Pick and Freeze estimation of sensitivity index for static and dynamic models with dependent inputs

  • Mathilde Grandjacques
  • Benoit Delinchant
  • Olivier Adrot


This article addresses the estimation of the Sobol index for dependent 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 an invariance property for conditional expectation between a subset of inputs and their image that allows to use the Pick and Freeze method. We first focus on the static case. The general case and the Gaussian case are detailed . In the non Gaussian case we apply the conditional quantile function generally used to simulate random vectors in a new framework. In the Gaussian case the dependent variables are separated into two groups of independent variables. 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 for which in general there is no sufficient information to get a model, we propose to use a copula model to get back to Gaussian inputs. Different cases are studied in order to underline on the weakness, in sensitivity studies, to use the correlations like the measures of dependence.