Predictive performance of power posteriors

TL;DR

This paper investigates how tempering likelihoods affects posterior predictions, showing that in large samples, tempering does not influence predictive performance despite its impact in small samples.

Contribution

It provides a formal analysis demonstrating that tempering likelihoods does not affect posterior predictions in moderate-to-large samples.

Findings

Tempering impacts predictive performance in small samples.

In large samples, tempering does not affect posterior predictions.

Formal proof supporting the insensitivity of predictions to tempering in large samples.

Abstract

We analyse the impact of using tempered likelihoods in the production of posterior predictions. While the choice of temperature has an impact on predictive performance in small samples, we formally show that in moderate-to-large samples, tempering does not impact posterior predictions.