Global sensitivity indices for nonlinear mathematical models and their Monte Carlo estimates
Mathematics and Computers in Simulation - IMACS sponsored Special issue on the second IMACS seminar on Monte Carlo methods
Derivative based global sensitivity measures and their link with global sensitivity indices
Mathematics and Computers in Simulation
Design and Analysis of Simulation Experiments
Design and Analysis of Simulation Experiments
| Hi-index | 0.00 |
The estimation of variance-based importance measures (called Sobol' indices) of the input variables of a numerical model can require a large number of model evaluations. It turns to be unacceptable for high-dimensional model involving a large number of input variables (typically more than ten). Recently, Sobol and Kucherenko have proposed the derivative-based global sensitivity measures (DGSM), defined as the integral of the squared derivatives of the model output, showing that it can help to solve the problem of dimensionality in some cases. We provide a general inequality link between DGSM and total Sobol' indices for input variables belonging to the class of Boltzmann probability measures, thus extending the previous results of Sobol and Kucherenko for uniform and normal measures. The special case of log-concave measures is also described. This link provides a DGSM-based maximal bound for the total Sobol indices. Numerical tests show the performance of the bound and its usefulness in practice.