Conditioning on posterior samples for flexible frequentist goodness-of-fit testing

原文摘要

Summary Tests of goodness of fit are used in nearly every domain where statistics is applied. One powerful and flexible approach is to sample artificial datasets that are exchangeable with the real data under the null hypothesis (but not under the alternative), as this allows the analyst to conduct a valid test using any test statistic they desire. Such sampling is typically done by conditioning on either an exact or an approximate sufficient statistic, but existing methods for doing so have significant limitations, which either preclude their use or substantially reduce their power or computational tractability for many important models. In this article, we propose to condition on samples from a Bayesian posterior distribution, which constitute a very different type of approximate sufficient statistic than those considered in previous work. Our approach, termed approximately co-sufficient sampling via Bayes, considerably expands the scope of thisflexible type of goodness-of-fit testing. We prove the approximate validity of the resulting test and demonstrate its utility on three common null models to which no existing methods apply, as well as its superior performance on models to which existing methods do apply.

摘要来源：Crossref