Multilevel sequential Monte Carlo samplers

Handle URI:
http://hdl.handle.net/10754/622315
Title:
Multilevel sequential Monte Carlo samplers
Authors:
Beskos, Alexandros; Jasra, Ajay; Law, Kody; Tempone, Raul ( 0000-0003-1967-4446 ) ; Zhou, Yan
Abstract:
In this article we consider the approximation of expectations w.r.t. probability distributions associated to the solution of partial differential equations (PDEs); this scenario appears routinely in Bayesian inverse problems. In practice, one often has to solve the associated PDE numerically, using, for instance finite element methods which depend on the step-size level . hL. In addition, the expectation cannot be computed analytically and one often resorts to Monte Carlo methods. In the context of this problem, it is known that the introduction of the multilevel Monte Carlo (MLMC) method can reduce the amount of computational effort to estimate expectations, for a given level of error. This is achieved via a telescoping identity associated to a Monte Carlo approximation of a sequence of probability distributions with discretization levels . ∞>h0>h1⋯>hL. In many practical problems of interest, one cannot achieve an i.i.d. sampling of the associated sequence and a sequential Monte Carlo (SMC) version of the MLMC method is introduced to deal with this problem. It is shown that under appropriate assumptions, the attractive property of a reduction of the amount of computational effort to estimate expectations, for a given level of error, can be maintained within the SMC context. That is, relative to exact sampling and Monte Carlo for the distribution at the finest level . hL. The approach is numerically illustrated on a Bayesian inverse problem. © 2016 Elsevier B.V.
KAUST Department:
Center for Uncertainty Quantification in Computational Science and Engineering (SRI-UQ)
Citation:
Beskos A, Jasra A, Law K, Tempone R, Zhou Y (2016) Multilevel sequential Monte Carlo samplers. Stochastic Processes and their Applications. Available: http://dx.doi.org/10.1016/j.spa.2016.08.004.
Publisher:
Elsevier BV
Journal:
Stochastic Processes and their Applications
Issue Date:
29-Aug-2016
DOI:
10.1016/j.spa.2016.08.004
Type:
Article
ISSN:
0304-4149
Sponsors:
AJ, KL & YZ were supported by an AcRF tier 2 grant: R-155-000-143-112. AJ is affiliated with the Risk Management Institute and the Center for Quantitative Finance at NUS. RT, KL & AJ were additionally supported by King Abdullah University of Science and Technology (KAUST). KL was further supported by ORNLDRD Strategic Hire grant. AB was supported by the Leverhulme Trust Prize. We thank the referees for their comments which have greatly improved the article.
Additional Links:
http://www.sciencedirect.com/science/article/pii/S0304414916301326
Appears in Collections:
Articles

Full metadata record

DC FieldValue Language
dc.contributor.authorBeskos, Alexandrosen
dc.contributor.authorJasra, Ajayen
dc.contributor.authorLaw, Kodyen
dc.contributor.authorTempone, Raulen
dc.contributor.authorZhou, Yanen
dc.date.accessioned2017-01-02T09:08:25Z-
dc.date.available2017-01-02T09:08:25Z-
dc.date.issued2016-08-29en
dc.identifier.citationBeskos A, Jasra A, Law K, Tempone R, Zhou Y (2016) Multilevel sequential Monte Carlo samplers. Stochastic Processes and their Applications. Available: http://dx.doi.org/10.1016/j.spa.2016.08.004.en
dc.identifier.issn0304-4149en
dc.identifier.doi10.1016/j.spa.2016.08.004en
dc.identifier.urihttp://hdl.handle.net/10754/622315-
dc.description.abstractIn this article we consider the approximation of expectations w.r.t. probability distributions associated to the solution of partial differential equations (PDEs); this scenario appears routinely in Bayesian inverse problems. In practice, one often has to solve the associated PDE numerically, using, for instance finite element methods which depend on the step-size level . hL. In addition, the expectation cannot be computed analytically and one often resorts to Monte Carlo methods. In the context of this problem, it is known that the introduction of the multilevel Monte Carlo (MLMC) method can reduce the amount of computational effort to estimate expectations, for a given level of error. This is achieved via a telescoping identity associated to a Monte Carlo approximation of a sequence of probability distributions with discretization levels . ∞>h0>h1⋯>hL. In many practical problems of interest, one cannot achieve an i.i.d. sampling of the associated sequence and a sequential Monte Carlo (SMC) version of the MLMC method is introduced to deal with this problem. It is shown that under appropriate assumptions, the attractive property of a reduction of the amount of computational effort to estimate expectations, for a given level of error, can be maintained within the SMC context. That is, relative to exact sampling and Monte Carlo for the distribution at the finest level . hL. The approach is numerically illustrated on a Bayesian inverse problem. © 2016 Elsevier B.V.en
dc.description.sponsorshipAJ, KL & YZ were supported by an AcRF tier 2 grant: R-155-000-143-112. AJ is affiliated with the Risk Management Institute and the Center for Quantitative Finance at NUS. RT, KL & AJ were additionally supported by King Abdullah University of Science and Technology (KAUST). KL was further supported by ORNLDRD Strategic Hire grant. AB was supported by the Leverhulme Trust Prize. We thank the referees for their comments which have greatly improved the article.en
dc.publisherElsevier BVen
dc.relation.urlhttp://www.sciencedirect.com/science/article/pii/S0304414916301326en
dc.subjectBayesian inverse problemsen
dc.subjectMultilevel Monte Carloen
dc.subjectSequential Monte Carloen
dc.titleMultilevel sequential Monte Carlo samplersen
dc.typeArticleen
dc.contributor.departmentCenter for Uncertainty Quantification in Computational Science and Engineering (SRI-UQ)en
dc.identifier.journalStochastic Processes and their Applicationsen
dc.contributor.institutionDepartment of Statistical Science, University College London, London, WC1E 6BT, UKen
dc.contributor.institutionDepartment of Statistics and Applied Probability, National University of Singapore, Singapore, 117546, Singaporeen
dc.contributor.institutionComputer Science and Mathematics Division, Oak Ridge National Laboratory, Oak Ridge, 37934 TN, USAen
kaust.authorTempone, Raulen
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