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International Journal for Uncertainty Quantification
IF: 3.259 5-Year IF: 2.547 SJR: 0.417 SNIP: 0.8 CiteScore™: 1.52

ISSN Print: 2152-5080
ISSN Online: 2152-5099

Open Access

International Journal for Uncertainty Quantification

DOI: 10.1615/Int.J.UncertaintyQuantification.2019028372
pages 493-514

SHAPLEY EFFECTS FOR SENSITIVITY ANALYSIS WITH CORRELATED INPUTS: COMPARISONS WITH SOBOL' INDICES, NUMERICAL ESTIMATION AND APPLICATIONS

Bertrand Iooss
EDF Lab Chatou, 6 Quai Watier, 78401 Chatou, France; Institut de Mathématiques de Toulouse, 31062, Toulouse, France
Clementine Prieur
Université Grenoble Alpes, CNRS, LJK, F-38000 Grenoble, France; Inria Project/Team AIRSEA, France

ABSTRACT

The global sensitivity analysis of a numerical model aims to quantify, by means of sensitivity indices estimates, the contributions of each uncertain input variable to the model output uncertainty. The so-called Sobol' indices, which are based on functional variance analysis, present a difficult interpretation in the presence of statistical dependence between inputs. The Shapley effects were 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. 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.

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