Advanced Multilevel Monte Carlo Methods

Handle URI:
http://hdl.handle.net/10754/626463
Title:
Advanced Multilevel Monte Carlo Methods
Authors:
Jasra, Ajay; Law, Kody; Suciu, Carina
Abstract:
This article reviews the application of advanced Monte Carlo techniques in the context of Multilevel Monte Carlo (MLMC). MLMC is a strategy employed to compute expectations which can be biased in some sense, for instance, by using the discretization of a associated probability law. The MLMC approach works with a hierarchy of biased approximations which become progressively more accurate and more expensive. Using a telescoping representation of the most accurate approximation, the method is able to reduce the computational cost for a given level of error versus i.i.d. sampling from this latter approximation. All of these ideas originated for cases where exact sampling from couples in the hierarchy is possible. This article considers the case where such exact sampling is not currently possible. We consider Markov chain Monte Carlo and sequential Monte Carlo methods which have been introduced in the literature and we describe different strategies which facilitate the application of MLMC within these methods.
KAUST Department:
Center for Uncertainty Quantification in Computational Science & Engineering, King Abdullah University of Science and Technology, Thuwal, 23955-6900, KSA
Publisher:
arXiv
Issue Date:
24-Apr-2017
ARXIV:
arXiv:1704.07272
Type:
Preprint
Additional Links:
http://arxiv.org/abs/1704.07272v1; http://arxiv.org/pdf/1704.07272v1
Appears in Collections:
Other/General Submission

Full metadata record

DC FieldValue Language
dc.contributor.authorJasra, Ajayen
dc.contributor.authorLaw, Kodyen
dc.contributor.authorSuciu, Carinaen
dc.date.accessioned2017-12-28T07:32:11Z-
dc.date.available2017-12-28T07:32:11Z-
dc.date.issued2017-04-24en
dc.identifier.urihttp://hdl.handle.net/10754/626463-
dc.description.abstractThis article reviews the application of advanced Monte Carlo techniques in the context of Multilevel Monte Carlo (MLMC). MLMC is a strategy employed to compute expectations which can be biased in some sense, for instance, by using the discretization of a associated probability law. The MLMC approach works with a hierarchy of biased approximations which become progressively more accurate and more expensive. Using a telescoping representation of the most accurate approximation, the method is able to reduce the computational cost for a given level of error versus i.i.d. sampling from this latter approximation. All of these ideas originated for cases where exact sampling from couples in the hierarchy is possible. This article considers the case where such exact sampling is not currently possible. We consider Markov chain Monte Carlo and sequential Monte Carlo methods which have been introduced in the literature and we describe different strategies which facilitate the application of MLMC within these methods.en
dc.publisherarXiven
dc.relation.urlhttp://arxiv.org/abs/1704.07272v1en
dc.relation.urlhttp://arxiv.org/pdf/1704.07272v1en
dc.rightsArchived with thanks to arXiven
dc.titleAdvanced Multilevel Monte Carlo Methodsen
dc.typePreprinten
dc.contributor.departmentCenter for Uncertainty Quantification in Computational Science & Engineering, King Abdullah University of Science and Technology, Thuwal, 23955-6900, KSAen
dc.eprint.versionPre-printen
dc.contributor.institutionDepartment of Statistics & Applied Probability, National University of Singapore, Singapore, 117546, SGen
dc.contributor.institutionComputer Science and Mathematics Division, Oak Ridge National Laboratory, Oak Ridge, 37934 TNen
dc.identifier.arxividarXiv:1704.07272en
kaust.authorSuciu, Carinaen
All Items in KAUST are protected by copyright, with all rights reserved, unless otherwise indicated.