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Abstract: Global sensitivity analysis of complex numerical models can be performed bycalculating variance-based importance measures of the input variables, such asthe Sobol indices. However, these techniques, requiring a large number of modelevaluations, are often unacceptable for time expensive computer codes. A wellknown and widely used decision consists in replacing the computer code by ametamodel, predicting the model responses with a negligible computation timeand rending straightforward the estimation of Sobol indices. In this paper, wediscuss about the Gaussian process model which gives analytical expressions ofSobol indices. Two approaches are studied to compute the Sobol indices: thefirst based on the predictor of the Gaussian process model and the second basedon the global stochastic process model. Comparisons between the two estimates,made on analytical examples, show the superiority of the second approach interms of convergence and robustness. Moreover, the second approach allows tointegrate the modeling error of the Gaussian process model by directly givingsome confidence intervals on the Sobol indices. These techniques are finallyapplied to a real case of hydrogeological modeling.

Autor: Amandine Marrel LMTE, Bertrand Iooss LCFR, Beatrice Laurent IMT, Olivier Roustant


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