Testing MCMC code
This addresses a practical issue for researchers and practitioners using MCMC in probabilistic modeling, but it is incremental as it focuses on testing methodologies rather than new algorithmic advances.
The paper tackles the problem of debugging and ensuring correctness in Markov Chain Monte Carlo (MCMC) algorithms, which are prone to silent failures, by outlining strategies for testing, including modular coding, unit testing, and integration testing, demonstrated with a Python Gibbs sampling example for a mixture of Gaussians model.
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.