Marginally Conditional Autoregressive Distributions for Misaligned Regions

• Activity Number: 659
• Type: Topic Contributed
• Date/Time: Thursday, August 5, 2010 : 10:30 AM to 12:20 PM
• Sponsor: Section on Bayesian Statistical Science
• Author(s): Chester Lee Schmaltz*+ and Dongchu Sun
• Companies: University of Missouri and University of Missouri
• Keywords: Areal Data ; Multivariate ; CAR Model ; Bayesian

Abstract

For many datasets, multiple variables measured on areal units are available. We wish to simultaneously model both the spatial relations within each variable, and the relations between variables. Unlike other approaches to constructing multivariate generalizations of the CAR model, we require that each marginal distribution is an ordinary CAR model. The method is based on transforming each variable to a new variable that is marginally standard normal, but with cross-covariance matrices between each pair proportional to a fixed region "overlap matrix" analogous to an adjacency matrix. This method allows the geographies of each variable differ from each other. The model is then used on the mortality counts for five cancer sites in the state of Missouri and while some advantages are found over the use of five independent CAR models, some problems with prior sensitivity are identified.