## 4 Results
### Integrating the Complexity Index into Interval Estimation  
According to the methods outlined in Stage 4, interval prediction models were developed and evaluated with and without an integrated complexity index to achieve Objective 3.  
Monte Carlo dropout and bootstrapping were employed to generate interval predictions for project cost and contingency; these results are illustrated in Figures 4 and 5, respectively. Table 8 summarizes the _uncertainty accuracy_ of the two approaches. The performance of the Monte Carlo dropout methods, which yielded narrower intervals, showed less accuracy, with _uncertainty accuracy_ values of 60% for contingency prediction. Bootstrapping achieved a higher _uncertainty accuracy_ (80%) by capturing a wider range of uncertainty. This difference is visually evident in Figures 4a and 5a. The comparative analysis suggests that the narrower intervals produced by Monte Carlo dropout may have contributed to its lower prediction accuracy. While Monte Carlo dropout provides more precise estimates, its limited ability to capture a wider range of uncertainty may result in underestimating cost variability. On the other hand, bootstrapping's broader intervals allow for a more comprehensive representation of uncertainty, which translates into improved predictive reliability.  
\begin{table}
\begin{tabular}{c c c} \hline \hline
**Features** & **Value** & **Rank** \\ \hline Approved project estimate & 151,976.32 & 1 \\ Complexity index & 121,533.38 & 2 \\ Contract contingency & 46,223.72 & 3 \\ Starting year & 14,185.36 & 4 \\ Completion year & 6729.28 & 5 \\ Project type & 1650.03 & 6 \\ Project estimate & 803.49 & 7 \\ \hline \hline \end{tabular}
\end{table}
Table 7: Permutation feature results.  
Figure 3: Results of permutation feature importance.  
The subsequent integration of the complexity index markedly improved the performance of interval predictions for both the Monte Carlo dropout and bootstrapping approaches. Specifically, the _uncertainty accuracy_ of cost interval predictions using Monte Carlo dropout increased by nearly 27%, rising from 60% to 76% (see Table 8). This improvement indicates that incorporating project complexity allows Monte Carlo dropout to better capture the underlying variability in cost and contingency estimations. As shown in Figure 4, a greater number of actual values fell within the predicted intervals post-integration, reinforcing the complexity index's role in refining model performance. Similar  
Figure 4: Comparison of testing results of interval predictions using Monte Carlo dropout: before and after integrating complexity index. (**a**) Contingency interval predictions before integrating complexity index. (**b**) Contingency interval predictions after integrating complexity index.  
Figure 5: Comparison of testing results of interval predictions using bootstrapping: before and after integrating complexity index. (**a**) Contingency interval predictions before integrating complexity index. (**b**) Contingency interval predictions after integrating complexity index.  
improvements were observed in the bootstrapping models; the _uncertainty accuracy_ of the interval predictions increased from 80% to 88% after incorporating the complexity index, as Table 8 shows. In addition, as illustrated in Figure 5b, this improvement signifies that the integration of the complexity index increased the alignment between the predicted intervals and actual data points, underscoring its effectiveness in refining the models' predictive capability. Overall, these findings demonstrate that while bootstrapping provides a higher uncertainty accuracy, Monte Carlo dropout can yield competitive results when coupled with a complexity-based approach. The fact that integration of the complexity index improves the reliability of both interval predictions suggests that project complexity is a critical factor influencing cost contingency materialization.