A Robust Bayesian Exponentially Tilted Empirical Likelihood Method

TL;DR

This paper introduces a robust Bayesian method based on exponentially tilted empirical likelihood to accurately analyze moment condition models in the presence of outliers, ensuring reliable inference.

Contribution

It develops a new robust BETEL (RBETEL) approach that effectively handles outliers in moment condition models, extending existing Bayesian empirical likelihood methods.

Findings

RBETEL provides reliable posterior inference despite outliers

Simulation shows RBETEL outperforms traditional methods with contaminated data

Empirical application demonstrates practical utility in biological data analysis

Abstract

This paper proposes a new Bayesian approach for analysing moment condition models in the situation where the data may be contaminated by outliers. The approach builds upon the foundations developed by Schennach (2005) who proposed the Bayesian exponentially tilted empirical likelihood (BETEL) method, justified by the fact that an empirical likelihood (EL) can be interpreted as the nonparametric limit of a Bayesian procedure when the implied probabilities are obtained from maximizing entropy subject to some given moment constraints. Considering the impact that outliers are thought to have on the estimation of population moments, we develop a new robust BETEL (RBETEL) inferential methodology to deal with this potential problem. We show how the BETEL methods are linked to the recent work of Bissiri, Holmes and Walker (2016) who propose a general framework to update prior belief via a loss function. A controlled simulation experiment is conducted to investigate the performance of the RBETEL method. We find that the proposed methodology produces reliable posterior inference for the fundamental relationships that are embedded in the majority of the data, even when outliers are present. The method is also illustrated in an empirical study relating brain weight to body weight using a dataset containing sixty-five different land animal species.