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Global sensitivity analysis aims at determining which uncertain inputparameters of a computational model primarily drives the variance of the outputquantities of interest. Sobol' indices are now routinely applied in thiscontext when the input parameters are modelled by classical probability theoryusing random variables. In many practical applications however, inputparameters are affected by both aleatory and epistemic (so-called polymorphic)uncertainty, for which imprecise probability representations have becomepopular in the last decade. In this paper, we consider that the uncertain inputparameters are modelled by parametric probability boxes (p-boxes). We proposeinterval-valued (so-called imprecise) Sobol' indices as an extension of theirclassical definition. An original algorithm based on the concepts of augmentedspace, isoprobabilistic transforms and sparse polynomial chaos expansions isdevised to allow for the computation of these imprecise Sobol' indices atextremely low cost. In particular, phantoms points are introduced to build anexperimental design in the augmented space (necessary for the calibration ofthe sparse PCE) which leads to a smart reuse of runs of the originalcomputational model. The approach is illustrated on three analytical andengineering examples which allows one to validate the proposed algorithmsagainst brute-force double-loop Monte Carlo simulation.

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