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dc.contributor.authorPeherstorfer, Benjamin
dc.contributor.authorMarzouk, Youssef M
dc.date.accessioned2020-07-23T15:14:06Z
dc.date.available2020-07-23T15:14:06Z
dc.date.issued2019-07
dc.identifier.issn1019-7168
dc.identifier.urihttps://hdl.handle.net/1721.1/126341
dc.description.abstractMarkov chain Monte Carlo (MCMC) sampling of posterior distributions arising in Bayesian inverse problems is challenging when evaluations of the forward model are computationally expensive. Replacing the forward model with a low-cost, low-fidelity model often significantly reduces computational cost; however, employing a low-fidelity model alone means that the stationary distribution of the MCMC chain is the posterior distribution corresponding to the low-fidelity model, rather than the original posterior distribution corresponding to the high-fidelity model. We propose a multifidelity approach that combines, rather than replaces, the high-fidelity model with a low-fidelity model. First, the low-fidelity model is used to construct a transport map that deterministically couples a reference Gaussian distribution with an approximation of the low-fidelity posterior. Then, the high-fidelity posterior distribution is explored using a non-Gaussian proposal distribution derived from the transport map. This multifidelity “preconditioned” MCMC approach seeks efficient sampling via a proposal that is explicitly tailored to the posterior at hand and that is constructed efficiently with the low-fidelity model. By relying on the low-fidelity model only to construct the proposal distribution, our approach guarantees that the stationary distribution of the MCMC chain is the high-fidelity posterior. In our numerical examples, our multifidelity approach achieves significant speedups compared with single-fidelity MCMC sampling methods.en_US
dc.description.sponsorshipUnited States. Office of Naval Research. Multidisciplinary University Research Initiative on multi-information sources of multi-physics systems (Award FA9550-15-1-0038)en_US
dc.language.isoen
dc.publisherSpringer Science and Business Media LLCen_US
dc.relation.isversionof10.1007/s10444-019-09711-yen_US
dc.rightsCreative Commons Attribution-Noncommercial-Share Alikeen_US
dc.rights.urihttp://creativecommons.org/licenses/by-nc-sa/4.0/en_US
dc.sourcearXiven_US
dc.titleA transport-based multifidelity preconditioner for Markov chain Monte Carloen_US
dc.typeArticleen_US
dc.identifier.citationPeherstorfer, Benjamin and Youssef Marzouk. “A transport-based multifidelity preconditioner for Markov chain Monte Carlo.” Advances in computational mathematics, vol. 45 2019, pp. 2321-2348 © 2019 The Author(s)en_US
dc.contributor.departmentMassachusetts Institute of Technology. Department of Aeronautics and Astronauticsen_US
dc.relation.journalAdvances in computational mathematicsen_US
dc.eprint.versionOriginal manuscripten_US
dc.type.urihttp://purl.org/eprint/type/JournalArticleen_US
eprint.statushttp://purl.org/eprint/status/NonPeerRevieweden_US
dc.date.updated2019-10-30T12:12:23Z
dspace.date.submission2019-10-30T12:12:30Z
mit.journal.volume45en_US


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