Forward Event-Chain Monte Carlo: Fast Sampling by Randomness Control in Irreversible Markov Chains

Irreversible and rejection-free Monte Carlo methods, recently developed in physics under the name event-chain and known in statistics as piecewise deterministic Monte Carlo (PDMC), have proven to produce clear acceleration over standard Monte Carlo methods, thanks to the reduction of their random-walk behavior. However, while applying such schemes to standard statistical models, one generally needs to introduce an additional randomization for sake of correctness. We propose here a new class of event-chain Monte Carlo methods that reduces this extra-randomization to a bare minimum. We compare the efficiency of this new methodology to standard PDMC and Monte Carlo methods. Accelerations up to several magnitudes and reduced dimensional scalings are exhibited. Supplementary materials for this article are available online.