Running Markov Chain Monte Carlo on Modern Hardware and Software

2024/11/06 by Pavel Sountsov, Colin Carroll, Sountsov, Pavel +3 · 4 voices · 7 citations
Decision Sciences · Mathematics · #Computer science #Machine learning #Markov chain #Markov chain Monte Carlo #Mathematics #Monte Carlo method #Operating system #Simulation Techniques and Applications #Software #Statistics

paper · pdf · doi:10.48550/arxiv.2411.04260

published in arXiv (Cornell University) (Cornell University)

openalex publication_date 2024/11/06 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Today, cheap numerical hardware offers huge amounts of parallel computing power, much of which is used for the task of fitting neural networks to data. Adoption of this hardware to accelerate statistical Markov chain Monte Carlo (MCMC) applications has been much slower. In this chapter, we suggest some patterns for speeding up MCMC workloads using the hardware (e.g., GPUs, TPUs) and software (e.g., PyTorch, JAX) that have driven progress in deep learning over the last fifteen years or so. We offer some intuitions for why these new systems are so well suited to MCMC, and show some examples (with code) where we use them to achieve dramatic speedups over a CPU-based workflow. Finally, we discuss some potential pitfalls to watch out for.

Cited by

• Global fits and the search for new physics: past, present and future
• Sampling on Metric Graphs
• Online and Interactive Bayesian Inference Debugging
• Parallelizing MCMC Across the Sequence Length
• Asymptotically exact variational flows via involutive MCMC kernels
• New affine invariant ensemble samplers and their dimensional scaling
• Faster parallel MCMC: Metropolis adjustment is best served warm

Discussions

• Nice paper from Deepmind on speeding up MCMC using GPUs/TPUs and PyTorch/JAX. Walks through code, motivation, and analysis in a way that might be useful as a more general tutorial for "gpgpu-ifying yo [bsky, 48 points, 2 comments]
• I recently got to work on a fun chapter, and the preprint is now available: arxiv.org/abs/2411.04260 We provide intuitions, examples, and recommendations for running MCMC in a world where GPUs and au [bsky, 16 points, 3 comments]
• @colcarroll.bsky.social and co have this nice review of HMC w modern systems; might have more examples arxiv.org/abs/2411.04260 [bsky, 5 points, 1 comments]
• Running Markov Chain Monte Carlo on Modern Hardware and Software by Sountsov, Carroll, and Hoffman, showing some new performance benchmarks. arxiv.org/abs/2411.04260 [bsky, 5 points, 0 comments]

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