GNGTS 2016 - Atti del 35° Convegno Nazionale

GNGTS 2016 S essione A matrice 53 Fig. 1 – Comparison between the observed and the expected daily number of events for the first 20 days of the sequence (August 24 - September 15) and for MF = 2.5 (panel a), 3.0 (panel b) and 4.0 (panel c). Panel d is a zoom for the first 3 days and for MF = 3.0. Blue points, black line and red lines mark the observations, the median forecasts and the 95% confidence bounds of forecasts, respectively. Fig. 2 – Parameters sensitivity analysis for the ETAS model. The plot compares observations and forecasts for MF = 2.5 and for the first 3 days of the sequence (August 24-27). Blue points, black line and red lines mark the observations, the median forecasts and the forecast given by the best model, respectively (The last two forecasts almost overlap). The 95% confidence bounds of forecasts are marked by the dotted black line. interval, uninterruptedly in the first three days. After this period, the observations (blue points) and the median forecasts (black line) overlap. These results improve for larger values of MF, for which the period of underestimation is smaller (Fig. 1). Previous results do not depend on the length of the forecast interval D i . None significant difference is found for D i equal to 3 hours, 1 day and 1 week, in the first 3 days of the sequence. A second check consists in quantifying the sensitivity of the model to uncertainty on model parameters (including the background spatial distribution). Specifically, Fig. 2 shows the variation of the expected number of events, by considering the uncertainty on parameters. These calculations include the actual time history, up to the end of the forecast interval. The calculations are done for interval times of 1 day, updated each hour, and for MF=2.5, by integrating the conditional intensity of the ETAS model (Lombardi, 2015). As Fig. 2 shows, the parameter sensitivity of the model is negligible. Some considerations on the improving of the ETAS model. Previous analysis shows that the ETAS model is able to describe the sequence, but for the first hours/days, due to the incompleteness of data. Clearly, the ETAS model has poor predictive ability before the main event. The probability of having an