Distributions of Outputs Given Subsets of Inputs and Dependent Generalized Sensitivity Indices

Better understanding mathematical and numerical models often requires investigating the impacts of inputs on the model outputs, as well as interactions. Quantifying such effects for models with non-independent input variables (NIVs) relies on conditional distributions of the outputs given every subset of inputs. In this paper, by firstly providing additional dependency models of NIVs, functional outputs are composed by dependency models (yielding equivalent representations of outputs) to derive distributions of outputs conditional on inputs. We then provide an algorithm for selecting the necessary and sufficient equivalent representations that allow for obtaining all the conditional distributions of outputs given every subset of inputs, and for assessing the main, total, and interaction effects (i.e., indices) of every subset of NIVs. Unbiased estimators of covariances of sensitivity functionals and consistent estimators of such indices are derived by distinguishing the case of the multivariate and/or functional outputs, including dynamic models. Finally, analytical results and numerical results are provided, including an illustration based on a dynamic model.