Derivative based global sensitivity analysis and its entropic link

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.