Recursive estimation procedure of Sobol' indices based on replicated designs

Laurent Gilquin 1, 2 Elise Arnaud 1 Clémentine Prieur 1, 2 Hervé Monod 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. A practical problem is how many model evaluations must be performed to guarantee a sufficient precision on the Sobol' estimates. This paper tackles this issue by rendering the replication procedure recursive. We consider the ability of adding new points to progressively increase the accuracy of the estimates. The key feature of this approach is the construction of nested 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 constructions of a nested orthogonal array are proposed. Regularity and uniformity properties of the nested designs are studied.
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Laurent Gilquin, Elise Arnaud, Clémentine Prieur, Hervé Monod. Recursive estimation procedure of Sobol' indices based on replicated designs. 2016. ⟨hal-01291769v3⟩

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