Run time optimisation with AUC-Score

[Arn-BAuA]

The method for the AUC-Score calculation runs very poorly. It would be great to implement an adaptive quadrature in C++ and include it as a submodule to substitute the current version of the calculation.

[Arn-BAuA]

Update: Upon researching the AUC-Score I found out, that the AUC-Score is identical to the Wilcoxon–Mann–Whitney test (Hanley, James A and McNeil, Barbara J: The meaning and use of the area under a receiver operating characteristic (ROC) curve. DOI: https://doi.org/10.1148/radiology.143.1.7063747). Computing the AUC-Score via quadrature from the ROC is in deed a bad idea. Not only does it introduce errors from the numeric integration, it also completely ignores the statistic errors that emerge from the sampling of the underlying distributions of normal and abnormal data. So instead of a quadrature error, like we are reporting at the moment, the correct way of reporting the error would be to use a statistic estimate for the variance like the one proposed by Qing Wang, Alexandria Guo (Qing Wang, Alexandria Guo: An efficient variance estimator of AUC and its applications
to binary classification: DOI: 10.1002/sim.8725). We will create a python version based on their work in the following days to evaluate AUC and the uncertainty for the AUC.