Using perturbed underdamped langevin dynamics to efficiently sample from probability distributions

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Title: Using perturbed underdamped langevin dynamics to efficiently sample from probability distributions
Author(s): Duncan, AB
Nusken, N
Pavliotis, GA
Item Type: Journal Article
Abstract: In this paper we introduce and analyse Langevin samplers that consist of perturbations of the standard underdamped Langevin dynamics. The perturbed dynamics is such that its invariant measure is the same as that of the unperturbed dynamics. We show that appropriate choices of the perturbations can lead to samplers that have improved properties, at least in terms of reducing the asymptotic variance. We present a detailed analysis of the new Langevin sampler for Gaussian target distributions. Our theoretical results are supported by numerical experiments with non-Gaussian target measures.
Publication Date: 1-Dec-2017
Date of Acceptance: 25-Oct-2017
URI: http://hdl.handle.net/10044/1/63415
DOI: https://dx.doi.org/10.1007/s10955-017-1906-8
ISSN: 1572-9613
Publisher: Springer Verlag
Start Page: 1098
End Page: 1131
Journal / Book Title: Journal of Statistical Physics
Volume: 169
Issue: 6
Sponsor/Funder: Engineering & Physical Science Research Council (EPSRC)
Engineering & Physical Science Research Council (EPSRC)
Engineering & Physical Science Research Council (EPSRC)
Engineering & Physical Science Research Council (EPSRC)
Funder's Grant Number: EP/J009636/1
EP/L025159/1
EP/L020564/1
EP/L024926/1
Copyright Statement: © 2017 The Author(s). This article is distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution, and reproduction in any medium, provided you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made.
Keywords: Science & Technology
Physical Sciences
Physics, Mathematical
Physics
ORNSTEIN-UHLENBECK OPERATORS
WHITE-NOISE LIMITS
VARIANCE REDUCTION
MONTE-CARLO
MOLECULAR-DYNAMICS
INVARIANT-MEASURES
DIFFUSIONS
EQUATIONS
SYSTEMS
EQUILIBRIUM
Science & Technology
Physical Sciences
Physics, Mathematical
Physics
ORNSTEIN-UHLENBECK OPERATORS
WHITE-NOISE LIMITS
VARIANCE REDUCTION
MONTE-CARLO
MOLECULAR-DYNAMICS
INVARIANT-MEASURES
DIFFUSIONS
EQUATIONS
SYSTEMS
EQUILIBRIUM
01 Mathematical Sciences
02 Physical Sciences
Fluids & Plasmas
Publication Status: Published
Open Access location: https://link.springer.com/article/10.1007/s10955-017-1906-8
Online Publication Date: 2017-11-02
Appears in Collections:Mathematics
Statistics
Applied Mathematics and Mathematical Physics



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