Multivariate sensitivity analysis and derivative-based global sensitivity measures with dependent variables

Highlights: • Generalized sensitivity indices of dependent input variables. • DGSM indices of dependent input variables. • Elementary effects of dependent input variables. • Spatio-temporal models, dynamic models. • Multivariate outputs. In this paper, we propose a new methodology for better assessing the single, overall and interactions contributions of dependent and/or correlated variables over the whole model outputs. Our methodology relies on our ability to extract a model that characterizes the dependency structures of any random vector. Such dependency model is then coupled with the initial model to perform uncertainty quantification, variance-based sensitivity analysis and derivative-based global sensitivity measures. Our methodology allows for defining the main-effect and total sensitivity indices of input(s) with the former index less than the latter. We provide derivative-based upper bounds of total indices, which can be used for screening dependent variables. We also extend Morris' methods to cope with dependent variables. For proposing such indices, we distinguish the case of the multivariate and/or functional outputs.