MCMC-based Updating of an Epidemiological Temporal Aftershock Forecasting Model

The first few days elapsed after the occurrence of a strong earthquake and in the presence of an ongoing aftershock sequence are quite critical for emergency decision-making purposes. Epidemic Type Aftershock Sequence (ETAS) models are used frequently for forecasting the spatio-Temporal evolution of seismicity in the short-Term. In such a context, the forecasted seismicity usually makes reference to a 24-hour forecasting interval. Focusing the attention on clustering of events in time only, a robust seismicity forecast based on (a simplified version of) the ETAS model takes into account the joint probability distribution for the model parameters conditioned on the events already registered with the ongoing sequence. The advanced simulation procedures such as Markov Chain Monte Carlo simulation provide very efficient means of estimating the robust seismicity forecasts. In addition to the uncertainty in model parameters, the robust simulation-based forecasting of seismicity can also take into account the uncertainty in the sequence of events that are going to happen during the sampling interval. With regard to a specific application to the L'Aquila 2009 seismic sequence, the daily robust ETAS forecasts in the first ten days elapsed after the main event can predict the seismicity within plus/minus one standard deviation interval