# On the overestimation of widely applicable Bayesian information criterion

arXiv: https://arxiv.org/abs/1908.10572 · HTML: https://mlsanity.com/paper/1908.10572/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 28 Aug 2019.

## Built on by (most cited first, 4 of 4)

- [The Local Learning Coefficient: A Singularity-Aware Complexity Measure](https://mlsanity.com/paper/2308.12108/) (2023)
- [Estimating the Local Learning Coefficient at Scale](https://mlsanity.com/paper/2402.03698/) (2024)
- [Learning under Singularity: An Information Criterion improving WBIC and sBIC](https://mlsanity.com/paper/2402.12762/) (2024)
- [An Asymptotic Equation Linking WAIC and WBIC in Singular Models](https://mlsanity.com/paper/2505.13902/) (2025)

## Abstract (arXiv)

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.