On the overestimation of widely applicable Bayesian information criterion
This work addresses a specific statistical issue for researchers using WBIC, offering an incremental improvement to correct bias in model selection.
The paper tackled the overestimation problem of the widely applicable Bayesian information criterion (WBIC) in model selection, identifying and adjusting an overestimating term to produce an asymptotically unbiased estimator that reduced bias in numerical experiments on both regular and singular models.
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.