Open Access
2020 Parseval inequalities and lower bounds for variance-based sensitivity indices
Olivier Roustant, Fabrice Gamboa, Bertrand Iooss
Electron. J. Statist. 14(1): 386-412 (2020). DOI: 10.1214/19-EJS1673


The so-called polynomial chaos expansion is widely used in computer experiments. For example, it is a powerful tool to estimate Sobol’ sensitivity indices. In this paper, we consider generalized chaos expansions built on general tensor Hilbert basis. In this frame, we revisit the computation of the Sobol’ indices with Parseval equalities and give general lower bounds for these indices obtained by truncation. The case of the eigenfunctions system associated with a Poincaré differential operator leads to lower bounds involving the derivatives of the analyzed function and provides an efficient tool for variable screening. These lower bounds are put in action both on toy and real life models demonstrating their accuracy.


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Olivier Roustant. Fabrice Gamboa. Bertrand Iooss. "Parseval inequalities and lower bounds for variance-based sensitivity indices." Electron. J. Statist. 14 (1) 386 - 412, 2020.


Received: 1 June 2019; Published: 2020
First available in Project Euclid: 22 January 2020

zbMATH: 07154992
MathSciNet: MR4054251
Digital Object Identifier: 10.1214/19-EJS1673

Primary: 26D10 , 62P30 , 65C60

Keywords: chaos expansion , derivative-based global sensitivity measures , Poincaré inequality , Sobol indices , Sobol-Hoeffding decomposition

Vol.14 • No. 1 • 2020
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