Electronic Journal of Statistics

Parseval inequalities and lower bounds for variance-based sensitivity indices

Olivier Roustant, Fabrice Gamboa, and Bertrand Iooss

Full-text: Open access

Abstract

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

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

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

Permanent link to this document
https://projecteuclid.org/euclid.ejs/1579662085

Digital Object Identifier
doi:10.1214/19-EJS1673

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

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

Rights
Creative Commons Attribution 4.0 International License.

Citation

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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