基于方差的敏感性分析：探索性与经济性之间更好的估计和设计
Variance-based sensitivity analysis: The quest for better estimators and designs between explorativity and economy
摘要：
基于方差的敏感性指数已成为模型输出的敏感性分析从业者的参考。基于方差的敏感性分析通常为被分析的数学模型的不确定因素产生一阶敏感性指数$S_j$和所谓的总效应敏感性指数$T_j$。分析的成本取决于获得稳定和准确的估计值所需的模型评估的数量。虽然有效的估计过程可用于$S_j$，但是这种可用性对于$T_j$来说是不太可能的。在估计这些指数时，可以使用基于样本的方法，其计算成本取决于因子的数量，或者使用基于Meta建模/仿真器的方法。目前的工作重点是基于样本的估计程序$T_j$和测试不同的途径，以实现算法的改进，现有的最佳实践。为了改进对输入因素空间（设计）和计算指标公式（估计量）的探索，我们提出了基于经济和探索性概念的策略。然后，我们将讨论如何执行现有的几个估计沿着这些特征。我们的结论是：a）基于使用多个矩阵以提高经济性的基于样本的方法优于使用较少矩阵但具有更好探索性的设计; b）在后者中，非对称设计表现最好，并且优于具有虚假相关校正项的对称设计; c）改进现有最佳实践充满困难;以及d）改善结果以引入额外的设计参数为代价。
英文摘要：
Variance-based sensitivity indices have established themselves as a reference among practitioners of sensitivity analysis of model outputs. A variance-based sensitivity analysis typically produces the first-order sensitivity indices $S_j$ and the so-called total-effect sensitivity indices $T_j$ for the uncertain factors of the mathematical model under analysis. The cost of the analysis depends upon the number of model evaluations needed to obtain stable and accurate values of the estimates. While efficient estimation procedures are available for $S_j$, this availability is less the case for $T_j$. When estimating these indices, one can either use a sample-based approach whose computational cost depends on the number of factors or use approaches based on meta modelling/emulators. The present work focuses on sample-based estimation procedures for $T_j$ and tests different avenues to achieve an algorithmic improvement over the existing best practices. To improve the exploration of the space of the input factors (design) and the formula to compute the indices (estimator), we propose strategies based on the concepts of economy and explorativity. We then discuss how several existing estimators perform along these characteristics. We conclude that: a) sample-based approaches based on the use of multiple matrices to enhance the economy are outperformed by designs using fewer matrices but with better explorativity; b) among the latter, asymmetric designs perform the best and outperform symmetric designs having corrective terms for spurious correlations; c) improving on the existing best practices is fraught with difficulties; and d) ameliorating the results comes at the cost of introducing extra design parameters.
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