Sensitivity indices for independent groups of variables

In this paper, we study sensitivity indices in an additive model and for independent groups of variables. We show in this case that most of the Sobol indices are equal to zero and that Shapley effects can be estimated more efficiently. We then apply this study to Gaussian linear models and we provide an eficient algorithm to compute the theoretical sensitivity indices. In numerical experiments, we show that this algorithm compares favourably to other existing methods.