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

Laurent Gilquin 1, 2, * Clémentine Prieur 2, 1 Elise Arnaud 3
* Auteur correspondant
2 AIRSEA - Mathematics and computing applied to oceanic and atmospheric flows
Inria Grenoble - Rhône-Alpes, LJK - Laboratoire Jean Kuntzmann, UJF - Université Joseph Fourier - Grenoble 1, INPG - Institut National Polytechnique de Grenoble
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.
Type de document :
Article dans une revue
Information and Inference, Oxford University Press (OUP), 2015, Information and Inference, 4 (4), pp. 354-379. 〈10.1093/imaiai/iav010〉
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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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