# Receiver operating characteristic

## Diagnostic plot of binary classifier ability / From Wikipedia, the free encyclopedia

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A **receiver operating characteristic curve**, or **ROC curve**, is a graphical plot that illustrates the performance of a binary classifier model (can be used for multi class classification as well) at varying threshold values.

The ROC curve is the plot of the true positive rate (TPR) against the false positive rate (FPR) at each threshold setting.

The ROC can also be thought of as a plot of the statistical 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 false positive rate.

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 $-\infty$ 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.

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