## 4 Discussion
### Validation of the Models  
The Bayesian GLM was evaluated using validation SCPT data from Hungary to assess its predictive performance. Figure 10 presents the comparison between the measured and predicted Vs values across varying depths. Figure 10a displays the mean predictions (blue diamonds) with 95% credible intervals (2.5-97.5%), along with the measured Vs values (red stars). The close alignment of the predicted mean values with the measured values  
Figure 8: Convergence diagnostic plot showing Rhat values against the number of iterations. Figure 9: Trace plots depicting the sampling dynamics and convergence behavior of each model parameter in the Bayesian GLM. \begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Parameters** & **Mean** & **STD** & **MCSE (\%)** & **Rhat** & **n\_eff** \\ \hline Intercept & 5.387 & 0.006 & 0.004 & 1.000 & 32,562 \\ qc\_mean & 0.079 & 0.010 & 0.007 & 0.999 & 19,341 \\ qc\_cv & 0.015 & 0.007 & 0.004 & 1.000 & 28,913 \\ fs\_mean & 0.092 & 0.010 & 0.007 & 1.000 & 19,305 \\ ov & 0.092 & 0.786 & 0.65 & 0.999 & 14,770 \\ Depth & 0.109 & 0.787 & 0.65 & 1.000 & 14,771 \\ \hline \hline \end{tabular}
\end{table} 
Table 5: MCMC diagnostics for the Bayesian GLM. across the entire depths demonstrates the model's accuracy and reliability. The lower plots (Figure 10b,c) provide a detailed analysis of predictions at a depth of 10 m (selected for illustration purpose only). The histogram (Figure 10c) shows the posterior distribution of Vs prediction at this depth. The blue curve represents the fitted probability density curve. It can be observed that the distribution follows lognormal distribution (attributable to data transformation during fitting the model). The vertical red arrow marks the measured value of Vs, while the blue arrows mark the 2.5% (left), mean prediction (middle), and 97.5% (right) credible interval. The 95% credible interval for this depth (142-627 m/s) encompasses the measured value (258 m/s). Additionally, Figure 10b summarizes the predictors used for this prediction. In general, the results demonstrate robustness of Bayesian GLM in capturing uncertainty and its capability to provide reliable predictions for Vs across varying depths. The use of credible intervals and posterior distributions further underscores its significance in quantifying prediction reliability. In Figure 11, the predictive performance of the XGBoost model was compared against measured Vs values and Bayesian GLM predictions for the same validation dataset. The analysis involved comparing the outputs of the XGBoost model and the mean predictions of the Bayesian GLM across the Vs profile depth. For the Bayesian GLM, the 95% credible interval was also included to capture the uncertainty in the Vs predictions. It can be observed that both the XGBoost model's predictions and the Bayesian GLM's mean predictions align well with the measured Vs values across depths. Notably, the XGBoost model's predictions fall within the 95% credible interval across the entire depth, showcasing its excellent  
Figure 10: Predictive performance Bayesian GLM, (**a**) comparison of predicted Vs against measured Vs, (**b**) predictor values at 10 m depth and obtained results, and (**c**) histogram of predicted Vs values at 10 m depth. predictive performance of the Vs. The uncertainty captured by the Bayesian GLM (the credible intervals) is crucial for site response analysis, where accounting for variability in Vs is essential. These intervals can be used to conduct sensitivity studies by varying the Vs profile within the predicted bounds, enabling the estimation of a range of possible seismic responses for the site. This approach minimizes the risk of underestimating hazards and provides a foundation for prioritizing additional site investigations in areas with significant uncertainty. Furthermore, to quantitatively assess the predictive performance of the two models, linear correlation coefficients \((r)\) were computed.