Replication procedure for grouped Sobol' indices estimation in dependent uncertainty spaces

Laurent Gilquin 1, 2, * Clémentine Prieur 2, 1 Elise Arnaud 3
* Corresponding author
2 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
3 STEEP - Sustainability transition, environment, economy and local policy
Inria Grenoble - Rhône-Alpes, LJK - Laboratoire Jean Kuntzmann
Abstract : This paper deals with the estimation of grouped Sobol' indices in the case where the dependence inside each group is given by sets of linear ordered constraints. In the framework of independent inputs, the replication method allows to estimate first-order indices with only two designs. Through the use of orthogonal arrays of strength two the replication method can be applied to estimate closed second-order indices. We extend this methodology to estimate first-order and closed second-order grouped Sobol' indices under sets of linear constraints. The construction of the two designs required by the replication method is now based on the simplex geometric structure to handle the constraints within each set. We propose a space filling strategy to construct these designs.
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Laurent Gilquin, Clémentine Prieur, Elise Arnaud. Replication procedure for grouped Sobol' indices estimation in dependent uncertainty spaces. Information and Inference, Oxford University Press (OUP), 2015, Information and Inference, 4 (4), pp. 354-379. ⟨10.1093/imaiai/iav010⟩. ⟨hal-01045034⟩

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