Minimum mean square error estimation and approximation of the Bayesian update

Handle URI:
http://hdl.handle.net/10754/624069
Title:
Minimum mean square error estimation and approximation of the Bayesian update
Authors:
Litvinenko, Alexander ( 0000-0001-5427-3598 ) ; Matthies, Hermann G.; Zander, Elmar
Abstract:
Given: a physical system modeled by a PDE or ODE with uncertain coefficient q(w), a measurement operator Y (u(q); q), where u(q; w) uncertain solution. Aim: to identify q(w). The mapping from parameters to observations is usually not invertible, hence this inverse identification problem is generally ill-posed. To identify q(w) we derived non-linear Bayesian update from the variational problem associated with conditional expectation. To reduce cost of the Bayesian update we offer a functional approximation, e.g. polynomial chaos expansion (PCE). New: We derive linear, quadratic etc approximation of full Bayesian update.
KAUST Department:
Computer, Electrical and Mathematical Sciences & Engineering (CEMSE)
Conference/Event name:
Advances in Uncertainty Quantification Methods, Algorithms and Applications (UQAW 2015)
Issue Date:
7-Jan-2015
Type:
Poster
Appears in Collections:
Posters; Conference on Advances in Uncertainty Quantification Methods, Algorithms and Applications (UQAW 2015)

Full metadata record

DC FieldValue Language
dc.contributor.authorLitvinenko, Alexanderen
dc.contributor.authorMatthies, Hermann G.en
dc.contributor.authorZander, Elmaren
dc.date.accessioned2017-06-05T08:35:47Z-
dc.date.available2017-06-05T08:35:47Z-
dc.date.issued2015-01-07-
dc.identifier.urihttp://hdl.handle.net/10754/624069-
dc.description.abstractGiven: a physical system modeled by a PDE or ODE with uncertain coefficient q(w), a measurement operator Y (u(q); q), where u(q; w) uncertain solution. Aim: to identify q(w). The mapping from parameters to observations is usually not invertible, hence this inverse identification problem is generally ill-posed. To identify q(w) we derived non-linear Bayesian update from the variational problem associated with conditional expectation. To reduce cost of the Bayesian update we offer a functional approximation, e.g. polynomial chaos expansion (PCE). New: We derive linear, quadratic etc approximation of full Bayesian update.en
dc.titleMinimum mean square error estimation and approximation of the Bayesian updateen
dc.typePosteren
dc.contributor.departmentComputer, Electrical and Mathematical Sciences & Engineering (CEMSE)en
dc.conference.dateJanuary 6-9, 2015en
dc.conference.nameAdvances in Uncertainty Quantification Methods, Algorithms and Applications (UQAW 2015)en
dc.conference.locationKAUSTen
dc.contributor.institutionTU Braunschweigen
kaust.authorLitvinenko, Alexanderen
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