Semiparametric Bayesian forecasting of SpatioTemporal earthquake occurrences

The Epidemic Type Aftershock Sequence (ETAS) model is a selfexciting point process which is used to model and forecast the occurrence of earthquakes in a geographical region. The ETAS model assumes that the occurrence of mainshock earthquakes follows an inhomogeneous spatial point process, with their aftershock earthquakes modelled via a separate triggering kernel. Most previous studies of the ETAS model have relied on point estimates of the model parameters due to the complexity of the likelihood function, and the difficulty in estimating an appropriate spatial mainshock distribution. In order to take estimation uncertainty into account, we instead propose a fully Bayesian formulation of the ETAS model which uses a nonparametric Dirichlet process mixture prior to capture the spatial mainshock process, and show how efficient parameter inference can be carried out using auxiliary latent variables. We demonstrate how our model can be used for medium-term earthquake forecasts in a number of geographical regions.