Electronic Journal of Statistics

Parseval inequalities and lower bounds for variance-based sensitivity indices

Olivier Roustant, Fabrice Gamboa, and Bertrand Iooss

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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.

Article information

Electron. J. Statist., Volume 14, Number 1 (2020), 386-412.

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

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Primary: 65C60: Computational problems in statistics 26D10: Inequalities involving derivatives and differential and integral operators 62P30: Applications in engineering and industry

Chaos expansion Sobol-Hoeffding decomposition Sobol indices derivative-based global sensitivity measures Poincaré inequality

Creative Commons Attribution 4.0 International License.


Roustant, Olivier; Gamboa, Fabrice; Iooss, Bertrand. Parseval inequalities and lower bounds for variance-based sensitivity indices. Electron. J. Statist. 14 (2020), no. 1, 386--412. doi:10.1214/19-EJS1673. https://projecteuclid.org/euclid.ejs/1579662085

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