## 4 Discussion and Conclusions
The N-tests, M-test, R-test, and T-test were performed to evaluate the goodness of the models' results in the forecasting time interval \([T_{e},\,\,T_{e}+\Delta T]\) by comparison of the simulated results and observed seismicity. The number of the forecasted earthquakes was evaluated by the N-test and the results are shown in Figures 10 and A9 for both cases. In both cases, for the Anchorage sequence, a more accurate forecast for the number of earthquakes was accomplished by the ETAS model, while for two other sequences the OU law performed better. It should be noted as a result of the branching nature of the ETAS model, it shows a-wider confidence interval range compared to the OU law. The obtained results from the M-test demonstrate higher consistency in generating the distribution of the magnitudes for the ETAS model compared to the OU law for both cases, Figures 11 and A11. For the model comparison, the R-test was performed (Figure 12). The \(\alpha\) quantile score is higher than the thresholds representing the rejection of the OU hypothesis in favor of the ETAS model. The T-test results are given in Figure 13. The ETAS model performed better in case of the Denali and Kodiak sequences, however, the OU model was more accurate in estimating the rate and the corresponding forecasting performance in case of the Anchorage sequence in its early days. This is also evident when plotting the information gain both for the fixed forecasting time interval \(\Delta T=7\) days with varying training time intervals and in case of the fixed training time interval with varying forecasting time intervals (Figure 13c). The posterior predictive \(p\)-value test was performed to assess the fit of the posterior distribution of Bayesian models by comparison of the posterior predictive distribution and the observed data. In Figure 14 the results of Bayesian p-value analysis are given. They indicate that the forecasts based both on the ETAS model and OU formula are consistent in reproducing the maximum event during each corresponding forecasting time interval. The obtained results indicate that for the sequences analyzed the forecasting based on the ETAS model and the OU formula produce comparable results for shorter time intervals after the mainshocks. However, the EAST model is more realistic in terms of reproducing the seismicity on longer time scales. Moreover, the ETAS model performs better when the mainshock sequence is preceded by a well defined foreshock sequence [3]. The ETAS model typically performs better with increased number of events in the sequence. However, this is limited by the current earthquake catalogues which typically have relatively high level of completeness that results in fewer events. Conceptualization, M.S. and R.S. ; methodology, M.S. and R.S. ; software, M.S. and R.S. ; validation, M.S. and R.S. ; writing--original draft preparation, M.S. ; writing--review and editing, R.S. ; visualization, M.S. and R.S. ; supervision, R.S. ; project administration, R.S. ; funding acquisition, R.S. All authors have read and agreed to the published version of the manuscript. M.S. and R.S. would like to acknowledge the support from the UWO IDI grant. R.S. was partially supported by NSERC Discovery grant. Not applicable. The United States Geological Survey (USGS) search engine was used to extract the earthquake catalogue [[https://earthquake.usgs.gov/earthquakes/search/](https://earthquake.usgs.gov/earthquakes/search/)]([https://earthquake.usgs.gov/earthquakes/search/](https://earthquake.usgs.gov/earthquakes/search/)) (accessed on 18 December 2021). The United States Geological Survey (USGS), was used to obtain the Quaternary fault and fold database for the United States [33]. The mainshock focal mechanism was obtained from the USGS Moment Tensor catalogue [34; 35; 36]. The data analysis was performed using a computer code written in Matlab and can be requested from the author. The authors would like to thank [PERSON] and two other anonymous reviewers for their useful and constructive comments that helped to improve the paper.