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A piecewise deterministic scaling limit of Lifted Metropolis-Hastings in the Curie-Weiss model
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Bierkens, Joris and Roberts, Gareth O. (2017) A piecewise deterministic scaling limit of Lifted Metropolis-Hastings in the Curie-Weiss model. Annals of Applied Probability, 27 (2). pp. 846-882. doi:10.1214/16-AAP1217 ISSN 1050-5164.
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Official URL: https://doi.org/10.1214/16-AAP1217
Abstract
In Turitsyn, Chertkov and Vucelja (2011) a non-reversible Markov Chain Monte Carlo (MCMC) 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 non-reversible piecewise deterministic exponentially ergodic ‘zig-zag’ Markov process.
| Item Type: | Journal Article | ||||||||
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| Divisions: | Faculty of Science, Engineering and Medicine > Science > Statistics | ||||||||
| Journal or Publication Title: | Annals of Applied Probability | ||||||||
| Publisher: | Institute of Mathematical Statistics | ||||||||
| ISSN: | 1050-5164 | ||||||||
| Official Date: | 2017 | ||||||||
| Dates: |
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| Volume: | 27 | ||||||||
| Number: | 2 | ||||||||
| Page Range: | pp. 846-882 | ||||||||
| DOI: | 10.1214/16-AAP1217 | ||||||||
| Status: | Peer Reviewed | ||||||||
| Publication Status: | Published | ||||||||
| Access rights to Published version: | Restricted or Subscription Access | ||||||||
| Date of first compliant deposit: | 10 April 2017 | ||||||||
| Date of first compliant Open Access: | 17 August 2017 | ||||||||
| Related URLs: | |||||||||
| Open Access Version: |
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