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.
"Invariant P-values for model checking." Ann. Statist. 38 (1) 512 - 525, February 2010. https://doi.org/10.1214/09-AOS727