Objective Bayesian Analysis for Gaussian Hierarchical Models with Intrinsic Conditional Autoregressive Priors

• Activity Number: 234 - Bayesian Conditional Models and Updates
• Type: Contributed
• Date/Time: Monday, July 31, 2017 : 2:00 PM to 3:50 PM
• Sponsor: Section on Bayesian Statistical Science
• Author(s): Matthew J. Keefe and Marco Ferreira* and Christopher T. Franck
• Companies: Virginia Tech and Virginia Tech and Virginia Tech Department of Statistics
• Keywords: Conditional autoregressive models ; Hierarchical spatial models ; Objective priors ; Reference priors ; Spatial statistics

Abstract

We derive several objective Bayes priors for Gaussian spatial hierarchical models with an intrinsic CAR prior for spatial random effects. Specifically, we derive for these models two Jeffreys priors and one reference prior. The choice of appropriate prior distributions for the parameters in these hierarchical models is necessary and challenging. Even though vague proper prior distributions have frequently been used for this class of model, they may influence the analysis in unexpected and undesirable ways. We show that the independence Jeffreys and Jeffreys-rule priors result in improper posterior distributions, while the reference prior results in a proper posterior distribution. A simulation study shows that, when compared to priors previously used in the literature, our proposed Bayesian analysis based on the reference prior results in credible intervals with favorable frequentist coverage and interval length, as well as point estimates with smaller mean squared error. Finally, we illustrate our methodology with a spatial analysis of the 2012 housing foreclosure rates in the counties of Ohio.