  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.
