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

A model function f(x1,…,xn) defined in the unit hypercube Hn with Lebesque measure dx=dx1…dxn is considered. If the function is square integrable, global sensitivity indices provide adequate estimates for the influence of individual factors xi or groups of such factors. Alternative estimators that require less computer time can also be used. If the function f is differentiable, functionals depending on ∂f/∂xi have been suggested as estimators for the influence of xi. The Morris importance measure modified by Campolongo, Cariboni and Saltelli μ* is an approximation of the functional μi=∫Hn∂f/∂xidx.