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dc.contributor.authorLitvinenko, Alexander
dc.contributor.authorMatthies, Hermann G.
dc.date.accessioned2017-05-23T07:50:14Z
dc.date.available2017-05-23T07:50:14Z
dc.date.issued2013-12-18
dc.identifier.urihttp://hdl.handle.net/10754/623698
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. This is especially the case as 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 is derived from the variational problem associated with conditional expectation. This formulation in general calls for further discretisa- tion 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 quadratic Bayesian update on the small but taxing example of the chaotic Lorenz 84 model, where we experiment with the influence of different observation or measurement operators on the update.
dc.description.sponsorshipKAUST, DFG
dc.relation.ispartofseriesSubjects: Numerical Analysis (math.NA) MSC classes: 62F15, 65N21, 62P30, 60H15, 60H25, 74G75, 80A23, 74C05
dc.relation.urlhttps://arxiv.org/abs/1312.5048
dc.subjectinverse problems
dc.subjectBayesian update surrogate
dc.subjectBayesian update PCE
dc.subjectPolynomial chaos expansion
dc.subjectsampling free non-linear
dc.subjectLorenz 84
dc.subjectconditional expectation
dc.subjectMMSE
dc.titleInverse problems and uncertainty quantification
dc.typeTechnical Report
dc.contributor.departmentSRI Uncertainty Quantification Center
dc.contributor.departmentExtreme Computing Research Center
dc.contributor.institutionTechnische Universitaet Braunschweig
dc.identifier.arxividarXiv:1312.5048
refterms.dateFOA2018-06-13T16:21:12Z


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We develop an approximation of the expensive Bayesian update formula

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