Derivative-based global sensitivity measures and their link with Sobol sensitivity indices

TL;DR

This paper reviews derivative-based global sensitivity measures (DGSM), their connection to Sobol indices, and introduces bounds to estimate Sobol indices efficiently, especially for high-dimensional models.

Contribution

It provides a comprehensive survey of DGSM, new bounds linking DGSM to Sobol indices, and practical methods for estimating Sobol indices more efficiently.

Findings

DGSM are computationally cheaper than Sobol indices.

New bounds effectively estimate Sobol total sensitivity indices.

Illustrative examples demonstrate practical application of DGSM.

Abstract

The variance-based method of Sobol sensitivity indices is very popular among practitioners due to its efficiency and easiness of interpretation. However, for high-dimensional models the direct application of this method can be very time consuming and prohibitively expensive to use. One of the alternative global sensitivity analysis methods known as the method of derivative based global sensitivity measures (DGSM) has recently become popular among practitioners. It has a link with the Morris screening method and Sobol sensitivity indices. DGSM are very easy to implement and evaluate numerically. The computational time required for numerical evaluation of DGSM is generally much lower than that for estimation of Sobol sensitivity indices. We present a survey of recent advances in DGSM and new results concerning new lower and upper bounds on the values of Sobol total sensitivity indices. Using these bounds it is possible in most cases to get a good practical estimation of the values of Sobol total sensitivity indices. Several examples are used to illustrate an application of DGSM.