Volume 18, 2014
|Page(s)||342 - 364|
|Published online||03 October 2014|
Asymptotic normality and efficiency of two Sobol index estimators
1 Laboratoire Jean Kuntzmann, Université Joseph Fourier,
INRIA/MOISE, 51 rue des Mathématiques, BP 53, 38041 Grenoble cedex 9, France
2 Laboratoire de Statistique et Probabilités, Institut de Mathématiques Université Paul Sabatier (Toulouse 3), 31062 Toulouse cedex 9, France
Revised: 26 March 2013
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.
Mathematics Subject Classification: 62G05 / 62G20
Key words: Sensitivity analysis / sobol indices / asymptotic efficiency / asymptotic normality / confidence intervals / metamodelling / surface response methodology
© EDP Sciences, SMAI 2014
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