Asymptotic normality and efficiency of two Sobol index estimators

Alexandre Janon; Thierry Klein; Agnès Lagnoux; Maëlle Nodet; Clémentine Prieur

ESAIM: Probability and Statistics (2014)

  • Volume: 18, page 342-364
  • ISSN: 1292-8100

Abstract

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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.

How to cite

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Janon, Alexandre, et al. "Asymptotic normality and efficiency of two Sobol index estimators." ESAIM: Probability and Statistics 18 (2014): 342-364. <http://eudml.org/doc/273644>.

@article{Janon2014,
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.},
author = {Janon, Alexandre, Klein, Thierry, Lagnoux, Agnès, Nodet, Maëlle, Prieur, Clémentine},
journal = {ESAIM: Probability and Statistics},
keywords = {sensitivity analysis; sobol indices; asymptotic efficiency; asymptotic normality; confidence intervals; metamodelling; surface response methodology; Sobol indices},
language = {eng},
pages = {342-364},
publisher = {EDP-Sciences},
title = {Asymptotic normality and efficiency of two Sobol index estimators},
url = {http://eudml.org/doc/273644},
volume = {18},
year = {2014},
}

TY - JOUR
AU - Janon, Alexandre
AU - Klein, Thierry
AU - Lagnoux, Agnès
AU - Nodet, Maëlle
AU - Prieur, Clémentine
TI - Asymptotic normality and efficiency of two Sobol index estimators
JO - ESAIM: Probability and Statistics
PY - 2014
PB - EDP-Sciences
VL - 18
SP - 342
EP - 364
AB - 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.
LA - eng
KW - sensitivity analysis; sobol indices; asymptotic efficiency; asymptotic normality; confidence intervals; metamodelling; surface response methodology; Sobol indices
UR - http://eudml.org/doc/273644
ER -

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