# Bayesian Goodness of Fit Tests: A Conversation for David Mumford

arXiv: https://arxiv.org/abs/1803.11251 · HTML: https://mlsanity.com/paper/1803.11251/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 29 Mar 2018.

## Built on by (most cited first, 1 of 1)

- [Markov chain Monte Carlo without evaluating the target: an auxiliary variable approach](https://mlsanity.com/paper/2406.05242/) (2024)

## Abstract (arXiv)

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.