Measuring Bayesian Robustness Using R\'enyi Divergence

TL;DR

This paper introduces a method to quantify Bayesian robustness by analyzing the curvature of Renyi divergence between posterior distributions under different prior classes, using simulated and real data.

Contribution

It proposes a novel robustness measure based on Renyi divergence curvature for two classes of contaminated priors, expanding robustness analysis tools.

Findings

Robustness measure effectively distinguishes prior classes.

Method applied successfully to simulated data.

Real data examples demonstrate practical utility.

Abstract

This paper deals with measuring the Bayesian robustness of classes of contaminated priors. Two different classes of priors in the neighborhood of the elicited prior are considered. The first one is the well-known $\epsilon$-contaminated class, while the second one is the geometric mixing class. The proposed measure of robustness is based on computing the curvature of R\'enyi divergence between posterior distributions. Examples are used to illustrate the results by using simulated and real data sets.