Bayesian Benchmarking Small Area Estimation via Entropic Tilting

TL;DR

This paper introduces a Bayesian benchmarking method for small area estimation using entropic tilting, providing a unified framework for point estimates and uncertainty quantification, improving upon ad-hoc existing approaches.

Contribution

It proposes a principled Bayesian approach with entropic tilting for benchmarking, including Monte Carlo methods and analytical solutions for empirical Bayes models.

Findings

Effective in simulation studies

Applicable to empirical data

Provides coherent uncertainty quantification

Abstract

Benchmarking estimation and its risk evaluation is a practically important issue in small area estimation. While Bayesian methods have been widely adopted in small area estimation, existing benchmarking approaches are often ad-hoc, such as projecting each MCMC draw to satisfy the constraint. In contrast, our work provides a unified Bayesian formulation based on entropic tilting, which offers a more principled way to define the benchmarked posterior distribution. This approach yields benchmarked point estimates together with coherent uncertainty quantification. We first introduce general Monte Carlo methods for obtaining a benchmarked posterior under hierarchical Bayesian approaches and then show that the benchmarked posterior under empirical Bayesian frameworks can be obtained in an analytical form for some small area models. We demonstrate the usefulness of the proposed method through simulation and empirical studies.