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

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.