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Reliability of global sensitivity indices

机译：全球敏感性指数的可靠性

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摘要

Uncertainty and sensitivity analysis is an essential ingredient of model development and applications. For many uncertainty and sensitivity analysis techniques, sensitivity indices are calculated based on a relatively large sample to measure the importance of parameters in their contributions to uncertainties in model outputs. To statistically compare their importance, it is necessary that uncertainty and sensitivity analysis techniques provide standard errors of estimated sensitivity indices. In this paper, a delta method is used to analytically approximate standard errors of estimated sensitivity indices for a popular sensitivity analysis method, the Fourier amplitude sensitivity test (FAST). Standard errors estimated based on the delta method were compared with those estimated based on 20 sample replicates. We found that the delta method can provide a good approximation for the standard errors of both first-order and higher-order sensitivity indices. Finally, based on the standard error approximation, we also proposed a method to determine a minimum sample size to achieve the desired estimation precision for a specified sensitivity index. The standard error estimation method presented in this paper can make the FAST analysis computationally much more efficient for complex models.
机译：不确定性和敏感性分析是模型开发和应用的重要组成部分。对于许多不确定性和敏感性分析技术，将基于相对较大的样本来计算敏感性指数，以衡量参数对模型输出不确定性的贡献的重要性。为了从统计学上比较它们的重要性，不确定性和灵敏度分析技术必须提供估计灵敏度指数的标准误差。在本文中，对于一种流行的灵敏度分析方法，即傅立叶振幅灵敏度测试（FAST），使用增量法来分析估计的灵敏度指标的标准误差。将基于增量法估算的标准误与基于20个样本重复估算的标准误进行了比较。我们发现，增量法可以为一阶和高阶灵敏度指标的标准误差提供良好的近似值。最后，基于标准误差近似值，我们还提出了一种确定最小样本量的方法，以针对指定的敏感度指标实现所需的估计精度。本文提出的标准误差估计方法可使FAST分析在复杂模型上的计算效率更高。

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