and data augmentation. Using a factor-analytic representation of the correlation matrix we are able to avoid expensive matrix inversions during MCMC sampling. In contrast with some other parameter-expanded priors our induced prior on the correlation matrix is of known form and readily analyzed, allowing for informative specifications. This prior not only regularizes estimators of the correlation matrix but also provides a decomposition analogous to traditional factor analysis and model-based principal component analysis which is of inferential and exploratory interest on its own.