  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.
