Innovative probabilistic model for assessing earthquake rupture occurrence. The model accounts for the complexity of time and space interactions of ruptures. The rupture occurrence is modeled as a time-varying Multivariate Bernoulli according to the last rupture at different locations of the fault. The likelihood of rupture propagation is accounted by a spatial correlation model. This model resolves the inconsistency problem of current methodologies noticed in the time-dependent earthquake hazard estimation of California. The model was tested on the subduction zone of Peru, and it closely matched the average release of energy and the histogram of the earthquake magnitudes on the fault (see figure at the right).