Asymptotic normality and efficiency of two Sobol index estimators
By Alexandre Janon, Thierry Klein, Agnès Lagnoux-Renaudie, Maëlle Nodet, Clémentine Prieur. 2013
256 citations recorded by the source corpus.
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.
Subfields: Computational Theory and Mathematics, Mechanics of Materials, Statistics and Probability
View Paper: https://www.semanticscholar.org/paper/0fe665d8a6436a44e5d6ee1fd35f227abf690035
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In Computational Theory and Mathematics
In Statistics and Probability
Citations in the corpus
- A Review on Global Sensitivity Analysis Methods (2014, unknown): “[40]), but estimating total Sobol’ indices at low cost is a problem of primary importance in applications (see Saltelli et al.”
- Sensitivity analysis for multidimensional and functional outputs (2013, methodology): “As in dimension 1, one can see that this new index can also be seen as the solution of the following least-squares problem (see [6]) Argmin a E‖Y u − aY ‖(2).”
- The Future of Sensitivity Analysis: An essential discipline for systems modeling and policy support (2020, unknown): “Their emphasis has particularly been placed on linking SA and asymptotic statistical theory (Janon et al., 2014a; Gamboa et al., 2016), space-filling designs of experiments (Tissot and Prieur, 2015; Gilquin et al., 2020), structural reliability (Fort et al., 2016), and Bayesian estimation…”
- Global Sensitivity Analysis: a new generation of mighty estimators based on rank statistics (2020, unknown): “The corresponding Pick-Freeze approach from [13, 14, 20] relies on expressing the variances of the conditional expectations in terms of covariances which are easily and well estimated by their empirical versions.”