  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.
