Special Issue: SAMO-MASCOT Journal of Statistical Computation and Simulation Generalized Sobol sensitivity indices for dependent variables:

The hierarchically orthogonal functional decomposition of any measurable function η of a random vector X = (X1, · · ·,Xp) consists in decomposing η(X) into a sum of increasing dimension func-tions depending only on a subvector of X. Even when X1, · · · , Xp are assumed to be dependent, this decomposition is unique if the components are hierarchically orthogonal. That is, two of the components are orthogonal whenever all the variables involved in one of the summands are a subset of the variables involved in the other. Setting Y = η(X), this decomposition leads to the definition of generalized sensitivity indices able to quantify the uncertainty of Y due to each dependent input in X [1]. In this paper, a numerical method is developed to identify the component functions of the decomposition using the hierarchical orthogonality property. Furthermore, the asymptotic properties of the components estimation is studied, as well as the numerical estimation of the generalized sen-sitivity indices of a toy model. Lastly, the method is applied to a model arising from a real-world problem