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