On dependent generalized sensitivity indices and asymptotic distributions

In this paper, we propose a novel methodology for better performing uncertainty and sensitivity analysis for complex mathematical models under constraints and/or with dependent input variables, including correlated variables. Our approach allows for assessing the single, overall and interactions effects of any subset of input variables, that account for the dependencies structures inferred by the constraints. Using the variance as importance measure among others, we define the main-effect and total sensitivity indices of input(s) with the former index less than the latter. We also derive the consistent estimators and asymptotic distributions of such indices by distinguishing the case of the multivariate and/or functional outputs, including spatio-temporal models and dynamic models.