## 4 Discussion
### Evaluation of the Models
The improvements can be attributable to the feature selection and data preprocessing step. Figure 7 shows SHAP analysis results, where the input features are displayed on the y-axis in descending order based on their contribution to the Vs prediction. The most influential feature appears at the top. The x-axis represents SHAP values, which quantify the contribution of each feature to the model's prediction. A positive SHAP value indicates that the feature increases the predicted Vs, whereas a negative SHAP value indicates a decrease in the predicted Vs. The SHAP values are represented by colored points that indicate the influence of the features on the model (Figure 7a). Each point reflects the impact of specific features on an observation from the entire database. The red color in the figure indicates high feature values while the blue color indicates low feature values. Positive SHAP values (red points) increase the Vs prediction while the negative SHAP \begin{table}
\begin{tabular}{c c c} \hline \hline
**Performance Metrics** & **Test Dataset** & **Train Dataset** \\ \hline \(R^{2}\) & 0.54 & 0.91 \\ IA & 0.84 & 0.97 \\ KGE & 0.65 & 0.82 \\ MSE & 3792 & 781 \\ RMSRE & 0.39 & 0.22 \\ MAE & 41 & 19.6 \\ MARE & 0.21 & 0.11 \\ MSRE & 0.15 & 0.05 \\ MBE & 1.12 & 0.13 \\ MaxARE & 3.30 & 3.95 \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Performance of XGBoost model on test and train dataset. Figure 6: Predictive performance of the XGBoost model: (**a**) scatter plots of predicted Vs versus measured Vs for the training and testing datasets; (**b**) residual scatter and histogram plots for training and testing datasets. value (blue points) decrease Vs prediction. For instance, for cone tip resistance (qc_mean), the red points predominantly on the positive side indicate higher qc_mean value generally increase Vs. On the other hand, the blue points on the negative side indicate lower qc_mean values generally decrease Vs. Interestingly, the instances of red points on the left or blue points on the right indicate a non-linear relationship between the feature and Vs. The global impact of features on Vs is shown by the mean absolute SHAP values of each feature (Figure 7b). Features with higher bar length indicate significant impact on the Vs. It can be observed that total overburden stress \(\sigma\),\(\
u\) is the most influential feature, followed by cone tip resistance and sleeve frictions. On the other hand, the depth and soil behavior type index have lower impact on Vs. It is important to note that less impactful features were removed from the model, and only these features were incorporated into the final model. The Bayesian GLM was fitted on the complete dataset using the final predictors identified through partial dependence analysis. It is important to note that the term \"predictors\" is more appropriate for the Bayesian GLM, while the term \"input features\" is suited for the ML models. In this study, both terms refer to the same geotechnical parameters. The model was developed using rstanarm package with four independent Markov chains, each consisting of 10,000 iterations, of which the first 1000 iterations were discarded as burn-in period. Weakly informative prior (normal prior \((0,2.5)\) for the intercept and coefficients, and an exponential prior \((\lambda=1)\) for the variance of the error term) were used. The performance of the model was evaluated using Rhat convergence diagnostic (evaluation of the agreement between between-chain and within-chain estimates for the model parameters), Monte Carlo Standard Error, MCSE (the ratio of standard deviation of the model parameters to the square root of the effective sample size), and trace plots of the parameters. Figure 8 illustrates the convergence of Rhat values across the first 6000 iterations (burn-in period excluded) for the model fitted using four independent Markov chains. As can be observed, Rhat values remained consistently close to one (0.996-1.016) across iterations for each model parameter. This indicates the effective convergence of Markov chains.