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

Journal article (2017)

Authors

G.N.J.C. Bierkens Statistics -

Gareth Roberts University of Warwick

Research Group

Statistics () (TU Delft)

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

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Published Date

2017

Language

English

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Faculty

Electrical Engineering, Mathematics and Computer Science

Department

Delft Institute of Applied Mathematics

Research Group

Statistics

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 n^1/2 for LMH, which should be compared to n for MH. At the critical temperature, the required jump rate equals n^3/4 for LMH and n^3/2 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.

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