  In this paper, we derive copula-based and empirical dependency models (DMs)
for simulating non-independent variables, and then propose a new way for
determining the distribution of the model outputs conditional on every subset
of inputs. Our approach relies on equivalent representations of the model
outputs using DMs, and an algorithm is provided for selecting the
representations that are necessary and sufficient for deriving the distribution
of the model outputs given each subset of inputs. In sensitivity analysis, the
selected representations allow for assessing the main, total and interactions
effects of each subset of inputs. We then introduce the first-order and total
indices of every subset of inputs with the former index less than the latter.
Consistent estimators of such indices are provided, including their asymptotic
distributions. Analytical and numerical results are provided using single and
multivariate response models.
