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Jump Markov chains and rejection-free Metropolis algorithms

Author

Listed:
  • Jeffrey S. Rosenthal

    (University of Toronto)

  • Aki Dote

    (University of Toronto
    Fujitsu Laboratories Ltd.)

  • Keivan Dabiri

    (University of Toronto)

  • Hirotaka Tamura

    (Fujitsu Laboratories Ltd.)

  • Sigeng Chen

    (University of Toronto)

  • Ali Sheikholeslami

    (University of Toronto)

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.

Suggested Citation

  • Jeffrey S. Rosenthal & Aki Dote & Keivan Dabiri & Hirotaka Tamura & Sigeng Chen & Ali Sheikholeslami, 2021. "Jump Markov chains and rejection-free Metropolis algorithms," Computational Statistics, Springer, vol. 36(4), pages 2789-2811, December.
    • Handle: RePEc:spr:compst:v:36:y:2021:i:4:d:10.1007_s00180-021-01095-2
    DOI: 10.1007/s00180-021-01095-2
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    1. repec:dau:papers:123456789/3578 is not listed on IDEAS
    2. A. Doucet & M. K. Pitt & G. Deligiannidis & R. Kohn, 2015. "Efficient implementation of Markov chain Monte Carlo when using an unbiased likelihood estimator," Biometrika, Biometrika Trust, vol. 102(2), pages 295-313.
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