A simple algorithm for global sensitivity analysis with Shapley effects

Takashi Goda

doi:10.1016/j.ress.2021.107702

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arXiv · 2009.00874

A simple algorithm for global sensitivity analysis with Shapley effects

Takashi Goda

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Abstract

Global sensitivity analysis aims at measuring the relative importance of different variables or groups of variables for the variability of a quantity of interest. Among several sensitivity indices, so-called Shapley effects have recently gained popularity mainly because the Shapley effects for all the individual variables are summed up to the overall variance, which gives a better interpretability than the classical sensitivity indices called main effects and total effects. In this paper, assuming that all the input variables are independent, we introduce a quite simple Monte Carlo algorithm to estimate the Shapley effects for all the individual variables simultaneously, which drastically simplifies the existing algorithms proposed in the literature. We present a short Matlab implementation of our algorithm and show some numerical results. A possible extension to the case where the input variables are dependent is also discussed.

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Takashi Goda. 2021-04-26. A simple algorithm for global sensitivity analysis with Shapley effects. https://doi.org/10.1016/j.ress.2021.107702

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