A simple algorithm for global sensitivity analysis with Shapley effects

TL;DR

This paper introduces a simple Monte Carlo algorithm for efficiently estimating Shapley effects in global sensitivity analysis, improving interpretability and computational simplicity, especially under the assumption of independent input variables.

Contribution

The paper presents a novel, simplified Monte Carlo algorithm for estimating Shapley effects, enhancing computational efficiency and ease of implementation in global sensitivity analysis.

Findings

Algorithm effectively estimates Shapley effects for all variables simultaneously.

Numerical results demonstrate the algorithm's accuracy and simplicity.

Discussion on extending the method to dependent variables.

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.