Pick and Freeze estimation of sensitivity index for static and dynamic models with dependent inputs
Résumé
This article addresses the estimation of the Sobol index for static and dynamic inputs. We study transformations in the input, whose image is an input with independent components. They have the basic property to give the equality of the σ-algebra between a subset of inputs and their image that allows to compute the Pick and Freeze method. We first focus on the static case. The Gaussian and non Gaussian cases are detailed. In the Gaussian case the dependent variables are separated into two groups of independent variables. In the non Gaussian case we apply the conditional quantile function generally used to simulate random vectors. In the dynamic case the definition of the index has been slightly modified in order to take into account the two dimensions of dependence (temporal and spatial). For Gaussian processes the same method as previously is used. For non Gaussian processes, we propose to use a meta-model copula to get back to Gaussian inputs. Different meta-models are studied in order to focus on the limit, in sensitivity studies, of correlations taken as measures of dependence.
Domaines
Statistiques [stat]
Origine : Fichiers produits par l'(les) auteur(s)
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