ABSTRACT
Chapter 2 was concerned exclusively with theoretical concepts in the development of ROC analysis. Thus we merely assumed the existence of a random vector X of measurements taken on individuals, each of which belonged to one of two populations P and N, together with a classification function S(X) that could be used to allocate any chosen individual to one of these populations. The mechanism for doing so was to relate the classification score s(x) of an individual having value x of X to a threshold t, and to allocate this individual to P or N according as the score exceeded or did not exceed t. Furthermore, if p(s|P) and p(s|N) denote the probability density functions of the classification scores pertaining to individuals coming from populations P and N, then the four fundamental quantities tp = p(s > t|P), fp = p(s > t|N), tn = p(s ≤ t|N), and fn = p(s ≤ t|P) governed much of the rest of the development.
