Variance-based Sobol' sensitivity is one of the most well-known measures in global sensitivity analysis (GSA). However, uncertainties with certain distributions, such as highly skewed distributions or those with a heavy tail, cannot be adequately characterised using the second central moment only. Entropy-based GSA can consider the entire probability density function, but its application has been limited because it is difficult to estimate. Here we present a novel derivative-based upper bound for conditional entropies, to efficiently rank uncertain variables and to work as a proxy for entropy-based total effect indices. To overcome the non-desirable issue of negativity for differential entropies as sensitivity indices, we discuss an exponentiation of the total effect entropy and its proxy. Numerical verifications demonstrate that the upper bound is tight for monotonic functions and it provides the same input variable ranking as the entropy-based indices for about three-quarters of the 1000 random functions tested. We found that the new entropy proxy performs similarly to the variance-based proxies for a river flood physics model with 8 inputs of different distributions, and these two proxies are equivalent in the special case of linear functions with Gaussian inputs. We expect the new entropy proxy to increase the variable screening power of derivative-based GSA and to complement Sobol'-indices proxy for a more diverse type of distributions.

翻译：基于方差的Sobol'敏感性指标是全局敏感性分析中最著名的度量之一。然而，仅使用二阶中心矩无法充分表征某些分布（如高度偏态分布或重尾分布）的不确定性。基于熵的全局敏感性分析能够考虑完整的概率密度函数，但由于其难以估计，应用一直受限。本文提出了一种基于导数的条件熵上界新方法，可有效对不确定变量进行排序，并作为基于熵的总效应指标的代理指标。为解决微分熵作为敏感性指标可能出现的非期望负值问题，我们探讨了总效应熵及其代理指标的指数化处理。数值验证表明，该上界对于单调函数具有紧致性，在测试的1000个随机函数中，约四分之三的案例提供了与基于熵的指标相同的输入变量排序。研究发现，对于具有8个不同分布输入的河流洪水物理模型，新熵代理指标的表现与基于方差的代理指标相似，且在线性函数与高斯输入的特殊情况下两者等价。我们预期新熵代理指标将增强基于导数的全局敏感性分析的变量筛选能力，并为更广泛类型的分布提供对Sobol'指标代理的补充。