Evaluation of spatial Bayesian Empirical Likelihood models in analysis of small area data

Area of Science:

• Spatial statistics
• Bayesian inference
• Small area estimation

Background:

• Bayesian empirical likelihood (BEL) models are gaining traction as flexible alternatives to parametric models.
• Their application to spatial data analysis, particularly for small area estimation, is a recent development.

Purpose of the Study:

• To develop and evaluate spatial Bayesian empirical likelihood (BEL) models for small area estimation.
• To compare the performance of these new models against parametric spatial models and existing BEL models with different priors.

Main Methods:

• Development of spatial BEL models incorporating Conditional Autoregressive (CAR) priors (BYM and Leroux).
• Comparison with parametric spatial models and BEL models using independent Gaussian and generalized Moran basis priors.
• Application to benchmark spatial datasets, simulation studies, and COVID-19 data.

Main Results:

• Spatial BEL models demonstrate promising capabilities for uncovering new insights in spatial data.
• The proposed spatial BEL models with CAR priors outperform parametric spatial models, especially when distributional assumptions are violated.
• These models provide a robust framework for small area estimation with spatial dependencies.

Conclusions:

• Spatial BEL models, particularly those utilizing CAR priors, represent a significant advancement in spatial data analysis for small area estimation.
• They offer a valuable tool for situations where traditional parametric assumptions may not hold.
• Further research into BEL models can yield deeper understanding of complex spatial phenomena.