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

By Bertrand Iooss, Clémentine Prieur. International Journal for Uncertainty Quantification, 2017

129 citations recorded by the source corpus.

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 this http URL 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.

Subfields: Computational Theory and Mathematics, Statistical and Nonlinear Physics, Statistics and Probability

View Paper: https://www.semanticscholar.org/paper/2bbfe701698fc2014286b5dade63b2659ac82c97

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In Computational Theory and Mathematics

1. Fabrice Gamboa
2. Thierry Klein
3. Pierre-Alain Gremaud
4. Agnès Lagnoux

In Statistical and Nonlinear Physics

1. Fabrice Gamboa
2. Thierry Klein
3. Pierre-Alain Gremaud
4. Agnès Lagnoux

In Statistics and Probability

1. Fabrice Gamboa
2. Agnès Lagnoux
3. Thierry Klein
4. Pierre-Alain Gremaud

Citations in the corpus

• The Future of Sensitivity Analysis: An essential discipline for systems modeling and policy support (2020, unknown): “…of the Hoeffding--Sobol ’ decomposition (Chastaing et al., 2012), regression-based methods (Xu and Gertner, 2008), copula-based methods (Kucherenko, 2012; Do and Razavi, 2020; Sheikholeslami et al., 2020) and game-theory concepts (Owen, 2014; Owen and Prieur, 2017; Iooss and Prieur, 2019).”
• Global Sensitivity Analysis: a new generation of mighty estimators based on rank statistics (2020, methodology): “We refer to [28, 35, 29, 19] and the references therein for more details on Shapley effects.”