# Scenario Optimisation and Sensitivity Analysis for Safe Automated Driving Using Gaussian Processes
## 6 Results
### Probabilistic Sensitivity Analysis of Scenario Data Sets
#### 6.3.1 Sensitivity Analysis of the Pedestrian Step-Out Scenario  
As described above, the probabilistic SA measures are very important to evaluate the influence of the input parameters on the scenario outcome. Additionally, the SA would aid in simplifying the final model formulating the AV scenario. Reducing the dimensionality of the parameter space would be very practical in better visualising the performance boundary of the scenarios with a dimensionality larger than three. In this section, the probabilistic SA measures for the pedestrian step-out scenarios will be efficiently computed and illustrated using the GP-based method, as described in Section 4.2.  
For the pedestrian step-out scenario, it is not feasible to examine the main effects from a plot of all the executed concrete scenarios, as the dimensionality of parameters is larger than 3. Thus a probabilistic sensitivity analysis is here more appropriate than for a simple scenario as presented in Reference [8]. The main effects are shown in Figure 5 and discernibly linear, with parameter \(S_{1}\) having an opposite influence on the scenario outcome than \(S_{2}\) and \(d\). The almost horizontal lines of parameters \(SR\) and \(H\) and low values of their first-order sensitivity indices (c.f. Table 2) imply a negligible influence on the scenario outcome. This information can, for example, be used to change the sampling behaviour for these two parameters to be more conservative, as their effect on the scenario outcome is small. More dense sampling is however advised on \(S_{2}\) and \(d\) and especially \(S_{1}\), as it has the highest impact on the variability of the output.  
By comparing the total effect sensitivity indices with the first-order sensitivity indices in Table 2, it is evident that interaction effects between input parameters are largely negligible. Table 2 presents the SA indices to evaluate the sensitivity of the scenario outcome with respect to changes in the input parameters presented in Table 1.  
It is evident that'speed of ego car (\(S_{1}\))' and'speed of pedestrian stepping onto street (\(S_{2}\))' are the most influencing factors affecting the outcome of the pedestrian step-out scenario according to their variance contributions, 28% and 17.5%, respectively. It should be noted that SA indices reported in Table 2 are all computed based on 100 data points selected using the LHC sampling method. We can also say that 54.5% of total variance can be explained by the first-order interaction between (\(S_{1},S_{2}\)), which is very significant. In other words, we can say that the total variance of the scenario outcome can be explained based on \(S_{1}\), \(S_{2}\) and their first-order interaction. The estimated posterior mean and variance of the fitted GP to this data set were reported to be 0.83 and 0.028, respectively.  
Figure 5 and Table 2 illustrate the first order (\(S_{i}\)) and total effect (\(S_{T_{i}}\)) variance-based sensitivity indices for the input parameters. Using these sensitivity measures, we can similarly conclude that the outcome of the pedestrian step-out scenario is more sensitive to \(S_{1}\), \(d\) (distance between pedestrian and ego vehicle), and \(S_{2}\), consecutively. It seems the conclusions taken from these SA indices are slightly different from those taken from the main and the first-order interaction effects. We can argue that the interaction between the speeds of ego vehicle and pedestrian could be somehow represented in terms of the distance between pedestrian and ego car. Furthermore, these variance-based sensitivity indices suggest that both the sensor range and horizontal field-of-view of the sensor donot have a manoeuvresignificant impact on the outcome of the scenario (i.e., its minimum time-to-collision).