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dc.contributor.authorMatthies, Hermann G.
dc.contributor.authorZander, Elmar
dc.contributor.authorRosić, Bojana V.
dc.contributor.authorLitvinenko, Alexander
dc.contributor.authorPajonk, Oliver
dc.date.accessioned2016-02-17T08:52:16Z
dc.date.available2016-02-17T08:52:16Z
dc.date.issued2016-02-13
dc.identifier.isbn978-3-319-27994-7
dc.identifier.issn1871-3033
dc.identifier.doi10.1007/978-3-319-27996-1_10
dc.identifier.urihttp://hdl.handle.net/10754/596466
dc.description.abstractIn a Bayesian setting, inverse problems and uncertainty quantification (UQ)—the propagation of uncertainty through a computational (forward) model—are strongly connected. In the form of conditional expectation the Bayesian update becomes computationally attractive. We give a detailed account of this approach via conditional approximation, various approximations, and the construction of filters. Together with a functional or spectral approach for the forward UQ there is no need for time-consuming and slowly convergent Monte Carlo sampling. The developed sampling-free non-linear Bayesian update in form of a filter is derived from the variational problem associated with conditional expectation. This formulation in general calls for further discretisation to make the computation possible, and we choose a polynomial approximation. After giving details on the actual computation in the framework of functional or spectral approximations, we demonstrate the workings of the algorithm on a number of examples of increasing complexity. At last, we compare the linear and nonlinear Bayesian update in form of a filter on some examples.
dc.language.isoen
dc.publisherSpringer Science + Business Media
dc.relation.urlhttp://link.springer.com/chapter/10.1007%2F978-3-319-27996-1_10
dc.relation.urlhttp://arxiv.org/abs/1511.00524
dc.rightsThe final publication is available at Springer via http://dx.doi.org/10.1007/978-3-319-27996-1_10
dc.titleInverse Problems in a Bayesian Setting
dc.typeBook Chapter
dc.contributor.departmentComputer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division
dc.identifier.journalComputational Methods for Solids and Fluids
dc.eprint.versionPost-print
dc.contributor.institutionTU Braunschweig, Brunswick, Germany
dc.contributor.institutionElektrobit, Braunschweig, Germany
dc.contributor.institutionSchlumberger Information Solutions AS, Instituttveien 8, Kjeller, Norway
dc.contributor.affiliationKing Abdullah University of Science and Technology (KAUST)
dc.identifier.arxividarXiv:1511.00524
kaust.personLitvinenko, Alexander
refterms.dateFOA2017-02-13T00:00:00Z


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