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dc.contributor.authorXu, Yaxian
dc.contributor.authorJasra, Ajay
dc.contributor.authorLaw, Kody J. H.
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 (SPDE). 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 of [11] 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 advanced method such as sequential Monte Carlo (SMC). We show how one can use the MIMC method by renormalizing the MI identity and approximating the resulting identity using the SMC$^2$ method of [5]. We prove that our approach can reduce the cost to obtain a given mean square error (MSE), relative to just using SMC$^2$ 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. AJ was supported by an AcRF tier 2 grant: R-155-000-161-112. AJ is affiliated with the Risk Management Institute, the Center for Quantitative Finance and the OR & Analytics cluster at NUS. AJ was supported by a KAUST CRG4 grant ref: 2584. KJHL was supported by the School of Mathematics at the University of Manchester and The Alan Turing Institute. He was also funded in part by Oak Ridge National Laboratory Directed Research and Development Seed funding.
dc.publisherSubmitted to begelhouse
dc.rightsArchived with thanks to arXiv
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.contributor.departmentComputer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division
dc.identifier.journalSubmitted to International Journal on Uncertainty Quantification
dc.contributor.institutionDepartment of Statistics & Applied Probability, National University of Singapore, Singapore, 117546, SG.
dc.contributor.institutionSchool of Mathematics, University of Manchester, Manchester, M13 9PY, UK.
dc.contributor.affiliationKing Abdullah University of Science and Technology (KAUST)
kaust.personJasra, Ajay
kaust.grant.numberCRG4 grant ref: 2584

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