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2021 Risk of estimators for Sobol’ sensitivity indices based on metamodels
Ivan Panin
Electron. J. Statist. 15(1): 235-281 (2021). DOI: 10.1214/20-EJS1793


Sobol’ sensitivity indices allow to quantify the respective effects of random input variables and their combinations on the variance of mathematical model output. We focus on the problem of Sobol’ indices estimation via a metamodeling approach where we replace the true mathematical model with a sample-based approximation to compute sensitivity indices. We propose a new method for indices quality control and obtain asymptotic and non-asymptotic risk bounds for Sobol’ indices estimates based on a general class of metamodels. Our analysis is closely connected with the problem of nonparametric function fitting using the orthogonal system of functions in the random design setting. It considers the relation between the metamodel quality and the error of the corresponding estimator for Sobol’ indices and shows the possibility of fast convergence rates in the case of noiseless observations. The theoretical results are complemented with numerical experiments for the approximations based on multivariate Legendre and Trigonometric polynomials.


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Ivan Panin. "Risk of estimators for Sobol’ sensitivity indices based on metamodels." Electron. J. Statist. 15 (1) 235 - 281, 2021.


Received: 1 December 2019; Published: 2021
First available in Project Euclid: 6 January 2021

Digital Object Identifier: 10.1214/20-EJS1793

Primary: 62J05, 62J10
Secondary: 65T40


Vol.15 • No. 1 • 2021
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