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Risk of estimators for Sobol’ sensitivity indices based on metamodels. (English) Zbl 1460.62116

Sobol’ sensitivity indices allow for quantifying the respective effects of random input variables and their combinations on the variance of mathematical model output. A new method for estimating Sobol’s indices is proposed. The author focuses on the problem of Sobol’ indices estimation via a metamodeling approach where he replaces the true mathematical model with a sample-based approximation to compute sensitivity indices. The explicit relation of the errors of Sobol’ indices (total-effects) and the quality of the approximation was obtained. His results lead directly to a simple, practical method for the estimation of indices errors. He obtains asymptotic and non-asymptotic risk bounds for Sobol’ indices estimates. He 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 tested on numerical experiments for the approximations based on multivariate Legendre, Chebyshev and trigonometric polynomials.

MSC:

62J10 Analysis of variance and covariance (ANOVA)
62J05 Linear regression; mixed models
65T40 Numerical methods for trigonometric approximation and interpolation

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