Bayesian semiparametric hierarchical empirical likelihood spatial models

• Development of an explicitly spatial Bayesian empirical likelihood model.
• Demonstration of improved predictive model performance on three datasets.
• Demonstration of improved predictive performance via simulation.
• Proof of propriety of Moran’s I lattice prior.

We introduce a general hierarchical Bayesian framework that incorporates a flexible nonparametric data model specification through the use of empirical likelihood methodology, which we term semiparametric hierarchical empirical likelihood (SHEL) models. Although general dependence structures can be readily accommodated, we focus on spatial modeling, a relatively underdeveloped area in the empirical likelihood literature. Importantly, the models we develop naturally accommodate spatial association on irregular lattices and irregularly spaced point-referenced data. We illustrate our proposed framework by means of a simulation study and through three real data examples. First, we develop a spatial Fay–Herriot model in the SHEL framework and apply it to the problem of small area estimation in the American Community Survey. Next, we illustrate the SHEL model in the context of areal data (on an irregular lattice) through the North Carolina sudden infant death syndrome (SIDS) dataset. Finally, we analyze a point-referenced dataset from the North American Breeding Bird Survey that considers dove counts for the state of Missouri. In all cases, we demonstrate superior performance of our model, in terms of mean squared prediction error, over standard parametric analyses.