2017•arXiv (Cornell University)Open access

Forward Event-Chain Monte Carlo: a general rejection-free and irreversible Markov chain simulation method

Manon Michel, Stéphane Sénécal

Abstract

This paper considers Event-Chain Monte Carlo simulation schemes in order to design an original irreversible Markov Chain Monte Carlo (MCMC) algorithm for the sampling of complex statistical models. The functioning principles of MCMC sampling methods are firstly recalled, as well as standard Event-Chain Monte Carlo simulation schemes are described. Then, a Forward Event-Chain Monte Carlo sampling methodology is proposed and introduced. This nonreversible MCMC rejection-free simulation algorithm is tested and run for the sampling of high-dimensional ill-conditioned Gaussian statistical distributions. Numerical experiments demonstrate the efficiency of the proposed approach, compared to standard Event-Chain and standard Monte Carlo sampling methods. Accelerations up to several magnitudes are exhibited.

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Key concepts: Markov chain Monte Carlo, Monte Carlo method, Rejection sampling, Hybrid Monte Carlo, Monte Carlo molecular modeling, Monte Carlo method in statistical physics, Slice sampling, Monte Carlo integration