New sensitivity analysis subordinated to a contrast

In a model of the form Y=h(X1,ldots,Xd) where the goal is to estimate a parameter of the probability distribution of Y, we define new sensitivity indices which quantify the importance of each variable Xi with respect to this parameter of interest. The aim of this paper is to define it goal oriented sensitivity indices and we will show that Sobol indices are sensitivity indices associated to a particular characteristic of the distribution Y. We name the framework we present as it Goal Oriented Sensitivity Analysis (GOSA).