Making best use of permutations to compute sensitivity indices with replicated designs

Laurent Gilquin 1 Elise Arnaud 1, 2 Clémentine Prieur 1, 2 Alexandre Janon 2, 3
1 AIRSEA - Mathematics and computing applied to oceanic and atmospheric flows
Grenoble INP - Institut polytechnique de Grenoble - Grenoble Institute of Technology, UGA - Université Grenoble Alpes, LJK - Laboratoire Jean Kuntzmann, Inria Grenoble - Rhône-Alpes
Abstract : In the field of sensitivity analysis, Sobol' indices are widely used to assess the importance of inputs of a model to its output. Among the methods that estimate these indices, the replication procedure is noteworthy for its efficient cost. However, gaining in efficiency and assessing the estimate precision still remains an issue, all the more important when one is dealing with limited computational budget. In this paper, we propose a new strategy to estimate the full set of first-order and second-order Sobol' indices with only two replicated designs based on orthogonal arrays of strength two. Such a procedure increases the precision of the estimation for a given computation budget. We also propose a bootstrap procedure for producing confidence intervals, that are compared to asymptotic ones in the case of first-order indices. Numerical simulations and applications to benchmarks assess the interest of our contributions.
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Laurent Gilquin, Elise Arnaud, Clémentine Prieur, Alexandre Janon. Making best use of permutations to compute sensitivity indices with replicated designs. 2017. ⟨hal-01558915v1⟩

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