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. We found that the proposed new entropy proxy is equivalent to the proxy for variance-based GSA for linear functions with Gaussian inputs, but outperforms the latter for a river flood physics model with 8 inputs of different distributions. We expect the new entropy proxy to increase the variable screening power of derivative-based GSA and to complement Sobol'-index proxy for a more diverse type of distributions.

翻译：基于方差的Sobol'敏感性是全局敏感性分析（GSA）中最广为人知的度量之一。然而，对于某些具有特定分布的随机性（如高度偏斜分布或重尾分布），仅使用二阶中心矩无法充分描述其特性。基于熵的GSA能够考虑完整的概率密度函数，但由于估计困难而限制了其应用。本文提出了一种新颖的基于导数的条件熵上界，用于高效地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。为了克服微分熵作为敏感性指标存在负值的非理想问题，我们讨论了总效应熵及其代理的指数化处理。研究发现：对于具有高斯输入的线性函数，本文提出的新熵代理等同于基于方差的GSA代理；但在包含8个不同分布输入的河流洪水物理模型中，新熵代理的性能优于后者。我们预期这一新型熵代理能够增强基于导数的GSA的变量筛选能力，并补充Sobol'指数代理以适用于更多样化的分布类型。