On uncertainty-penalized Bayesian information criterion

TL;DR

This paper demonstrates that the uncertainty-penalized Bayesian information criterion (UBIC) is asymptotically equivalent to the traditional BIC when applied to overparameterized models, clarifying its theoretical properties in PDE model selection.

Contribution

The paper reveals the theoretical equivalence between UBIC and BIC for overparameterized models, providing insights into UBIC's asymptotic behavior.

Findings

UBIC is equivalent to BIC on overparameterized models

Asymptotic properties of UBIC and BIC are identical

UBIC's theoretical foundation aligns with classical BIC theory

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.