Maqola

Asymptotic normality and efficiency of two Sobol index estimators

Alexandre JanonLaboratoire Jean Kuntzmann, Université Joseph Fourier, INRIA/MOISE, 51 rue des Mathématiques, BP 53, 38041 Grenoble cedex 9, FranceThierry KleinLaboratoire de Statistique et Probabilités, Institut de Mathématiques Université Paul Sabatier (Toulouse 3), 31062 Toulouse cedex 9, FranceAgnès LagnouxLaboratoire de Statistique et Probabilités, Institut de Mathématiques Université Paul Sabatier (Toulouse 3), 31062 Toulouse cedex 9, FranceMaëlle NodetLaboratoire Jean Kuntzmann, Université Joseph Fourier, INRIA/MOISE, 51 rue des Mathématiques, BP 53, 38041 Grenoble cedex 9, FranceClémentine PrieurLaboratoire Jean Kuntzmann, Université Joseph Fourier, INRIA/MOISE, 51 rue des Mathématiques, BP 53, 38041 Grenoble cedex 9, France

2013en

ABI

Annotatsiya

Many mathematical models involve input parameters, which are not precisely known. Global sensitivity analysis aims to identify the parameters whose uncertainty has the largest impact on the variability of a quantity of interest (output of the model). One of the statistical tools used to quantify the influence of each input variable on the output is the Sobol sensitivity index. We consider the statistical estimation of this index from a finite sample of model outputs: we present two estimators and state a central limit theorem for each. We show that one of these estimators has an optimal asymptotic variance. We also generalize our results to the case where the true output is not observable, and is replaced by a noisy version.

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Identifikatorlar

DOI: 10.1051/ps/2013040

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