ROCkurve

The ROCkurve (also known as the ROC curve) is a graphical representation used to evaluate the performance of a binary classifier across threshold settings. The curve plots the true positive rate (sensitivity) on the vertical axis against the false positive rate (1 − specificity) on the horizontal axis. To construct it, one computes TPR and FPR for a range of decision thresholds using the model's predicted scores or probabilities.

The area under the ROCkurve (AUC) is a summary statistic that measures discriminative ability. An AUC of 1 indicates perfect discrimination, while 0.5 corresponds to random chance. The AUC can be interpreted as the probability that a randomly chosen positive example is ranked higher than a randomly chosen negative one by the classifier.

ROC curves are used to compare models and to select operating points by trading off sensitivity and specificity. They are common in medicine and radiology, as well as in machine learning and finance. Variants and extensions include partial AUC, confidence intervals via bootstrapping, and calibration analysis. In imbalanced datasets, precision-recall curves may be more informative about positive class performance.

Limitations: The ROC curve does not reflect class prevalence or calibration of predicted probabilities, and AUC can be misleading if the costs of false positives and false negatives differ substantially.