Mean-reverting Proposals for the Markov Chain Monte Carlo Algorithms

Abstract

Recently, mean-reversion proposals have become more common in the Monte Carlo literature on Markov chains. We review some of them, such as the (mixed) preconditioned Crank–Nicolson kernel, the Beta-Gamma kernel, and the Chi-square kernel. We also review piecewise deterministic Markov processes used in Monte Carlo methods such as the Bouncy particle sampler and the Zig-zag sampler. Finally, we review the boomerang sampler which has been proposed as a mean-reverting version of the bouncing particle sampler.