Generalized Hierarchical Multivariate CAR Models for Areal Data

• Activity Number: 272
• Type: Contributed
• Date/Time: Tuesday, August 10, 2004 : 2:00 PM to 3:50 PM
• Sponsor: Section on Bayesian Statistical Science
• Author(s): Xiaoping Jin*+ and Brad Carlin
• Companies: University of Minnesota and University of Minnesota
• Keywords: areal data ; conditionally autoregressive (CAR) ; hierarchical Bayesian model ; Markov chain Monte Carlo ; multivariate data ; spatial statistics

Abstract

In the fields of medicine and public health, a common application of spatial areal models is the study of geographical patterns of disease. When we have several measurements recorded at each spatial location (for example, p>2 diseases available from the same population groups or regions), we need to consider multivariate spatial areal models, in order to handle the dependence among the multivariate components, as well as the spatial dependence between sites. We propose a new flexible class of generalized multivariate conditional autoregressive (GMCAR) models for areal data, and show how it enriches the existing MCAR class. Our approach differs from earlier ones in that it directly specifies the joint distribution for a multivariate Markov random-filed (MRF) through specification of simpler conditional and marginal models. This in turn leads to a significant reduction in the computational burden in hierarchical spatial random effect modeling, where posterior summaries are computed using Markov chain Monte Carlo. We compare our approach with existing MCAR models in the literature via simulation, using average mean square error.