论文标题
用于全球灵敏度分析的简单算法，具有沙普利效应
A simple algorithm for global sensitivity analysis with Shapley effects
论文作者
论文摘要
全球灵敏度分析旨在衡量不同变量或变量组的相对重要性对于兴趣数量的变异性。在几个灵敏度指数中，所谓的Shapley效应最近获得了流行，主要是因为所有单个变量的Shapley效应均应到总体方差，这比称为主要效应和总效应的经典灵敏度指数具有更好的解释性。在本文中，假设所有输入变量都是独立的，那么我们引入了一种非常简单的蒙特卡洛算法，以同时估算所有单个变量的沙普利效应，从而大大简化了文献中提出的现有算法。我们提供了算法的简短实现，并显示了一些数值结果。还讨论了输入变量取决于的情况的可能扩展。
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.
