In recent years, cases of unexplained, elevated levels of radioactive particles have demonstrated an increasing need for efficient and robust source localization methods. In this study, a Bayesian method for source localization is developed and applied to two cases. First, the method is validated against the European tracer experiment (ETEX) and then applied to the still unaccounted for release of Ru-106 in the fall of 2017. The ETEX dataset, however, differs significantly from the Ru-106 dataset with regard to time resolution and the distance from the release site to the nearest measurements. Therefore, sensitivity analyses are conducted in order to test the method's sensitivity to these parameters. The analyses show that the resulting source localization depends on both the observed temporal resolution and the existence of sampling stations close to the source. However, the method is robust, in the sense that reducing the amount of information in the dataset merely reduces the accuracy, and hence, none of the results are contradictory. When applied to the Ru-106 case, the results indicate that the Southern Ural region is the most plausible release area, and, as hypothesized by other studies, that the Mayak nuclear facility is the most likely release location.