  In global sensitivity analysis, the well known Sobol' sensitivity indices aim
to quantify how the variance in the output of a mathematical model can be
apportioned to the different variances of its input random variables. These
indices are based on the functional variance decomposition and their
interpretation become difficult in the presence of statistical dependence
between the inputs. However, as there is dependence in many application
studies, that enhances the development of interpretable sensitivity indices.
Recently, the Shapley values developed in the field of cooperative games theory
have been connected to global sensitivity analysis and present good properties
in the presence of dependencies. Nevertheless, the available estimation methods
don't always provide confidence intervals and require a large number of model
evaluation. In this paper, we implement a bootstrap sampling in the existing
algorithms to estimate confidence intervals of the indice estimations. We also
proposed to consider a metamodel in substitution of a costly numerical model.
The estimation error from the Monte-Carlo sampling is combined with the
metamodel error in order to have confidence intervals on the Shapley effects.
Besides, we compare for different examples with dependent random variables the
results of the Shapley effects with existing extensions of the Sobol' indices.
