Jump Markov Chains and Rejection-Free Metropolis Algorithms

TL;DR

This paper explores rejection-free Markov jump algorithms to improve the efficiency of Metropolis-based sampling methods, analyzing their properties and demonstrating their advantages in various computational settings.

Contribution

It introduces Markov jump chains as a rejection-free alternative to traditional Metropolis algorithms and shows how they can leverage parallelism for more efficient sampling.

Findings

Jump chains avoid repeated states, increasing efficiency.

Parallelism can be exploited in jump chain algorithms.

Applications include Bayesian models and Ising models.

Abstract

We consider versions of the Metropolis algorithm which avoid the inefficiency of rejections. We first illustrate that a natural Uniform Selection Algorithm might not converge to the correct distribution. We then analyse the use of Markov jump chains which avoid successive repetitions of the same state. After exploring the properties of jump chains, we show how they can exploit parallelism in computer hardware to produce more efficient samples. We apply our results to the Metropolis algorithm, to Parallel Tempering, to a Bayesian model, to a two-dimensional ferromagnetic 4 x 4 Ising model, and to a pseudo-marginal MCMC algorithm.