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Metamodel construction for sensitivity analysis

Abstract : We propose to estimate a metamodel and the sensitivity indices of a complex model m in the Gaussian regression framework. Our approach combines methods for sensitivity analysis of complex models and statistical tools for sparse non-parametric estimation in multivariate Gaussian regression model. It rests on the construction of a metamodel for aproximating the Hoeffding-Sobol decomposition of m. This metamodel belongs to a reproducing kernel Hilbert space constructed as a direct sum of Hilbert spaces leading to a functional ANOVA decomposition. The estimation of the metamodel is carried out via a penalized least-squares minimization allowing to select the subsets of variables that contribute to predict the output. It allows to estimate the sensitivity indices of m. We establish an oracle-type inequality for the risk of the estimator, describe the procedure for estimating the metamodel and the sensitivity indices, and assess the performances of the procedure via a simulation study.
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Sylvie Huet, Marie-Luce Taupin. Metamodel construction for sensitivity analysis. ESAIM: Proceedings and Surveys, EDP Sciences, 2017, 60-2017, pp.27-69. ⟨10.1051/proc/201760027⟩. ⟨hal-02618899⟩

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