Efficient Estimation of Sensitivity Indices

TL;DR

This paper introduces an efficient method for estimating Sobol sensitivity indices by reducing the problem to estimating crossed quadratic functionals, with demonstrated effectiveness on analytical functions and a reservoir engineering case.

Contribution

It proposes a novel, asymptotically efficient estimation approach for Sobol indices based on functional integral estimation techniques.

Findings

Efficient estimation of Sobol indices achieved through quadratic functional estimation.

Method validated on analytical functions showing accurate sensitivity estimates.

Application demonstrated on reservoir engineering case with promising results.

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.