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Fast Langevin based algorithm for MCMC in high dimensions
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Durmus, Alain, Roberts, Gareth O., Vilmart, Gilles and Zygalakis, Konstantinos C. (2017) Fast Langevin based algorithm for MCMC in high dimensions. The Annals of Applied Probability, 27 (4). pp. 2195-2237. doi:10.1214/16-AAP1257 ISSN 1050-5164.
An open access version can be found in:
Official URL: http://dx.doi.org/10.1214/16-AAP1257
Abstract
We introduce new Gaussian proposals to improve the efficiency of the standard Hastings–Metropolis algorithm in Markov chain Monte Carlo (MCMC) methods, used for the sampling from a target distribution in large dimension d. The improved complexity is O(d1/5) compared to the complexity O(d1/3) of the standard approach. We prove an asymptotic diffusion limit theorem and show that the relative efficiency of the algorithm can be characterised by its overall acceptance rate (with asymptotical value 0.704), independently of the target distribution. Numerical experiments confirm our theoretical findings.
Item Type: | Journal Article | ||||||||
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Divisions: | Faculty of Science, Engineering and Medicine > Science > Statistics | ||||||||
Journal or Publication Title: | The Annals of Applied Probability | ||||||||
Publisher: | Institute of Mathematical Statistics | ||||||||
ISSN: | 1050-5164 | ||||||||
Official Date: | 30 August 2017 | ||||||||
Dates: |
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Volume: | 27 | ||||||||
Number: | 4 | ||||||||
Page Range: | pp. 2195-2237 | ||||||||
DOI: | 10.1214/16-AAP1257 | ||||||||
Status: | Peer Reviewed | ||||||||
Publication Status: | Published | ||||||||
Access rights to Published version: | Restricted or Subscription Access | ||||||||
Open Access Version: |
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