Bayesian Estimation of the ETAS Model for Earthquake Occurrences

Abstract

ABSTRACT The epidemic-type aftershock sequence (ETAS) model is widely used in seismic forecasting. However, most studies of ETAS use point estimates for the model parameters, which ignores the inherent uncertainty that arises from estimating these from historical earthquake catalogs, resulting in misleadingly optimistic forecasts. In contrast, Bayesian statistics allows parameter uncertainty to be explicitly represented and fed into the forecast distribution. Despite its growing popularity in seismology, the application of Bayesian statistics to the ETAS model has been limited by the complex nature of the resulting posterior distribution, which makes it infeasible to apply to catalogs containing more than a few hundred earthquakes. To combat this, we develop a new framework for estimating the ETAS model in a fully Bayesian manner, which can be efficiently scaled up to large catalogs containing thousands of earthquakes. We also provide easy-to-use software that implements our method.