Non-reversible Metropolis-Hastings

Joris Bierkens*

*Corresponding author for this work

Research output: Contribution to JournalArticleAcademicpeer-review


The classical Metropolis-Hastings (MH) algorithm can be extended to generate non-reversible Markov chains. This is achieved by means of a modification of the acceptance probability, using the notion of vorticity matrix. The resulting Markov chain is non-reversible. Results from the literature on asymptotic variance, large deviations theory and mixing time are mentioned, and in the case of a large deviations result, adapted, to explain how non-reversible Markov chains have favorable properties in these respects. We provide an application of NRMH in a continuous setting by developing the necessary theory and applying, as first examples, the theory to Gaussian distributions in three and nine dimensions. The empirical autocorrelation and estimated asymptotic variance for NRMH applied to these examples show significant improvement compared to MH with identical stepsize.

Original languageEnglish
Pages (from-to)1213-1228
Number of pages16
JournalStatistics and Computing
Issue number6
Publication statusPublished - 1 Nov 2016
Externally publishedYes


  • Asymptotic variance
  • Langevin sampling
  • Large deviations
  • Markov Chain Monte Carlo
  • MCMC
  • Metropolis-Hastings
  • Non-reversible Markov processes


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