The problem of selecting parameters for stochastic model updating is one that has been studied for decades, yet no method exists that guarantees the ‘correct’ choice. In this paper, a method is formulated based on global sensitivity analysis using a new evaluation function and a composite sensitivity index that discriminates explicitly between sets of parameters with correctly-modelled and erroneous statistics. The method is applied successfully to simulated data for a pin-jointed truss structure model in two studies, for the cases of independent and correlated parameters respectively. Finally, experimental validation of the method is carried out on a frame structure with uncertainty in the position of two masses. The statistics of mass positions are confirmed by the proposed method to be correctly modelled using a Kriging surrogate.