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On the Convergence Time of Some Non-Reversible Markov Chain Monte Carlo Methods

Author

Listed:
  • Marie Vialaret

    (Université Paris-Saclay)

  • Florian Maire

    (Université de Montréal)

Abstract

It is commonly admitted that non-reversible Markov chain Monte Carlo (MCMC) algorithms usually yield more accurate MCMC estimators than their reversible counterparts. In this note, we show that in addition to their variance reduction effect, some non-reversible MCMC algorithms have also the undesirable property to slow down the convergence of the Markov chain. This point, which has been overlooked by the literature, has obvious practical implications. We illustrate this phenomenon for different non-reversible versions of the Metropolis-Hastings algorithm on several discrete state space examples and discuss ways to mitigate the risk of a small asymptotic variance/slow convergence scenario.

Suggested Citation

  • Marie Vialaret & Florian Maire, 2020. "On the Convergence Time of Some Non-Reversible Markov Chain Monte Carlo Methods," Methodology and Computing in Applied Probability, Springer, vol. 22(3), pages 1349-1387, September.
    • Handle: RePEc:spr:metcap:v:22:y:2020:i:3:d:10.1007_s11009-019-09766-w
    DOI: 10.1007/s11009-019-09766-w
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    References listed on IDEAS

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    1. Yuen, Wai Kong, 2000. "Applications of geometric bounds to the convergence rate of Markov chains on," Stochastic Processes and their Applications, Elsevier, vol. 87(1), pages 1-23, May.
    2. Hwang, Chii-Ruey & Normand, Raoul & Wu, Sheng-Jhih, 2015. "Variance reduction for diffusions," Stochastic Processes and their Applications, Elsevier, vol. 125(9), pages 3522-3540.
    3. Chen, Ting-Li & Hwang, Chii-Ruey, 2013. "Accelerating reversible Markov chains," Statistics & Probability Letters, Elsevier, vol. 83(9), pages 1956-1962.
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