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Asymptotic normality and efficiency of two Sobol index estimators

Published online by Cambridge University Press:  03 October 2014

Alexandre Janon ,
Thierry Klein ,
Agnès Lagnoux ,
Maëlle Nodet  and
Clémentine Prieur
Alexandre Janon
Affiliation:
Laboratoire Jean Kuntzmann, Université Joseph Fourier, INRIA/MOISE, 51 rue des Mathématiques, BP 53, 38041 Grenoble cedex 9, France. alexandre.janon@imag.fr
Thierry Klein
Affiliation:
Laboratoire de Statistique et Probabilités, Institut de Mathématiques Université Paul Sabatier (Toulouse 3), 31062 Toulouse cedex 9, France
Agnès Lagnoux
Affiliation:
Laboratoire de Statistique et Probabilités, Institut de Mathématiques Université Paul Sabatier (Toulouse 3), 31062 Toulouse cedex 9, France
Maëlle Nodet
Affiliation:
Laboratoire Jean Kuntzmann, Université Joseph Fourier, INRIA/MOISE, 51 rue des Mathématiques, BP 53, 38041 Grenoble cedex 9, France. alexandre.janon@imag.fr
Clémentine Prieur
Affiliation:
Laboratoire Jean Kuntzmann, Université Joseph Fourier, INRIA/MOISE, 51 rue des Mathématiques, BP 53, 38041 Grenoble cedex 9, France. alexandre.janon@imag.fr
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Abstract

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.

Keywords

Sensitivity analysissobol indicesasymptotic efficiencyasymptotic normalityconfidence intervalsmetamodellingsurface response methodology
Type
Research Article
Information
ESAIM: Probability and Statistics , Volume 18 , 2014 , pp. 342 - 364
Copyright
© EDP Sciences, SMAI 2014

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