Bayesian Goodness of Fit Tests: A Conversation for David Mumford

TL;DR

This paper introduces Bayesian goodness of fit tests for practical use, focusing on uniformity testing, and discusses computational challenges and solutions using modern MCMC techniques.

Contribution

It presents a new class of Bayesian goodness of fit tests inspired by Mumford, Wu, and Zhu, addressing the challenge of doubly intractable distributions.

Findings

Modern MCMC techniques can handle the computational challenges.

The paper provides a didactic overview to encourage further research.

Focuses on practical Bayesian testing for uniformity and related problems.

Abstract

The problem of making practical, useful goodness of fit tests in the Bayesian paradigm is largely open. We introduce a class of special cases (testing for uniformity: have the cards been shuffled enough; does my random generator work) and a class of sensible Bayes tests inspired by Mumford, Wu and Zhu. Calculating these tests presents the challenge of 'doubly intractable distributions'. In present circumstances, modern MCMC techniques are up to the challenge. But many other problems remain. Our paper is didactic, we hope to induce the reader to help take it further.