A Custom Precision Based Architecture for Accelerating Parallel Tempering MCMC on FPGAs without Introducing Sampling Error

Markov Chain Monte Carlo (MCMC) is a method used to draw samples from probability distributions in order to estimate - otherwise intractable - integrals. When the distribution is complex, simple MCMC becomes inefficient and advanced, computationally intensive MCMC methods are employed to make sampling possible. This work proposes a novel streaming FPGA architecture to accelerate Parallel Tempering, a widely adopted MCMC method designed to sample from multimodal distributions. The proposed architecture demonstrates how custom precision can be intelligently employed without introducing sampling errors, in order to save resources and increase the sampling throughg put. Speedups of up to two orders of magnitude compared to software and 1.53x-76.88x compared to a GPGPU implementation are achieved when performing Bayesian inference for a mixture model.