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