p-values for model evaluation

Citations Over TimeTop 18% of 2011 papers

Abstract

Deciding whether a model provides a good description of data is often based on a goodness-of-fit criterion summarized by a $p$-value. Although there is considerable confusion concerning the meaning of $p$-values, leading to their misuse, they are nevertheless of practical importance in common data analysis tasks. We motivate their application using a Bayesian argumentation. We then describe commonly and less commonly known discrepancy variables and how they are used to define $p$-values. The distribution of these are then extracted for examples modeled on typical data analysis tasks, and comments on their usefulness for determining goodness-of-fit are given.

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