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Nonlinear methods for inverse statistical problems

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  • Barbillon, Pierre
  • Celeux, Gilles
  • Grimaud, Agnès
  • Lefebvre, Yannick
  • De Rocquigny, Étienne

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.

Suggested Citation

  • Barbillon, Pierre & Celeux, Gilles & Grimaud, Agnès & Lefebvre, Yannick & De Rocquigny, Étienne, 2011. "Nonlinear methods for inverse statistical problems," Computational Statistics & Data Analysis, Elsevier, vol. 55(1), pages 132-142, January.
    • Handle: RePEc:eee:csdana:v:55:y:2011:i:1:p:132-142
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    References listed on IDEAS

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    1. Marrel, Amandine & Iooss, Bertrand & Van Dorpe, François & Volkova, Elena, 2008. "An efficient methodology for modeling complex computer codes with Gaussian processes," Computational Statistics & Data Analysis, Elsevier, vol. 52(10), pages 4731-4744, June.
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    1. Picheny, Victor & Ginsbourger, David, 2014. "Noisy kriging-based optimization methods: A unified implementation within the DiceOptim package," Computational Statistics & Data Analysis, Elsevier, vol. 71(C), pages 1035-1053.

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