Invariant $P$-values for model checking

TL;DR

This paper discusses the development of invariant $P$-values for model checking, aiming to improve the reliability of $P$-values in assessing the fit of statistical models despite ongoing criticisms.

Contribution

It introduces a new framework for defining invariant $P$-values that are more appropriate for model checking, addressing issues of invariance and interpretability.

Findings

Proposes invariant $P$-values for model assessment

Addresses criticisms of traditional $P$-values

Provides a theoretically sound approach for model checking

Abstract

$P$-values have been the focus of considerable criticism based on various considerations. Still, the $P$-value represents one of the most commonly used statistical tools. When assessing the suitability of a single hypothesized distribution, it is not clear that there is a better choice for a measure of surprise. This paper is concerned with the definition of appropriate model-based $P$-values for model checking.