Shapley effects for sensitivity analysis with correlated inputs: comparisons with Sobol' indices, numerical estimation and applications

The global sensitivity analysis of a numerical model aims to quantify, by of sensitivity indices estimate, the contributions of each uncertain variable to the model output uncertainty. The so-called Sobol' indices, are based on the functional variance analysis, present a difficult in the presence of statistical dependence between inputs. The effect was recently introduced to overcome this problem as they the mutual contribution (due to correlation and interaction) of a of inputs to each individual input within the group. In this paper, using new analytical results, we study the effects of linear correlation some Gaussian input variables on Shapley effects, and compare these to classical first-order and total Sobol' indices. This illustrates the, in terms of sensitivity analysis setting and interpretation, of the effects in the case of dependent inputs. For the practical issue of demanding computer models, we show that the substitution of the model by a metamodel (here, kriging) makes it possible to estimate indices with precision at a reasonable computational cost.