A piecewise deterministic scaling limit of lifted Metropolis-Hastings in the Curie-Weiss model

Joris Bierkens, Gareth Roberts

Research output: Contribution to JournalArticleAcademicpeer-review

Abstract

In Turitsyn, Chertkov and Vucelja [Phys. D 240 (2011) 410-414] a nonreversible Markov Chain Monte Carlo (MCMC) method on an augmented state space was introduced, here referred to as Lifted Metropolis-Hastings (LMH). A scaling limit of the magnetization process in the Curie-Weiss model is derived for LMH, as well as for Metropolis-Hastings (MH). The required jump rate in the high (supercritical) temperature regime equals n1/2 for LMH, which should be compared to n for MH. At the critical temperature, the required jump rate equals n3/4 for LMH and n3/2 for MH, in agreement with experimental results of Turitsyn, Chertkov and Vucelja (2011). The scaling limit of LMH turns out to be a nonreversible piecewise deterministic exponentially ergodic "zig-zag" Markov process.

Original languageEnglish
Pages (from-to)846-882
Number of pages37
JournalAnnals of Applied Probability
Volume27
Issue number2
DOIs
Publication statusPublished - 1 Apr 2017
Externally publishedYes

Keywords

  • Exponential ergodicity
  • Markov chain Monte Carlo
  • Phase transition
  • Piecewise deterministic Markov process
  • Weak convergence

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