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Abstract:
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Bayesian hierarchical models are commonly used for modeling spatially correlated areal data. However, choosing appropriate prior distributions for the parameters in these models can be challenging. In particular, an improper 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 talk, we derive several objective priors for the Gaussian hierarhical model with an improper CAR component and discuss their properties. We show that the Jeffreys rule and independence Jeffreys priors result in improper posterior distributions, while the reference prior results in a proper posterior distribution. We present results from a simulation study that compare frequentist properties of Bayesian procedures that use several competing priors. We demonstrate that the reference prior results in favorable coverage, interval length, and mean squared error. Finally, we illustrate our methodology with an application to 2012 foreclosure rates in the 67 counties of Pennsylvania.
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