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March 2019 Objective Bayesian Analysis for Gaussian Hierarchical Models with Intrinsic Conditional Autoregressive Priors
Matthew J. Keefe, Marco A. R. Ferreira, Christopher T. Franck
Bayesian Anal. 14(1): 181-209 (March 2019). DOI: 10.1214/18-BA1107

Abstract

Bayesian hierarchical models are commonly used for modeling spatially correlated areal data. However, choosing appropriate prior distributions for the parameters in these models is necessary and sometimes challenging. In particular, an intrinsic conditional autoregressive (CAR) hierarchical component is often used to account for spatial association. Vague proper prior distributions have frequently been used for this type of model, but this requires the careful selection of suitable hyperparameters. In this paper, we derive several objective priors for the Gaussian hierarchical model with an intrinsic CAR component and discuss their properties. 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. 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. Finally, we illustrate our methodology with an application to 2012 housing foreclosure rates in the 88 counties of Ohio.

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Matthew J. Keefe. Marco A. R. Ferreira. Christopher T. Franck. "Objective Bayesian Analysis for Gaussian Hierarchical Models with Intrinsic Conditional Autoregressive Priors." Bayesian Anal. 14 (1) 181 - 209, March 2019. https://doi.org/10.1214/18-BA1107

Information

Published: March 2019
First available in Project Euclid: 19 April 2018

zbMATH: 07001980
MathSciNet: MR3910043
Digital Object Identifier: 10.1214/18-BA1107

Subjects:
Primary: 62F15, 62H11
Secondary: 62M30

JOURNAL ARTICLE
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Vol.14 • No. 1 • March 2019
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