Jump Markov chains and rejection-free Metropolis algorithms

Jeffrey S. Rosenthal (), Aki Dote, Keivan Dabiri, Hirotaka Tamura, Sigeng Chen and Ali Sheikholeslami
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Jeffrey S. Rosenthal: University of Toronto
Aki Dote: University of Toronto
Keivan Dabiri: University of Toronto
Hirotaka Tamura: Fujitsu Laboratories Ltd.
Sigeng Chen: University of Toronto
Ali Sheikholeslami: University of Toronto

Computational Statistics, 2021, vol. 36, issue 4, No 18, 2789-2811

Abstract: 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 $$\times $$ × 4 Ising model, and to a pseudo-marginal MCMC algorithm.

Date: 2021
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DOI: 10.1007/s00180-021-01095-2

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