  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.
