Efficient Estimation of Sensitivity Indices

Sébastien da Veiga (1, 2) , Fabrice Gamboa (2, 3)

1 IFPEN - IFP Energies nouvelles
2 GdR MASCOT-NUM - Méthodes d'Analyse Stochastique des Codes et Traitements Numériques
3 IMT - Institut de Mathématiques de Toulouse UMR5219

In this paper we address the problem of efficient estimation of Sobol sensitivy indices. First, we focus on general functional integrals of conditional moments of the form $\E(\psi(\E(\varphi(Y)|X)))$ where $(X,Y)$ is a random vector with joint density $f$ and $\psi$ and $\varphi$ are functions that are differentiable enough. In particular, we show that asymptotical efficient estimation of this functional boils down to the estimation of crossed quadratic functionals. An efficient estimate of first-order sensitivity indices is then derived as a special case. We investigate its properties on several analytical functions and illustrate its interest on a reservoir engineering case.

Mots clés: Density Estimation; semiparametric Cramér-Rao bound; global sensitivity analysis

Domaines: Statistiques [math.ST]; Théorie [stat.TH]

Sébastien da Veiga, Fabrice Gamboa. Efficient Estimation of Sensitivity Indices. 2012. ⟨hal-00266110v2⟩