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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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WRAP-Bouncy-particle-sampler-nonreversible-rejection-free Markov-Vollmer-2018.pdf - Accepted Version - Requires a PDF viewer. Download (2197Kb) | Preview |
Official URL: http://dx.doi.org/10.1080/01621459.2017.1294075
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 | |||||||||||||||||||||
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| 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 | |||||||||||||||||||||
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| 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: |
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