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dc.contributor.authorJasra, Ajay
dc.contributor.authorLaw, Kody J.H.
dc.contributor.authorXu, Yaxian
dc.date.accessioned2021-04-21T07:22:38Z
dc.date.available2020-01-13T13:56:48Z
dc.date.available2021-04-21T07:22:38Z
dc.date.issued2021
dc.identifier.citationJasra, A., Law, K. J. H., & Xu, Y. (2021). MULTI-INDEX SEQUENTIAL MONTE CARLO METHODS FOR PARTIALLY OBSERVED STOCHASTIC PARTIAL DIFFERENTIAL EQUATIONS. International Journal for Uncertainty Quantification, 11(3), 1–25. doi:10.1615/int.j.uncertaintyquantification.2020033219
dc.identifier.issn2152-5099
dc.identifier.issn2152-5080
dc.identifier.doi10.1615/Int.J.UncertaintyQuantification.2020033219
dc.identifier.urihttp://hdl.handle.net/10754/661011
dc.description.abstractIn this paper we consider sequential joint state and static parameter estimation given discrete time observations associated to a partially observed stochastic partial differential equation. It is assumed that one can only estimate the hidden state using a discretization of the model. In this context, it is known that the multi-index Monte Carlo (MIMC) method can be used to improve over direct Monte Carlo from the most precise discretizaton. However, in the context of interest, it cannot be directly applied, but rather must be used within another method such as sequential Monte Carlo (SMC). We show how one can use the MIMC method by renormalizing the standard identity and approximating the resulting identity using the SMC2 method, which is an exact method that can be used in this context. We prove that our approach can reduce the cost to obtain a given mean square error, relative to just using SMC2 on the most precise discretization. We demonstrate this with some numerical examples.
dc.description.sponsorshipWe would like to thank Abdul-Lateef Haji-Ali for useful discussions relating to the material in this paper. A.J. was supported by a KAUST CRG4 grant ref: 2584 and KAUST baseline funding. K.J.H.L. and A.J. were supported by the U.S. Department of Energy, Office of Science, Office of Advanced Scientific Computing Research (ASCR), under field work proposal number ERKJ333. K.J.H.L. was additionally supported by The Alan Turing Institute under the EPSRC grant EP/N510129/1. He was also funded in part by Oak Ridge National Laboratory Directed Research and Development Seed funding.
dc.language.isoen
dc.publisherBegell House
dc.relation.urlhttp://www.dl.begellhouse.com/journals/52034eb04b657aea,6849ac9f50c363c1,3c52cac35ff03994.html
dc.rightsArchived with thanks to International Journal for Uncertainty Quantification
dc.subjectStochastic Partial Differential Equations
dc.subjectMulti-Index Monte Carlo
dc.subjectSequential Monte Carlo
dc.titleMulti-index sequential monte carlo methods for partially observed stochastic partial differential equations
dc.typeArticle
dc.contributor.departmentComputer, Electrical and Mathematical Science and Engineering (CEMSE) Division
dc.contributor.departmentComputer, Electrical and Mathematical Science and Engineering Division, King Abdullah University of Science and Technology, Thuwal, 23955-6900, Saudi Arabia
dc.identifier.journalInternational Journal for Uncertainty Quantification
dc.rights.embargodate2022-04-21
dc.eprint.versionPost-print
dc.contributor.institutionDepartment of Mathematics, University of Manchester, M39PL, United Kingdom
dc.identifier.volume11
dc.identifier.issue3
dc.contributor.affiliationKing Abdullah University of Science and Technology (KAUST)
dc.identifier.pages1-25
pubs.publication-statusSubmitted
dc.identifier.arxivid1805.00415
kaust.personJasra, Ajay
kaust.personXu, Yaxian
kaust.grant.numberCRG4 grant ref: 2584
dc.identifier.eid2-s2.0-85103982223
refterms.dateFOA2020-01-13T13:56:48Z
kaust.acknowledged.supportUnitCRG
kaust.acknowledged.supportUnitKAUST baseline funding
dc.date.posted2018-05-01


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