# Efficient Estimation of Sensitivity Indices

Abstract : 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.
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https://hal.archives-ouvertes.fr/hal-00266110
Contributor : Fabrice Gamboa <>
Submitted on : Tuesday, March 13, 2012 - 4:46:23 PM
Last modification on : Monday, April 29, 2019 - 3:44:19 PM
Long-term archiving on : Wednesday, December 14, 2016 - 12:50:08 PM

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EfficientSA_newversion.pdf
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### Identifiers

• HAL Id : hal-00266110, version 2
• ARXIV : 1203.2899

### Citation

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

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