Print Email Facebook Twitter A piecewise deterministic scaling limit of lifted Metropolis-Hastings in the Curie-Weiss model Title A piecewise deterministic scaling limit of lifted Metropolis-Hastings in the Curie-Weiss model Author Bierkens, G.N.J.C. (TU Delft Statistics) Roberts, Gareth (University of Warwick) Date 2017 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. Subject Exponential ergodicityMarkov chain Monte CarloPhase transitionPiecewise deterministic Markov processWeak convergence To reference this document use: http://resolver.tudelft.nl/uuid:ecfd3959-35ff-415e-b43c-605610d219a5 DOI https://doi.org/10.1214/16-AAP1217 ISSN 1050-5164 Source Annals of Applied Probability, 27 (2), 846-882 Part of collection Institutional Repository Document type journal article Rights © 2017 G.N.J.C. Bierkens, Gareth Roberts Files PDF AAP1217.pdf 461.78 KB Close viewer /islandora/object/uuid:ecfd3959-35ff-415e-b43c-605610d219a5/datastream/OBJ/view