Geodesic
Metamodel construction for sensitivity analysis
Sylvie Huet1 ; Marie-Luce Taupin2, 1
1 UR 1404 MaIAGE, INRA Jouy-en-Josas, France; e-mail:
2 Laboratoire LaMME, UMR CNRS 8071- USC INRA, Université d’Evry Val d’Essonne, France; e-mail:
ESAIM. Proceedings, Tome 60 (2017), pp. 27-69.

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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.
DOI : 10.1051/proc/201760027

Sylvie Huet 1 ; Marie-Luce Taupin 2, 1

1 UR 1404 MaIAGE, INRA Jouy-en-Josas, France; e-mail:
2 Laboratoire LaMME, UMR CNRS 8071- USC INRA, Université d’Evry Val d’Essonne, France; e-mail: 
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Sylvie Huet; Marie-Luce Taupin. Metamodel construction for sensitivity analysis. ESAIM. Proceedings, Tome 60 (2017), pp. 27-69. doi : 10.1051/proc/201760027. http://geodesic.mathdoc.fr/articles/10.1051/proc/201760027/

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