Propagation of epistemic uncertainty in magnitude-frequency relations through PSHA using predictive distributions

The current practice of Probabilistic Seismic Hazard Analysis (PSHA) considers the inclusion of epistemic uncertainties involved in different parts of the analysis via the logic-tree approach. Given the complexity of modern PSHA models, numerous branches are needed, which in some cases leads to concerns regarding performance issues. We introduce the use of a magnitude exceedance rate which, following Bayesian conventions, we call predictive exceedance rate. This rate is the original Gutenberg-Richter relation after having included the effect of the epistemic uncertainty in parameter beta. The predictive exceedance rate was first proposed by Campbell but to our best knowledge is seldom used in current PSHA. We show that the predictive exceedance rate is as accurate as the typical logic-tree approach but allows for much faster computations, a very useful property given the complexity of some modern PSHA models.