Distribution-based global sensitivity analysis (GSA), such as variance-based and entropy-based approaches, can provide quantitative sensitivity information. However, they can be expensive to evaluate and are thus limited to low dimensional problems. Derivative-based GSA, on the other hand, require much fewer model evaluations. It is known that derivative-based GSA is closely linked to variance-based total sensitivity index, while its relationship with the entropy-based measure is unclear. To fill this gap, we introduce a log-derivative based functional to demonstrate that the entropy-based and derivative-based sensitivity measures are strongly connected. In particular, we give proofs that, similar to the case with variance-based GSA, there is an inequality relationship between entropy-based and derivative-based important measures. Both analytical and numerical verifications are provided. Examples show that the derivative-based methods give similar variable rankings as entropy-based index and can thus be potentially used as a proxy for both variance-based and entropy-based distribution-type GSA.

翻译：基于分布的全局敏感性分析（GSA），例如基于方差和基于熵的方法，可以提供定量的敏感性信息。然而，这些方法的评估成本较高，因此仅限于低维问题。相比之下，基于导数的全局敏感性分析所需的模型评估次数少得多。已知基于导数的GSA与基于方差的总敏感性指数密切相关，但其与基于熵的度量之间的关系尚不明确。为填补这一空白，我们引入了一个基于对数导数的泛函，以证明基于熵和基于导数的敏感性度量之间存在紧密联系。特别地，我们给出了证明，类似于基于方差的GSA情况，基于熵和基于导数的重要性度量之间存在不等式关系。本文提供了分析验证和数值验证。实例表明，基于导数的方法能够给出与基于熵的指标相似的变量排序，因此有望作为基于方差和基于熵的分布型GSA的替代工具。