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

Abstract

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.