Bayesian Semiparametric Hierarchical Empirical Likelihood Spatial Models

TL;DR

This paper introduces a flexible Bayesian hierarchical model using empirical likelihood for spatial data, effectively handling irregular spatial structures and demonstrating superior predictive performance in diverse real-world applications.

Contribution

It develops a novel semiparametric hierarchical empirical likelihood framework tailored for spatial modeling, including irregular lattices and point-referenced data, with demonstrated practical advantages.

Findings

Superior mean squared prediction error over parametric models

Effective modeling of irregular spatial data structures

Validated through simulations and three real datasets

Abstract

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.