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Sensitivity Analysis and Generalized Chaos Expansions. Lower Bounds for Sobol indices

Abstract : The so-called polynomial chaos expansion is widely used in computer experiments. For example, it is a powerful tool to estimate Sobol' sensitivity indices. In this paper, we consider generalized chaos expansions built on general tensor Hilbert basis. In this frame, we revisit the computation of the Sobol' indices and give general lower bounds for these indices. The case of the eigenfunctions system associated with a Poincaré differential operator leads to lower bounds involving the derivatives of the analyzed function and provides an efficient tool for variable screening. These lower bounds are put in action both on toy and real life models demonstrating their accuracy.
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Preprints, Working Papers, ...
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https://hal.archives-ouvertes.fr/hal-02140127
Contributor : Olivier Roustant <>
Submitted on : Monday, May 27, 2019 - 11:40:12 AM
Last modification on : Wednesday, June 9, 2021 - 1:34:04 PM

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Sobol_lower_bound.pdf
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  • HAL Id : hal-02140127, version 1
  • ARXIV : 1906.09883

Citation

Olivier Roustant, Fabrice Gamboa, Bertrand Iooss. Sensitivity Analysis and Generalized Chaos Expansions. Lower Bounds for Sobol indices. 2019. ⟨hal-02140127⟩

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