Default Bayesian Analysis for Hierarchical Spatial Multivariate Models

• Activity Number: 656
• Type: Topic Contributed
• Date/Time: Thursday, August 5, 2010 : 10:30 AM to 12:20 PM
• Sponsor: Section on Statistics in Epidemiology
• Author(s): Sarat C. Dass*+ and Chae Young Lim and Tapabrata Maiti
• Companies: Michigan State University and Michigan State University and Michigan State University
• Keywords: Generalized linear mixed models ; Conditional autoregressive models ; Default Bayesian analysis ; Health disparity

Abstract

In recent years, multivariate spatial models have been proven to be an effective tool for analyzing spatially related multidimensional data arising from a common underlying spatial process. The present article contributes towards the development of Bayesian inferential methodology for hierarchical spatial multivariate generalized linear mixed models. The two main contributions of this article are the development of a shrinkage-type default prior and innovative computational techniques for the Gibbs sampling implementation. The default prior elicitation is non-informative but results in a proper posterior on the related parameter spaces. This elicitation provides robust inference. In the computational step, a new transformation of the parameters is developed that avoids sampling from restricted domains. The methodology is also extended to missing responses.