Testing MCMC code

TL;DR

This paper discusses strategies for testing the correctness of MCMC algorithms, emphasizing modular code design and testing methods, demonstrated through a Python Gibbs sampling example.

Contribution

It introduces a modular testing framework for MCMC algorithms, combining unit and integration tests, with practical implementation guidance.

Findings

Modular code improves testability of MCMC algorithms

Unit and integration testing strategies are effective for debugging

Python example demonstrates practical testing approach

Abstract

Markov Chain Monte Carlo (MCMC) algorithms are a workhorse of probabilistic modeling and inference, but are difficult to debug, and are prone to silent failure if implemented naively. We outline several strategies for testing the correctness of MCMC algorithms. Specifically, we advocate writing code in a modular way, where conditional probability calculations are kept separate from the logic of the sampler. We discuss strategies for both unit testing and integration testing. As a running example, we show how a Python implementation of Gibbs sampling for a mixture of Gaussians model can be tested.