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dc.contributor.authorMartin, J.
dc.contributor.authorCui, Tiangang
dc.contributor.authorMarzouk, Youssef M.
dc.contributor.authorSolonen, Antti
dc.contributor.authorSpantini, Alessio
dc.date.accessioned2015-05-13T12:47:45Z
dc.date.available2015-05-13T12:47:45Z
dc.date.issued2014-10
dc.date.submitted2014-06
dc.identifier.issn0266-5611
dc.identifier.issn1361-6420
dc.identifier.urihttp://hdl.handle.net/1721.1/96973
dc.description.abstractThe intrinsic dimensionality of an inverse problem is affected by prior information, the accuracy and number of observations, and the smoothing properties of the forward operator. From a Bayesian perspective, changes from the prior to the posterior may, in many problems, be confined to a relatively low-dimensional subspace of the parameter space. We present a dimension reduction approach that defines and identifies such a subspace, called the 'likelihood-informed subspace' (LIS), by characterizing the relative influences of the prior and the likelihood over the support of the posterior distribution. This identification enables new and more efficient computational methods for Bayesian inference with nonlinear forward models and Gaussian priors. In particular, we approximate the posterior distribution as the product of a lower-dimensional posterior defined on the LIS and the prior distribution marginalized onto the complementary subspace. Markov chain Monte Carlo sampling can then proceed in lower dimensions, with significant gains in computational efficiency. We also introduce a Rao−Blackwellization strategy that de-randomizes Monte Carlo estimates of posterior expectations for additional variance reduction. We demonstrate the efficiency of our methods using two numerical examples: inference of permeability in a groundwater system governed by an elliptic PDE, and an atmospheric remote sensing problem based on Global Ozone Monitoring System (GOMOS) observations.en_US
dc.description.sponsorshipUnited States. Dept. of Energy. Office of Advanced Scientific Computing Research (Grant DE-SC0003908)en_US
dc.description.sponsorshipUnited States. Dept. of Energy. Office of Advanced Scientific Computing Research (Grant DE-SC0009297)en_US
dc.language.isoen_US
dc.publisherIOP Publishingen_US
dc.relation.isversionofhttp://dx.doi.org/10.1088/0266-5611/30/11/114015en_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.titleLikelihood-informed dimension reduction for nonlinear inverse problemsen_US
dc.typeArticleen_US
dc.identifier.citationCui, T, J Martin, Y M Marzouk, A Solonen, and A Spantini. “Likelihood-Informed Dimension Reduction for Nonlinear Inverse Problems.” Inverse Problems 30, no. 11 (October 29, 2014): 114015.en_US
dc.contributor.departmentMassachusetts Institute of Technology. Department of Aeronautics and Astronauticsen_US
dc.contributor.mitauthorCui, Tiangangen_US
dc.contributor.mitauthorMarzouk, Youssef M.en_US
dc.contributor.mitauthorSolonen, Anttien_US
dc.contributor.mitauthorSpantini, Alessioen_US
dc.relation.journalInverse Problemsen_US
dc.eprint.versionAuthor's final manuscripten_US
dc.type.urihttp://purl.org/eprint/type/JournalArticleen_US
eprint.statushttp://purl.org/eprint/status/PeerRevieweden_US
dspace.orderedauthorsCui, T; Martin, J; Marzouk, Y M; Solonen, A; Spantini, Aen_US
dc.identifier.orcidhttps://orcid.org/0000-0002-5527-408X
dc.identifier.orcidhttps://orcid.org/0000-0001-7359-4696
dc.identifier.orcidhttps://orcid.org/0000-0002-4840-8545
dc.identifier.orcidhttps://orcid.org/0000-0001-8242-3290
mit.licenseOPEN_ACCESS_POLICYen_US


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