3.3 ROC Analysis
Interestingly, according to (2.8), (2.11), and (3.5), no matter what the type of detector is, its detector statistics always turns out to be the likelihood ratio test (LRT). In other words, all the Bayes, minimax, or Neyman–Pearson detectors can be shown to have the same functional form determined by LRT. Nevertheless, NP detectors are the most practical detectors in real applications since they do not require prior knowledge of the cost function and probabilities of hypotheses that are generally unknown or difficult to obtain in practice. Instead, the performance is evaluated based on the four decisions described in Section 3.1 but with general descriptive terms given in the following:
As per the above decisions, ...
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