Receiver operating characteristic

A receiver operating characteristic curve, or ROC curve, is a graphical plot that illustrates the diagnostic ability of a binary classifier system as its discrimination threshold is varied. The ROC curve is the plot of the true positive rate (TPR) against the false positive rate (FPR), at various threshold settings. The ROC can also be thought of as a plot of the power as a function of the Type I Error of the decision rule (when the performance is calculated from just a sample of the population, it can be thought of as estimators of these quantities). The ROC curve is thus the sensitivity or recall as a function of fall-out. Given the probability distributions for both true positive and false positive are known, the ROC curve is obtained as the cumulative distribution function (CDF, area under the probability distribution from to the discrimination threshold) of the detection probability in the y-axis versus the CDF of the false positive probability on the x-axis. ROC analysis provides tools to select possibly optimal models and to discard suboptimal ones independently from (and prior to specifying) the cost context or the class distribution. ROC analysis is related in a direct and natural way to cost/benefit analysis of diagnostic decision making. There are a large number of synonyms for components of a ROC curve. They are tabulated on the right. The true-positive rate is also known as sensitivity, recall or probability of detection. The false-positive rate is also known as probability of false alarm and equals (1 − specificity). The ROC is also known as a relative operating characteristic curve, because it is a comparison of two operating characteristics (TPR and FPR) as the criterion changes. The ROC curve was first developed by electrical engineers and radar engineers during World War II for detecting enemy objects in battlefields, starting in 1941, which led to its name ("receiver operating characteristic"). It was soon introduced to psychology to account for perceptual detection of stimuli.