On uncertainty-penalized Bayesian information criterion

Graduate School of Information Science and Technology Osaka University Osaka, Japan thanasutives@ai.sanken.osaka-u.ac.jp Ken-ichi Fukui SANKEN (The Institute of Scientific and Industrial Research) Osaka University Osaka, Japan fukui@ai.sanken.osaka-u.ac.jp The uncertainty-penalized information criterion (UBIC) has been proposed as a new model-selection criterion for data-driven partial differential equation (PDE) discovery. In this paper, we show that using the UBIC is equivalent to employing the conventional BIC to a set of overparameterized models derived from the potential regression models of different complexity measures. The result indicates that the asymptotic property of the UBIC and BIC holds indifferently.