Bayesian Model Robustness via Disparities

TL;DR

This paper introduces a robust Bayesian inference approach using disparities like Hellinger distance, which improves robustness and efficiency, and extends to hierarchical models, demonstrated on real data.

Contribution

It develops a disparity-based Bayesian inference framework that enhances robustness while maintaining efficiency, extending to various hierarchical models.

Findings

Robust Bayesian estimates with a breakdown point of 1/2.

Disparity-based methods retain efficiency under correct model assumptions.

Successful application to real-world hierarchical data.

Abstract

This paper develops a methodology for robust Bayesian inference through the use of disparities. Metrics such as Hellinger distance and negative exponential disparity have a long history in robust estimation in frequentist inference. We demonstrate that an equivalent robustification may be made in Bayesian inference by substituting an appropriately scaled disparity for the log likelihood to which standard Monte Carlo Markov Chain methods may be applied. A particularly appealing property of minimum-disparity methods is that while they yield robustness with a breakdown point of 1/2, the resulting parameter estimates are also efficient when the posited probabilistic model is correct. We demonstrate that a similar property holds for disparity-based Bayesian inference. We further show that in the Bayesian setting, it is also possible to extend these methods to robustify regression models, random effects distributions and other hierarchical models. The methods are demonstrated on real world data.