General Robust Bayes Pseudo-Posterior: Exponential Convergence results with Applications

TL;DR

This paper introduces a robust pseudo-posterior Bayesian method with proven exponential convergence, enhancing inference reliability under data contamination and model misspecification across various models.

Contribution

It proposes a new general formulation of a Bayes pseudo-posterior with exponential convergence guarantees, applicable to diverse parametric models and regression settings.

Findings

Proves exponential convergence of the pseudo-posterior and estimators.

Demonstrates robustness against data contamination and model misspecification.

Provides applications to stationary and non-homogeneous models.

Abstract

Although Bayesian inference is an immensely popular paradigm among a large segment of scientists including statisticians, most applications consider objective priors and need critical investigations (Efron, 2013, Science). While it has several optimal properties, a major drawback of Bayesian inference is the lack of robustness against data contamination and model misspecification, which becomes pernicious in the use of objective priors. This paper presents the general formulation of a Bayes pseudo-posterior distribution yielding robust inference. Exponential convergence results related to the new pseudo-posterior and the corresponding Bayes estimators are established under the general parametric set-up and illustrations are provided for the independent stationary as well as non-homogeneous models. Several additional details and properties of the procedure are described, including the estimation under fixed-design regression models.