Estimation of high-order moment-independent importance measures for Shapley value analysis

•Estimation of high order Borgonovo’s sensitivity measures.•New sensitivity measures relative to Borgonovo’s indices with Shapley values•Estimation procedure based on copula theory.•Application to test cases taken from mechanical, hydrological and aerospace engineering. Moment-independent importance...

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Bibliographic Details
Published in:Applied Mathematical Modelling 2020-12, Vol.88, p.396-417
Main Authors: Sarazin, Gabriel, Derennes, Pierre, Morio, Jérôme
Format: Article
Language:English
Subjects:
Boreholes
Computer Science
Dependent inputs
Engineering Sciences
Global sensitivity analysis
Input-output models
Mathematics
Moment-independent importance measures
Multivariate copula distributions
Physics
Sensitivity
Shapley value
Water flow
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Summary:•Estimation of high order Borgonovo’s sensitivity measures.•New sensitivity measures relative to Borgonovo’s indices with Shapley values•Estimation procedure based on copula theory.•Application to test cases taken from mechanical, hydrological and aerospace engineering. Moment-independent importance measures are increasingly used by practitioners to understand how output uncertainty may be shared between a set of stochastic inputs. Computing Borgonovo's sensitivity indices for a large group of inputs is still a challenging problem due to the curse of dimensionality and it is addressed in this article. An estimation scheme taking the most of recent developments in copula theory is developed. Furthermore, the concept of Shapley value is used to derive new sensitivity indices, which makes the interpretation of Borgonovo's indices much easier. The resulting importance measure offers a double advantage compared with other existing methods since it allows to quantify the impact exerted by one input variable on the whole output distribution after taking into account all possible dependencies and interactions with other variables. The validity of the proposed methodology is established on several analytical examples and the benefits in terms of computational efficiency are illustrated with real-life test cases such as the study of the water flow through a borehole. In addition, a detailed case study dealing with the atmospheric re-entry of a launcher first stage is completed.
ISSN:0307-904X
1088-8691
0307-904X
1872-8480
DOI:10.1016/j.apm.2020.06.036