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The electroencephalogram (EEG) is one of the techniques used for the non-invasive diagnosis of patients suffering from epilepsy. EEG source localization identifies the neural activity, starting from measured EEG. This numerical localization procedure has a resolution, which is difficult to determine due to uncertainties in the EEG forward models. More specifically, the conductivities of the brain and the skull in the head models are not precisely known. In this paper, we propose the use of a non-intrusive stochastic method based on a polynomial chaos decomposition for quantifying the possible errors introduced by the uncertain conductivities of the head tissues. The accuracy and computational advantages of this non-intrusive method for EEG source analysis is illustrated. Further, the method is validated by means of Monte Carlo simulations.