Achieving Accurate Computation in Bayesian Scale-Usage Models

• Activity Number: 302
• Type: Contributed
• Date/Time: Tuesday, August 3, 2010 : 8:30 AM to 10:20 AM
• Sponsor: Section on Bayesian Statistical Science
• Author(s): Chris Hans*+ and Greg Allenby and Peter F. Craigmile and Ju Hee Lee and Steven MacEachern and Xinyi Xu
• Companies: The Ohio State University and The Ohio State University and The Ohio State University and The Ohio State University and The Ohio State University and The Ohio State University
• Keywords: approximate transition kernel ; convergence rate ; limiting distribution ; MCMC ; multivariate ordinal probit ; truncated multivariate normal

Abstract

A common modeling approach for data collected on discrete scales is to introduce continuous latent variables linked to the observations via a censoring mechanism. Bayesian approaches typically use data augmentation to simplify analysis, avoiding direct evaluation of the likelihood. However, if not carefully implemented, the cost of data augmentation is that Markov chain mixing can be severely degraded. Motivated by the need to consider complex models where the latent variables are not independently distributed, we introduce a covariance decomposition for the analysis of discrete data models with multivariate normal latent variables. Our decomposition results in an MCMC algorithm that only requires univariate normal integrals. We provide theoretical and practical guidance for choosing a good decomposition and present an illustration that demonstrates the effectiveness of the approach.