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dc.contributor.authorLe Maitre, Olivier
dc.date.accessioned2017-06-08T06:32:29Z
dc.date.available2017-06-08T06:32:29Z
dc.date.issued2016-01-06
dc.identifier.urihttp://hdl.handle.net/10754/624849
dc.description.abstractThe Bayesian inference is a popular probabilistic method to solve inverse problems, such as the identification of field parameter in a PDE model. The inference rely on the Bayes rule to update the prior density of the sought field, from observations, and derive its posterior distribution. In most cases the posterior distribution has no explicit form and has to be sampled, for instance using a Markov-Chain Monte Carlo method. In practice the prior field parameter is decomposed and truncated (e.g. by means of Karhunen- Lo´eve decomposition) to recast the inference problem into the inference of a finite number of coordinates. Although proved effective in many situations, the Bayesian inference as sketched above faces several difficulties requiring improvements. First, sampling the posterior can be a extremely costly task as it requires multiple resolutions of the PDE model for different values of the field parameter. Second, when the observations are not very much informative, the inferred parameter field can highly depends on its prior which can be somehow arbitrary. These issues have motivated the introduction of reduced modeling or surrogates for the (approximate) determination of the parametrized PDE solution and hyperparameters in the description of the prior field. Our contribution focuses on recent developments in these two directions: the acceleration of the posterior sampling by means of Polynomial Chaos expansions and the efficient treatment of parametrized covariance functions for the prior field. We also discuss the possibility of making such approach adaptive to further improve its efficiency.
dc.relation.urlhttp://mediasite.kaust.edu.sa/Mediasite/Play/547f95dc86234609ace510407a6d4cb91d?catalog=ca65101c-a4eb-4057-9444-45f799bd9c52
dc.titlePolynomial Chaos Surrogates for Bayesian Inference
dc.typePresentation
dc.contributor.departmentComputer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division
dc.contributor.departmentComputer, Electrical and Mathematical Sciences & Engineering (CEMSE)
dc.conference.dateJanuary 5-10, 2016
dc.conference.nameAdvances in Uncertainty Quantification Methods, Algorithms and Applications (UQAW 2016)
dc.conference.locationKAUST
kaust.personLe Maitre, Olivier
refterms.dateFOA2018-06-13T14:53:48Z


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