A Generalized Class of Conditionally Autoregressive (CAR) Models

• Activity Number: 142
• Type: Invited
• Date/Time: Monday, July 30, 2012 : 10:30 AM to 12:20 PM
• Sponsor: Section on Bayesian Statistical Science
• Author(s): Veronica J Berrocal*+ and Alan Gelfand
• Companies: University of Michigan and Duke University
• Keywords: Conditionally Autoregressive model ; spatial random effects ; latent process ; Gaussian process ; areal data

Abstract

Areal or lattice data is usually analyzed by specifying a sampling model for the data that introduces spatial random effects provided with a conditionally autoregressive (CAR) prior. In a CAR specification the weights used to derive the full conditionals are constant over space and fixed a priori to be either binary or inversely proportional to the distances among subregions/cells. In this paper, we propose a generalized class of CAR models where the weights are non-constant and are random variables obtained by appropriately transforming a latent Gaussian process. The resulting class of CAR models is flexible, allows for non-stationarity and generalizes the class of fixed-weight CAR models, which arises as a special case. Marginal properties of the weights and of the spatial random effects can be derived. As an illustration we present applications in image restoration and disease mapping.