Global sensitivity analysis in the context of imprecise probabilities (p-boxes) using sparse polynomial chaos expansions.

• Global sensitivity analysis is extended to the context of imprecise probability theory (parametric p-boxes). • Imprecise Sobol' indices are defined and computed from a sparse polynomial chaos expansion (PCE) of the computational model. • The sparse PCE is built in an augmented space of input parameters and associated hyperparameters. • A smart experimental design using phantom points is devised to reduce the number of runs of the computational model. Global sensitivity analysis aims at determining which uncertain input parameters of a computational model primarily drives the output quantities of interest. Sobol' indices are now routinely applied in this context when the input parameters are modelled by classical probability theory using random variables. In many practical applications however, input parameters are affected by both aleatory and epistemic uncertainty. In this respect, imprecise probability theory have become popular in the last decade. In this paper, we consider that the uncertain input parameters are modelled by parametric probability boxes (p-boxes). We propose interval-valued (so-called imprecise) Sobol' indices as an extension of their classical definition. An original algorithm based on the concepts of augmented space, isoprobabilistic transforms and sparse polynomial chaos expansions is devised to allow for the computation of these imprecise Sobol' indices at extremely low cost. In particular, phantoms points are introduced to build an experimental design in the augmented space (necessary for the calibration of the sparse PCE) which leads to a smart reuse of runs of the original computational model. The approach is applied to three analytical and engineering examples which illustrate the efficiency of the algorithms against brute-force double-loop Monte Carlo simulation. Image, graphical abstract [ABSTRACT FROM AUTHOR]