Objective Bayesian Analysis of Gaussian Markov Random Fields

• Activity Number: 202
• Type: Invited
• Date/Time: Tuesday, August 10, 2004 : 10:30 AM to 12:20 PM
• Sponsor: Section on Bayesian Statistical Science
• Author(s): Victor De Oliveira*+
• Companies: University of Arkansas
• Keywords: Jeffrey's prior ; reference prior ; spatial statistics

Abstract

Gaussian Markov random fields (GMRF) are important families of distributions for the modeling of spatial data that have been widely used in different areas of spatial statistics. GMRFs have been used for the modeling of spatial data, both as models for the prior of latent processes/random effects, and as models for the sampling distribution of the observed data. We consider in this work the latter use of GMRFs. We present an objective Bayesian analysis for the parameters of some classes of GMRFs. Specifically, we compute explicit expressions for the Jeffreys and reference priors, and derive in each case conditions for posterior propriety of the model parameters. By way of a simulation experiment we study the frequentist properties of the Bayesian inferences about the model parameters resulting from the use of these priors, such as frequentist coverage of 95% credible intervals and the mean squared estimation errors. We illustrate the use of the proposed GMRF model for studying the spatial variability of gross domestic product (GDP) over the period 1980-1995 in 138 territorial units of 11 European countries.