2012/03/13 by Sébastien da Veiga, Fabrice Gamboa, Da Veiga, Sébastien +1 · 1 citation
Decision Sciences · Engineering · #FOS: Mathematics #Hydraulic Fracturing and Reservoir Analysis #Probabilistic and Robust Engineering Design #Reservoir Engineering and Simulation Methods #Statistics Theory (math.ST)
paper · pdf · doi:10.48550/arxiv.1203.2899
openalex publication_date 2012/03/13 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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(ψ(\E(φ(Y)|X))) where (X,Y) is a random vector with joint density f and ψ and φ 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.