# An Earthquake Early Warning Method Based on Bayesian Inference
## 6 Discussion and Conclusions  
In this paper, the 2014 \(M_{\rm j}=4.3\) earthquake in Mt. Fuji, Japan (14 data points), and the 2017 \(M_{\rm j}=5.5\) earthquake in Ibaraki, Japan (54 data points), were selected for the experimental analysis. Figure 7 displays the earthquake epicenters and the distribution of stations. The data of the first-three-second P- wave collected via 68 stations were selected to estimate the magnitude and PGV, and the earthquake hazard was predicted. The values obtained with the Bayesian-inference-based prediction method and the traditional fitting method are substituted into the discriminative model in this paper. Figure 8 presents the distribution of all seismic hazard discrimination results. Table 1 shows the missed and false alarms of the Bayesian inference and traditional approaches. Figure 6: Comparison of true PGV with conventional fitted predictions (a) and Bayesian-inference-based predictions (b). Figure 7: Distribution of epicenter stations for magnitudes \(M\)43.3 (a) and \(M\)j5.5 (b). Available online: www.kyoshin.bosai.go.jp (accessed on 6 July 2022). Figure 8 and Table 1 reveal that both the Bayesian-inference-based prediction method and the traditional fitting method suffer from underreporting and misreporting. An underprediction indicates that the estimated magnitude or PGV is smaller than the threshold and no earthquake alarm is issued, while actually the magnitude and PGV are greater than the threshold and an alarm should be issued. A false- prediction denotes that the estimated magnitude and PGV exceed the threshold and an earthquake alarm is issued, while actually the magnitude or PGV is smaller than the threshold and an alarm should not be issued. In the current 68 experimental results, the prediction method based on Bayesian inference has a miss rate of 2.94% and a false alarm rate of 5.88%; the conventional fitting method has a miss rate of 4.41% and a false alarm rate of 16.18%. The results are as follows: (1) The probabilistic algorithm founded on the predictive model of the magnitude from the average period (\(\tau_{c}\)) and PGV from the displacement amplitude (\(P_{d}\)) from the initial 3 s of the P wave is able to provide a fast and accurate estimation of the final magnitude and location. \begin{table}
\begin{tabular}{c c c c c} \hline \hline  & \multicolumn{2}{c}{**Missed Alarm**} & \multicolumn{2}{c}{**False Alarm**} \\ \cline{2-5}  & \multicolumn{1}{c}{**Number of**} & \multicolumn{1}{c}{**Nissed**} & \multicolumn{1}{c}{**Number of**} & \multicolumn{1}{c}{**False Alarm**} \\  & \multicolumn{1}{c}{**Missed**} & \multicolumn{1}{c}{**Alarm Rate**} & \multicolumn{1}{c}{**False Alarms**} & \multicolumn{1}{c}{**Rate**} \\ \hline Bayesian prediction method & 2 & 2.94\% & 4 & 5.88\% \\ \hline Traditional fitting method & 3 & 4.41\% & 11 & 16.18\% \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Comparison of missed and false alarms of the experimental results of the two methods. Figure 8: Comparison of the results obtained from the Bayesian-inference-based prediction methods (**a**,**c**) and the traditional fitting methods (**b**,**d**) with the true discriminant results. (2) The Bayesian inference approach for the earthquake hazard discrimination model has a 2.94% miss rate and a 5.88% false alarm rate, which is lower than that of the traditional fitting method, thus increasing the accuracy and reliability of earthquake hazard estimation. In this paper, a dual-parameter warning method of earthquake magnitude and PGV based on Bayesian inference is proposed to classify earthquake hazards into four levels. The results effectively improve the accuracy and reliability of early warning information. According to the real-time magnitude and PGV conditions, the \(\tau_{c}\) and \(P_{d}\) of the first-three-second P-wave are fitted to the magnitude and PGV, respectively, and the empirical prediction formula is obtained.