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Making best use of permutations to compute sensitivity indices with replicated orthogonal arrays

Laurent Gilquin 1, 2 Elise Arnaud 2 Clémentine Prieur 2 Alexandre Janon 3
2 AIRSEA - Mathematics and computing applied to oceanic and atmospheric flows
Inria Grenoble - Rhône-Alpes, Grenoble INP - Institut polytechnique de Grenoble - Grenoble Institute of Technology, UGA [2016-2019] - Université Grenoble Alpes [2016-2019], LJK - Laboratoire Jean Kuntzmann
Abstract : Among practitioners, the importance of inputs to a model output is commonly measured via the computation of Sobol' sensitivity indices. Various estimation strategies exist in the literature, most of them requiring a very high number of model evaluations. Designing methods that compete favorably both in terms of computational cost and accuracy is therefore an issue of crucial importance. In this paper, an efficient replication-based strategy is proposed to estimate the full set of first- and second-order Sobol' indices. It relies on a Sobol' pick-freeze estimation scheme and requires only two replicated designs based on randomized orthogonal arrays of strength two. The precision of this procedure is assessed with bootstrap confidence intervals, presented for the first time in the replication framework. Our developments are compared to known approaches and validated on numerical test cases. A way to estimate the full set of first-, second-order but also total-effect Sobol' indices at a very competitive cost is also described, as a combination of our procedure and the one introduced by Saltelli.
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Submitted on : Thursday, September 5, 2019 - 11:40:19 AM
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Laurent Gilquin, Elise Arnaud, Clémentine Prieur, Alexandre Janon. Making best use of permutations to compute sensitivity indices with replicated orthogonal arrays. Reliability Engineering and System Safety, Elsevier, 2019, 187, pp.28-39. ⟨10.1016/j.ress.2018.09.010⟩. ⟨hal-01558915v3⟩



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