The authors add probobilistic phase labels to the multiple-event joint probability function of Myers et al., 2007 that formerly included event locations, travel-time corrections, and arrival-time measurement precision. Prior information on any of the multiple-event parameters may be used. The phase-label model includes a null label that captures phases not belonging to the collection of phases under consideration. Using the Markov-Chain Monte Carlo method, samples are drawn from the multiple-event joint probability function to infer the posteriori distribution that is consistent with priors and the arrivaltime data set. Using this approach phase-label error can be accessed and phase-label error is propagated to all other multiple-event parameters. We test the method using a groundtruth data set of nuclear explosions at the Nevada Test Site. We find that posteriori phase labels agree with the meticulously analyzed data set in more than 97% of instances and the results are robust even when the input phase-label information is discarded. Only when a large percentage of the arrival-time data are corrupted does prior phase label information improve resolution of multiple-event parameters. Simultaneous modeling of the entire multiple-event system results in accurate posteriori probability regions for each multiple-event parameter.