Generalization of Jeffreys' divergence based priors for Bayesian hypothesis testing

TL;DR

This paper introduces divergence-based priors for Bayesian hypothesis testing that are simple, consistent, and applicable to complex models, extending Jeffreys' divergence concepts for broader use.

Contribution

It proposes divergence-based priors with desirable properties, including consistency and applicability to irregular and mixture models, and provides computational methods for Bayes factors.

Findings

DB priors are simple and have desirable properties.

They reproduce Jeffreys-Zellner-Siow priors in normal models.

They are well-defined for irregular and mixture models.

Abstract

In this paper we introduce objective proper prior distributions for hypothesis testing and model selection based on measures of divergence between the competing models; we call them divergence based (DB) priors. DB priors have simple forms and desirable properties, like information (finite sample) consistency; often, they are similar to other existing proposals like the intrinsic priors; moreover, in normal linear models scenarios, they exactly reproduce Jeffreys-Zellner-Siow priors. Most importantly, in challenging scenarios such as irregular models and mixture models, the DB priors are well defined and very reasonable, while alternative proposals are not. We derive approximations to the DB priors as well as MCMC and asymptotic expressions for the associated Bayes factors.