Abstract

Co-author: Doug VanDerwerken (Duke University)

Markov chain Monte Carlo is an inherently serial algorithm. Although the likelihood calculations for individual steps can sometimes be parallelized, the serial evolution of the process is widely viewed as incompatible with parallization, offering no speedup for sampling algorithms which require large numbers of iterations to converge to equilibrium. We provide a methodology for parallelizing Markov chain Monte Carlo across large numbers of independent, asynchronous processors. The method is originally motivated by sampling multimodal target distributions, where we see an exponential speed-up in running time. However we show that the approach is general purpose and applicable to all Markov chain Monte Carlo simulations, and demonstrate speed-ups proportional to the number of available processors on slowly mixing chains with unimodal target distributions. The approach is simple and easy to implement, and suggests additional directions for further research.