A Single SMC Sampler on MPI that Outperforms a Single MCMC Sampler

Markov Chain Monte Carlo (MCMC) is a well-established family of algorithms which are primarily used in Bayesian statistics to sample from a target distribution when direct sampling is challenging. Single instances of MCMC methods are widely considered hard to parallelise in a problem-agnostic fashion and hence, unsuitable to meet both constraints of high accuracy and high throughput. Sequential Monte Carlo (SMC) Samplers can address the same problem, but are parallelisable: they share with Particle Filters the same key tasks and bottleneck. Although a rich literature already exists on MCMC methods, SMC Samplers are relatively underexplored, such that no parallel implementation is currently available. In this paper, we first propose a parallel MPI version of the SMC Sampler, including an optimised implementation of the bottleneck, and then compare it with single-core Metropolis-Hastings. The goal is to show that SMC Samplers may be a promising alternative to MCMC methods with high potential for future improvements. We demonstrate that a basic SMC Sampler with 512 cores is up to 85 times faster or up to 8 times more accurate than Metropolis-Hastings.