On the overestimation of widely applicable Bayesian information criterion

TL;DR

This paper identifies and corrects the overestimation bias in the widely applicable Bayesian information criterion (WAIC), proposing an adjustment that yields more accurate model selection in both regular and singular models.

Contribution

The authors derive an adjustment to WAIC that reduces bias, providing an asymptotically unbiased estimator for the log marginal likelihood in diverse models.

Findings

Adjusted WAIC shows smaller bias in numerical experiments.

The correction improves model selection accuracy.

Applicable to both regular and singular models.

Abstract

A widely applicable Bayesian information criterion (Watanabe, 2013) is applicable for both regular and singular models in the model selection problem. This criterion tends to overestimate the log marginal likelihood. We identify an overestimating term of a widely applicable Bayesian information criterion. Adjustment of the term gives an asymptotically unbiased estimator of the leading two terms of asymptotic expansion of the log marginal likelihood. In numerical experiments on regular and singular models, the adjustment resulted in smaller bias than the original criterion.