Running Markov Chain Monte Carlo on Modern Hardware and Software

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.