A Generalized Conditionally Autoregressive (CAR) Model

• Activity Number: 222
• Type: Invited
• Date/Time: Monday, August 10, 2015 : 2:00 PM to 3:50 PM
• Sponsor: ENAR
• Author(s): Veronica J. Berrocal*
• Companies: University of Michigan
• Keywords: Gaussian Markov Random Field ; Conditionally Autoregressive ; Gaussian process ; areal data ; Bayesian inference

Abstract

Spatial areal data is encountered in a broad range of applications. Within the Bayesian framework, this type of data is most commonly analyzed by introducing, in the second stage of a hierarchical model, spatial random effects modeled as a Gaussian Markov random field, specified locally through a conditionally autoregressive (CAR) model (Besag 1974). The key specification in a CAR model is the proximity matrix, W, with entries wij , proximities that encode the strength of association among the various areal units. The most frequently adopted choice for the proximities is to assume that they are binary and based upon some notion of adjacency. In this paper, we propose an extension of the binary adjacency proximities CAR model where the proximities, defined through a suitable transformation of a latent Gaussian process, are random and directional, thus allowing for varying strength of association among an areal unit and its neighbors. Our specification of the proximities allows us to derive distributional properties of the proximities and of the spatial random effects, and leads to tractable Bayesian inference with closed form full conditionals.