The tuning of structural models to the experimental dynamic response entails the choice of a proper objective function. The goal of the so-called model updating process is the optimization of the chosen objective function, which measures the discrepancy between the experimental and simulated dynamic responses. This research focuses on the application of a non-parametric subspace-based objective function to the estimation of the modelling parameters of a beam-like structure. Differently from parametric optimization, non-parametric objective functions do not require the assessment of the modal parameters and descend from direct manipulation of the experimental and simulated data. The use of parametric optimization may lead to the discard of important information, which could be lost when extracting the modal parameters. Conversely, non-parametric optimization may store valuable information, which may lead to the estimation of both the stiffness and mass matrices even in the case of operational response, characterized by unknown excitation. In a second step, the research focuses on the quantification of the uncertainty of the estimand parameters following an elementary Bayesian approach. The authors attempt to estimate the probability density function of the parameters by isolating and quantifying two sources of uncertainties: the uncertainty of the structural model and that of the optimization method.