On uncertainty-penalized Bayesian information criterion
This is an incremental result for researchers in model selection and PDE discovery, clarifying the relationship between UBIC and BIC.
The paper shows that the uncertainty-penalized Bayesian information criterion (UBIC) for PDE discovery is equivalent to applying the conventional BIC to overparameterized models, indicating that their asymptotic properties are the same.
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.