Construction of bootstrap confidence intervals on sensitivity indices computed by polynomial chaos expansion

Abstract : Sensitivity analysis aims at quantifying influence of input parameters dispersion on the output dispersion of a numerical model. When the model evaluation is time consuming, the computation of Sobol' indices based on Monte Carlo method is not applicable and a surrogate model has to be used. Among all approximation methods, polynomial chaos expansion is one of the most efficient to calculate variance-based sensitivity indices. Indeed, their computation is analytically derived from the expansion coefficients but without error estimators of the meta-model approximation. In order to evaluate the reliability of these indices, we propose to build confidence intervals by bootstrap re-sampling on the experimental design used to estimate the polynomial chaos approximation. Since the evaluation of the sensitivity indices is obtained with confidence intervals, it is possible to find a design of experiments allowing the computation of sensitivity indices with a given accuracy.
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Sylvain Dubreuil, Marc Berveiller, Frank Petitjean, Michel Salaün. Construction of bootstrap confidence intervals on sensitivity indices computed by polynomial chaos expansion. Reliability Engineering and System Safety, Elsevier, 2014, vol. 121, pp. 263-275. ⟨10.1016/j.ress.2013.09.011⟩. ⟨hal-00933583⟩

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