  The Epidemic Type Aftershock Sequence (ETAS) model is one of the most
widely-used approaches to 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 on 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 which
implements our method.
