Recursive estimation procedure of Sobol' indices based on replicated designs

Laurent Gilquin 1, 2 Elise Arnaud 1 Clémentine Prieur 1, 2 Hervé Monod 3, 2
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 context of global sensitivity analysis, the replication procedure allows to estimate Sobol' indices at an efficient cost. However this method still requires a large number of model evaluations. In this paper, we consider the ability of increasing the number of evaluation points, thus the accuracy of estimates, by rendering the replication procedure recursive. The key feature of this approach is the construction of structured space-filling designs. For the estimation of first-order indices, we exploit a nested Latin Hypercube already introduced in the literature. For the estimation of closed second-order indices, two methods are proposed to construct iteratively an orthogonal array. One of the two leads to a partition of the coordinate space over a Galois field. Various space-filling criteria are used to evaluate our designs.
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Submitted on : Tuesday, March 22, 2016 - 9:50:53 AM
Last modification on : Friday, February 8, 2019 - 8:14:02 AM
Long-term archiving on : Sunday, November 13, 2016 - 10:03:29 PM

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Laurent Gilquin, Elise Arnaud, Clémentine Prieur, Hervé Monod. Recursive estimation procedure of Sobol' indices based on replicated designs. 2016. ⟨hal-01291769v1⟩

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