On uncertainty-penalized Bayesian information criterion

arXiv:2404.16881v1 Announce Type: new
Abstract: 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.

abstract arxiv bayesian bic criterion cs.lg data data-driven differential differential equation discovery equation information math.st paper regression set show stat.th type uncertainty