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Most binary classifiers work by processing the input to produce a scalarresponse and comparing it to a threshold value. The various measures ofclassifier performance assume, explicitly or implicitly, probabilitydistributions $P_s$ and $P_n$ of the response belonging to either class,probability distributions for the cost of each type of misclassification, andcompute a performance score from the expected cost.  In machine learning, classifier responses are obtained experimentally andperformance scores are computed directly from them, without any assumptions on$P_s$ and $P_n$. Here, we argue that the omitted step of estimating theoreticaldistributions for $P_s$ and $P_n$ can be useful. In a biometric securityexample, we fit beta distributions to the responses of two classifiers, onebased on logistic regression and one on ANNs, and use them to establish acategorisation into a small number of classes with different extremalbehaviours at the ends of the ROC curves.

Using theoretical ROC curves for analysing machine learning binary classifiers