Bayesian Model Selection Based on Proper Scoring Rules

TL;DR

This paper introduces a method for Bayesian model selection that uses proper scoring rules instead of marginal likelihood, overcoming issues with improper priors and enabling consistent model identification.

Contribution

It proposes replacing marginal likelihood with homogeneous proper scoring rules for Bayesian model selection, addressing prior scaling issues.

Findings

Proper scoring rules are insensitive to prior scaling constants.

The method enables consistent selection of the true model.

It provides a solution for Bayesian model selection with improper priors.

Abstract

Bayesian model selection with improper priors is not well-defined because of the dependence of the marginal likelihood on the arbitrary scaling constants of the within-model prior densities. We show how this problem can be evaded by replacing marginal log-likelihood by a homogeneous proper scoring rule, which is insensitive to the scaling constants. Suitably applied, this will typically enable consistent selection of the true model.