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

Marie Vialaret and Florian Maire ()
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Marie Vialaret: Université Paris-Saclay
Florian Maire: Université de Montréal

Methodology and Computing in Applied Probability, 2020, vol. 22, issue 3, 1349-1387

Abstract: 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.

Keywords: MCMC algorithms; Non-reversible Markov chain; Variance reduction; Convergence rate; 60J22; 60J10; 60J20; 65C05 (search for similar items in EconPapers)
Date: 2020
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DOI: 10.1007/s11009-019-09766-w

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