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Non linear methods for Inverse Statistical Problems

Abstract : In the uncertainty treatment framework considered, the intrinsic variability of the inputs of a physical simulation model is modelled by a multivariate probability distribution. The objective is to identify this probability distribution-the dispersion of which is independent of the sample size since intrinsic variability is at stake-based on observation of some model outputs. Moreover, in order to limit the number of (usually burdensome) physical model runs inside the inversion algorithm to a reasonable level, a nonlinear approximation methodology making use of Kriging and a stochastic EM algorithm is presented. It is compared with iterated linear approximation on the basis of numerical experiments on simulated data sets coming from a simplified but realistic modelling of a dyke overflow. Situations where this nonlinear approach is to be preferred to linearisation are highlighted.
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https://hal.inria.fr/hal-00943678
Contributor : Gilles Celeux <>
Submitted on : Saturday, February 8, 2014 - 12:18:34 PM
Last modification on : Monday, March 29, 2021 - 3:24:02 PM

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Pierre Barbillon, Gilles Celeux, Agnès Grimaud, Yannick Lefebvre, Etienne Rocquigny (de). Non linear methods for Inverse Statistical Problems. Computational Statistics and Data Analysis, Elsevier, 2010, 55, pp.132-142. ⟨10.1016/j.csda.2010.05.030⟩. ⟨hal-00943678⟩

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