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2020 Non-parametric adaptive estimation of order 1 Sobol indices in stochastic models, with an application to Epidemiology
Gwenaëlle Castellan, Anthony Cousien, Viet Chi Tran
Electron. J. Statist. 14(1): 50-81 (2020). DOI: 10.1214/19-EJS1627

Abstract

Global sensitivity analysis is a set of methods aiming at quantifying the contribution of an uncertain input parameter of the model (or combination of parameters) on the variability of the response. We consider here the estimation of the Sobol indices of order 1 which are commonly-used indicators based on a decomposition of the output’s variance. In a deterministic framework, when the same inputs always give the same outputs, these indices are usually estimated by replicated simulations of the model. In a stochastic framework, when the response given a set of input parameters is not unique due to randomness in the model, metamodels are often used to approximate the mean and dispersion of the response by deterministic functions. We propose a new non-parametric estimator without the need of defining a metamodel to estimate the Sobol indices of order 1. The estimator is based on warped wavelets and is adaptive in the regularity of the model. The convergence of the mean square error to zero, when the number of simulations of the model tend to infinity, is computed and an elbow effect is shown, depending on the regularity of the model. Applications in Epidemiology are carried to illustrate the use of non-parametric estimators.

Citation

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Gwenaëlle Castellan. Anthony Cousien. Viet Chi Tran. "Non-parametric adaptive estimation of order 1 Sobol indices in stochastic models, with an application to Epidemiology." Electron. J. Statist. 14 (1) 50 - 81, 2020. https://doi.org/10.1214/19-EJS1627

Information

Received: 1 October 2017; Published: 2020
First available in Project Euclid: 3 January 2020

zbMATH: 1430.49047
MathSciNet: MR4047594
Digital Object Identifier: 10.1214/19-EJS1627

Subjects:
Primary: 49Q12, 62G08, 62P10

JOURNAL ARTICLE
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Vol.14 • No. 1 • 2020
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