The objective of a global sensitivity analysis is to provide indices to rank the importance of each and every system input when considering the impact on a given system output. This paper discusses a few of the methods proposed throughout the literature when dealing with a linear model for which part of or all the input variables cannot be considered independently. The aim here is to review methods from the late 1980s in order to compare them to more recent developments, by investigating their underlying hypothesis, cost (in term of resource usage), and results. This paper focuses on the case where there is no assumption on the knowledge of the probability density functions, assuming that the analysis can be done from a provided sample, without the use of refined techniques which would require a dedicated surrogate model generation. After an introduction of the general problem, as often discussed in the independent approach, a review of solutions not solely relying on the variance decomposition is presented, along with their underlying hypothesis. A protocol is proposed, based on a statistical approach relying on random correlation matrix generation, to test and compare all methods with an increasingly complex, step-by-step procedure. Finally, dependencies with respect to parameters defining the problem, such as the input space size, the sample size, and the nature of the input laws, are tested before drawing conclusions on the methods and their usefulness.

中文翻译：

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相关输入的敏感性分析：线性情况下的指数比较

全局敏感性分析的目的是在考虑对给定系统输出的影响时，提供指数来对每个系统输入的重要性进行排序。本文讨论了在处理无法独立考虑部分或全部输入变量的线性模型时，整个文献中提出的一些方法。这里的目的是回顾 1980 年代后期的方法，以便通过调查它们的基本假设、成本（在资源使用方面）和结果，将它们与最近的发展进行比较。本文侧重于没有假设概率密度函数知识的情况，假设可以从提供的样本中进行分析，而无需使用需要专用代理模型生成的改进技术。在介绍了一般问题之后，正如在独立方法中经常讨论的那样，提出了对不仅仅依赖于方差分解的解决方案的回顾，以及它们的基本假设。基于依赖于随机相关矩阵生成的统计方法，提出了一种协议，以通过越来越复杂的逐步过程来测试和比较所有方法。最后，在对方法及其实用性得出结论之前，测试与定义问题的参数相关的依赖性，例如输入空间大小、样本大小和输入法则的性质。基于依赖于随机相关矩阵生成的统计方法，提出了一种协议，以通过越来越复杂的逐步过程来测试和比较所有方法。最后，在对方法及其实用性得出结论之前，测试与定义问题的参数相关的依赖性，例如输入空间大小、样本大小和输入法则的性质。基于依赖于随机相关矩阵生成的统计方法，提出了一种协议，以通过越来越复杂的逐步过程来测试和比较所有方法。最后，在对方法及其实用性得出结论之前，测试与定义问题的参数相关的依赖性，例如输入空间大小、样本大小和输入法则的性质。