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The bouncy particle sampler : a nonreversible rejection-free Markov chain Monte Carlo method

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Bouchard-Côté, Alexandre, Vollmer, Sebastian J. and Doucet, Arnaud (2018) The bouncy particle sampler : a nonreversible rejection-free Markov chain Monte Carlo method. Journal of the American Statistical Association, 113 (522). pp. 855-867. doi:10.1080/01621459.2017.1294075

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Official URL: http://dx.doi.org/10.1080/01621459.2017.1294075

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Abstract

Many Markov chain Monte Carlo techniques currently available rely on discrete-time reversible Markov processes whose transition kernels are variations of the Metropolis–Hastings algorithm. We explore and generalize an alternative scheme recently introduced in the physics literature (Peters and de With 2012) where the target distribution is explored using a continuous-time nonreversible piecewise-deterministic Markov process. In the Metropolis–Hastings algorithm, a trial move to a region of lower target density, equivalently of higher “energy,” than the current state can be rejected with positive probability. In this alternative approach, a particle moves along straight lines around the space and, when facing a high energy barrier, it is not rejected but its path is modified by bouncing against this barrier. By reformulating this algorithm using inhomogeneous Poisson processes, we exploit standard sampling techniques to simulate exactly this Markov process in a wide range of scenarios of interest. Additionally, when the target distribution is given by a product of factors dependent only on subsets of the state variables, such as the posterior distribution associated with a probabilistic graphical model, this method can be modified to take advantage of this structure by allowing computationally cheaper “local” bounces, which only involve the state variables associated with a factor, while the other state variables keep on evolving. In this context, by leveraging techniques from chemical kinetics, we propose several computationally efficient implementations. Experimentally, this new class of Markov chain Monte Carlo schemes compares favorably to state-of-the-art methods on various Bayesian inference tasks, including for high-dimensional models and large datasets. Supplementary materials for this article are available online.

Item Type: Journal Article
Subjects: Q Science > QA Mathematics
Divisions: Faculty of Science > Mathematics
Library of Congress Subject Headings (LCSH): Bayesian statistical decision theory, Markov processes -- Numerical solutions, Monte Carlo method, Poisson processes, Random fields
Journal or Publication Title: Journal of the American Statistical Association
Publisher: American Statistical Association
ISSN: 0162-1459
Official Date: 6 June 2018
Dates:
DateEvent
6 June 2018Published
28 February 2017Accepted
6 January 2017Updated
Date of first compliant deposit: 10 July 2020
Volume: 113
Number: 522
Page Range: pp. 855-867
DOI: 10.1080/01621459.2017.1294075
Status: Peer Reviewed
Publication Status: Published
Publisher Statement: “This is an Accepted Manuscript of an article published by Taylor & Francis in Journal of the American Statistical Association on 6/06/2018, available online: http://www.tandfonline.com/10.1080/01621459.2017.1294075
Access rights to Published version: Restricted or Subscription Access
RIOXX Funder/Project Grant:
Project/Grant IDRIOXX Funder NameFunder ID
UNSPECIFIED[NSERC] Natural Sciences and Engineering Research Council of Canadahttp://dx.doi.org/10.13039/501100000038
EP/K000276/1[EPSRC] Engineering and Physical Sciences Research Councilhttp://dx.doi.org/10.13039/501100000266
EP/K009850/1[EPSRC] Engineering and Physical Sciences Research Councilhttp://dx.doi.org/10.13039/501100000266
AFOSRA/AOARD-144042Air Force Office of Scientific Researchhttp://dx.doi.org/10.13039/100000181
EP/K009850/1[EPSRC] Engineering and Physical Sciences Research Councilhttp://dx.doi.org/10.13039/501100000266
EP/N000188/1[EPSRC] Engineering and Physical Sciences Research Councilhttp://dx.doi.org/10.13039/501100000266
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