A Simple Proof of Posterior Robustness

TL;DR

This paper presents a straightforward proof of Bayesian posterior robustness, introducing a new, practically relevant sufficient condition that simplifies previous complex proofs in the literature.

Contribution

It provides a simple, clear proof of posterior robustness with a novel sufficient condition that enhances practical applicability.

Findings

New simple proof of posterior robustness

Introduction of a practically relevant sufficient condition

Simplification of existing complex proofs

Abstract

Conditions for Bayesian posterior robustness have been examined in recent literature. However, many of the proofs seem to be long and complicated. In this paper, we first summarize some basic lemmas that have been applied implicitly or explicitly. Then, using them, we give a simple proof of posterior robustness. Our sufficient condition is new and practically relevant.