Derivative-based generalized sensitivity indices and Sobol’ indices

Abstract

In uncertainty quantification, multivariate sensitivity analysis (MSA), including variance-based sensitivity analysis, and derivative global sensitivity measure (DGSM) are widely used for assessing the effects of input factors on the model outputs. While MSA allows for identifying the order and the strength of interactions among inputs, DGSM provides only a global effect of inputs by making use of model derivatives. It is interesting to combine the advantages of both approaches and to come up with generalized sensitivity indices (GSIs) from MSA based on model derivatives. First, we derive the mathematical expressions of the total effect and total-interaction effect functionals based on derivatives. Second, we construct minimum variance unbiased estimators (MVUEs) of the total-effect and total-interaction effect covariance matrices, and third, we provide the estimators of the total and total-interaction GSIs as well as their consistency and asymptotic normality. Finally, we demonstrate the applicability of these new results by means of simulations.