In this paper, a local method of structure-borne noise source characterization is presented. It is based on measurements of transverse displacement and local structural operator knowledge and allows to localize and quantify sources without any need of boundary condition information. To fix the instability caused by measurement noise, the regularization step inherent to inverse problem is realized with a probabilistic approach, within the Bayesian framework. When a priori distributions about noise and sources are considered as Gaussian, the Bayesian regularization is equivalent to the well-known Tikhonov regularization. The optimization of the regularization is then performed by the Gibbs Sampling (GS) algorithm, which is part of Markov Chain Monte Carlo (MCMC) techniques. The whole probability of the regularized solution is inferred, providing access to confidence intervals. Both simulation and measurements of a beam excited by an harmonic point source are realized to validate this approach.