Today, the probabilistic seismic hazard assessment (PSHA) community relies on stochastic models to compute occurrence probabilities for large earthquakes. Considerable efforts have been devoted to extracting information from long catalogs of large earthquakes based on instrumental, historical, archeological and paleoseismological data. However, the models remain only and insufficiently constrained by these rare single-slip event data. Therefore, the selection of the models and their respective weights necessarily involves ruling by a panel of experts. Since cumulative slip data with high temporal and spatial resolution are now available, we propose a new approach to incorporate these pieces of evidence of mid- to long-term fault behavior into PSHA: the Cumulative Offset-Based Bayesian Recurrence Analysis (COBBRA). For the Dead Sea Fault, our method provides weights to the competing recurrence and rupture models, allows time-independent models to be ruled out, and provides a means to compute the cumulative probability of occurrence for the next full-segment event reflecting all available data.