Title: Objective Bayesian analysis for Gaussian hierarchical models with intrinsic conditional autoregressive priors
Authors: Matthew Keefe - Disney (United States)
Erica Porter - Virginia Tech Department of Statistics (United States)
Marco Ferreira - Virginia Tech (United States)
Christopher Franck - Virginia Tech (United States) [presenting]
Abstract: Bayesian hierarchical models are commonly used for modeling spatially correlated areal data. Vague proper prior distributions have frequently been used for this type of model, which requires the careful selection of suitable hyperparameters. We propose a reference prior for hierarchical models with intrinsic conditional autoregressive spatial random effects. We present results from a simulation study that compares frequentist properties of Bayesian procedures that use several competing priors, including the derived reference prior. We demonstrate that using the reference prior results in favorable coverage, interval length, and mean squared error. Thus, the reference prior is a convenient automatic approach for the analysis of spatially correlated areal data that exhibits favorable inferential properties. We illustrate our methodology with an application to 2012 housing foreclosure rates in the 88 counties of Ohio. Finally, we share open-source computational resources available to everyday practitioners for fitting hierarchical models with intrinsic conditional autoregressive spatial random effects.