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 dc.contributor.author Xu, Yaxian dc.contributor.author Jasra, Ajay dc.contributor.author Law, Kody J. H. dc.date.accessioned 2020-01-13T13:56:48Z dc.date.available 2020-01-13T13:56:48Z dc.date.issued 2019 dc.identifier.uri http://hdl.handle.net/10754/661011.1 dc.description.abstract In 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.sponsorship We 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.language.iso en dc.publisher Submitted to begelhouse dc.relation.url https://arxiv.org/pdf/1805.00415 dc.rights Archived with thanks to arXiv dc.subject Stochastic Partial Differential Equations dc.subject Multi-Index Monte Carlo dc.subject Sequential Monte Carlo dc.title Multi-Index Sequential Monte Carlo Methods for partially observed Stochastic Partial Differential Equations dc.type Preprint dc.contributor.department Computer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division dc.identifier.journal Submitted to International Journal on Uncertainty Quantification dc.eprint.version Pre-print dc.contributor.institution Department of Statistics & Applied Probability, National University of Singapore, Singapore, 117546, SG. dc.contributor.institution School of Mathematics, University of Manchester, Manchester, M13 9PY, UK. dc.contributor.affiliation King Abdullah University of Science and Technology (KAUST) pubs.publication-status Submitted dc.identifier.arxivid 1805.00415 kaust.person Jasra, Ajay kaust.grant.number CRG4 grant ref: 2584 refterms.dateFOA 2020-01-13T13:56:48Z dc.date.posted 2018-05-01
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