Bayesian Analysis

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

Matthew J. Keefe, Marco A. R. Ferreira, and Christopher T. Franck

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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.

Article information

Source
Bayesian Anal., Volume 14, Number 1 (2019), 181-209.

Dates
First available in Project Euclid: 19 April 2018

Permanent link to this document
https://projecteuclid.org/euclid.ba/1524124869

Digital Object Identifier
doi:10.1214/18-BA1107

Mathematical Reviews number (MathSciNet)
MR3910043

Zentralblatt MATH identifier
07001980

Subjects
Primary: 62H11: Directional data; spatial statistics 62F15: Bayesian inference
Secondary: 62M30: Spatial processes

Keywords
conditional autoregressive hierarchical models objective prior reference prior spatial statistics

Rights
Creative Commons Attribution 4.0 International License.

Citation

Keefe, Matthew J.; Ferreira, Marco A. R.; Franck, Christopher T. Objective Bayesian Analysis for Gaussian Hierarchical Models with Intrinsic Conditional Autoregressive Priors. Bayesian Anal. 14 (2019), no. 1, 181--209. doi:10.1214/18-BA1107. https://projecteuclid.org/euclid.ba/1524124869


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