A new derivative based importance criterion for groups of variables and its link with the global sensitivity indices

A new derivative based criterion τyτy for groups of input variables is presented. It is shown that there is a link between global sensitivity indices and the new derivative based measure. It is proved that small values of derivative based measures imply small values of total sensitivity indices. However, for highly nonlinear functions the ranking of important variables using derivative based importance measures can be different from that based on the global sensitivity indices. The computational costs of evaluating global sensitivity indices and derivative based measures, are compared and some important tests are considered.