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

机译：抑制福利价值分析的高阶矩的重要性措施

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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.
机译：从业者越来越多地使用时刻无关的重要性措施来了解如何在一组随机输入之间共享输出不确定性。由于诅咒维度，计算Borgonovo为一大群投入的敏感性指数仍然是一个具有挑战性的问题，并且在本文中解决了它。开发了一种估算方案，以拷贝理论的最新发展。此外，福利价值的概念用于推导新的敏感指数，这使得Borgonovo的指数的解释更容易。与其他现有方法相比，由此产生的重要性测量提供了双重优势，因为它允许在考虑所有可能的依赖性和与其他变量的交互后，在整个输出分布上量化在整个输出分布上施加的影响。在若干分析示例中建立了所提出的方法的有效性，并且在计算效率方面的益处具有现实寿命测试案例，例如通过钻孔的水流的研究。此外，处理发射器第一阶段的大气重新进入的详细案例研究已完成。

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