Relaciones de poder, los procesos cognitivos y el estado anímico de los niños /as en el aula.

The generation of an overall or full scale emulator that can be evaluated at all the locations investigated is challenging. There are many reasons that make this challenging. One of them is the spatial complications in the topography, where points located close to each other can have very different heights. Additionally, at some of the coastal locations, tsunami waves are unlikely to reach due to the elevation far inland. Furthermore, another issue that makes the full scale emulation challenging is the inversion of large matrices that is necessary for the generation process of GP emulators. To overcome these difficulties, a large number of separate emulators, one of each location, is generated, instead of a full scale one.

This approach is also followed by Spiller et al. [2014], where many statistical emulators are constructed simultaneously by considering only one map point at a time and fitting an em- ulator for the output at each point. The authors named these emulators “subemulators” and they described an automatic process that allows the process to be repeated in parallel for all the points, using only the initial set of computer model runs. Therefore, their approach is compu- tationally cheap and allows fast and flexible uncertainty quantification for multiple sources of uncertainty in probabilistic hazard mapping. Finally, they perform an assessment of each sub emulator using leave-one-out-tests.

Chapter 5. Cascadia study using VOLNA evaluations

a large number of gauges in Victoria area for the investigation in this section. The 40 inputs describing different seabed deformation cases, which have been used earlier in the analysis, are considered here as well. The first step is to remove all the gauges where water is not arriving. To do so, the choice of gauges was constrained only for ones that presenting at least 0.5m wave amplitude variations from maximum to minimum at some point in the whole time series. Furthermore, the gauges located more than 10 meters above the sea level, which are gauges in land and far away from the coast, are not taken into consideration. The total number of gauges at Victoria area satisfy these two criteria is 3023. Statistical emulation is applied to these gauges time series simultaneously. In order to get the best predictions and the process to be automatic, landmark registration is applied to the simulator evaluations, using an automatic selection process for the landmarks, and also PCs are used for the output regression functions in the emulation process.

As described earlier in Section 5.1.2, the first step is to generated the cubic B-splines with a general common smoothing parameter λ that is used for all the gauges. Different values of λ are tested for some gauges, and it is concluded that λ= 0.0001 works the best for most of the cases. The exact value of λ that is the best choice is hard to be obtained, due to the fact that the GCV curve is relatively flat around the minimum in most of the cases. Therefore, the choice of λ= 0.0001 for all the 3023 gauges is adequate. The next step in the analysis is the choice of landmarks. To do so, for each locations, two landmarks are selected automatically. The first one is the location of the first time each of the curve cross the horizontal axis from negative to positive. The second one is the location where each of the 40 time series reach the maximum amplitude.

Following the landmark registration, PCA is applied to the registered data and the first two principal components are selected, which are then used together with the mean value curve as output regression functions for the emulation. Moreover, the input regressors as well as the input and output covariance functions are selected, followed by the selection of the hyperpa- rameters, which is described in Section 3.1.1.2. An automatic procedure for the selection of hyperparameters is applied and therefore it is performed simultaneously for all the gauges. The selection of the input regression functions is given by Equation 5.6, whereas the input and out- put residuals covariance functions selection is shown in Equations 5.12 and 5.13, respectively. The correlation lengths selected are the ones that work the best for the two gauges investigated earlier, which are described in (5.14). The choices of functions and parameters are combined with the registered wave elevations to obtain statistical emulator predictions at all the gauges.

out of the 3023 gauges, since the process stops with an error for the rest of the gauges. The explanation for the errors is the selection of landmark points. Specifically, the automatic land- mark selection employed could not detect the specific landmarks at all of the gauges time series, resulting to an error. This prevents the process to continue to the generation of the statistical emulator. A more careful choice of landmarks or a better method of registration, such as con- tinuous registration, which does not require the selection of landmarks, could avoid these errors and result in successful statistical emulation for all the 3023 gauges. Nevertheless, the specific analysis in this sections presents some initial steps that can be further improved with better landmark registration. Unfortunately, due to the limited time, the improvements of this analysis did not take place at the end but it is going to be performed in the future.

Considering the emulators predictions at the 695 gauges, LOO diagnostics methods are ap- plied to validate them concluding that the predictions are satisfactory at almost all the locations. The RMSE and mean Credible Interval length are calculated for 22 locations, where the two of them are the ones with the maximum RMSE and mean Credible Interval length and the rest 20 are randomly selected, and their boxplots are presented in Figure 5.40. Also the maximum RMSE and mean CI length at all the 695 gauge are obtained and presented in Figure 5.41.

The location with the largest RMSE value as well as the largest mean CI length is the one presenting the worst emulator prediction and it is the gauge number 145. For this gauge, the LHD input points 20 and 24 give the largest RMSE and mean CI length, respectively. The leave- one-out diagnostic plots for the specific two inputs for gauge 145 are shown in Figure 5.42. On the other hand, the gauges 435 and 430 present the best emulation predictions, with the lowest RMSE and mean CI length, respectively. For both of these locations, the best predictions are obtained for input characteristics described by LHD number 7 and the corresponding LOO diagnostic plots are shown in Figure 5.43.

Therefore, it can be concluded that the application of statistical emulation for each location separately, without taking into consideration any spatial correlations between the gauges, and using an automatic process that can make this process simultaneous, can result in sufficiently reasonable predictions. This process can be improved further by a better choice of registration process. The generation of emulators for all the locations investigated can help in the perfor- mance of sensitivity and uncertainty analysis in the whole area.