Assigning a value to a power likelihood in a general Bayesian model

TL;DR

This paper explores how to assign a meaningful value to the power parameter in generalized Bayesian models, enhancing robustness when the model may not perfectly reflect reality.

Contribution

It provides a coherent method for specifying the power parameter in Bayesian models to improve robustness against model misspecification.

Findings

Proposes a new approach to set the power parameter coherently.

Enhances robustness of Bayesian inference under model misspecification.

Offers theoretical insights into the interpretation of the power parameter.

Abstract

Bayesian approaches to data analysis and machine learning are widespread and popular as they provide intuitive yet rigorous axioms for learning from data; see Bernardo and Smith (2004) and Bishop (2006). However, this rigour comes with a caveat that the Bayesian model is a precise reflection of Nature. There has been a recent trend to address potential model misspecification by raising the likelihood function to a power, primarily for robustness reasons, though not exclusively. In this paper we provide a coherent specification of the power parameter once the Bayesian model has been specified in the absence of a perfect model.