Criteria for Bayesian model choice with application to variable selection

TL;DR

This paper formalizes various criteria for objective Bayesian model selection, introduces a new criterion, and applies them to variable selection in linear models, resulting in a novel prior with desirable properties.

Contribution

It formalizes existing criteria, proposes a new criterion, and develops a new objective prior for variable selection in linear models.

Findings

Introduces a new criterion for Bayesian model choice.

Develops a new objective prior with favorable properties.

Demonstrates application to variable selection in linear models.

Abstract

In objective Bayesian model selection, no single criterion has emerged as dominant in defining objective prior distributions. Indeed, many criteria have been separately proposed and utilized to propose differing prior choices. We first formalize the most general and compelling of the various criteria that have been suggested, together with a new criterion. We then illustrate the potential of these criteria in determining objective model selection priors by considering their application to the problem of variable selection in normal linear models. This results in a new model selection objective prior with a number of compelling properties.