Fundamentals of Statistics contains material of various lectures and courses of H. Lohninger on statistics, data analysis and chemometrics......click here for more.  ## ROC Curve ROC curve of a classifier. The blue line indicates the resulting ROC values when varying the decision threshold of the classifier.
The Receiver Operating Characteristics, or ROC curve, is a diagram which plots the true positive rate (hit rate) against the false positive rate (false alarm rate), thus visualizing the trade-off between benefits (true positives) and costs (false positives) of a binary classifier. A perfect classifier will result in a point in the upper left corner of the ROC curve, which corresponds to a hitrate of 100% (all positive objects are found and classified as positive) and a false alarm rate of 0% (no negative object is classified as a positive one).

In the case the classification performance depends on a decision threshold, we may plot the ROC values of a classifier for a set of different thresholds. The resulting ROC curve (see figure at right) is a simple but effective means for determining the properties of the classifier. First of all we may determine the optimum threshold by searching the ROC value which shows the largest perpendicular distance to the diagonal.

Secondly, the area under the ROC curve (AUC) is a measure for the quality of the classifier. A classifier with no discriminating power yields a ROC curve which lies exactly on the diagonal. The higher the discriminating power the higher is AUC. The AUC can be interpreted as the probability of a positive value to be classified as positive.

 Hint: As the true positive rate is also called sensitivity and the false positive rate is equal to 1-specificity, the ROC diagram is sometimes called "sensitivity vs (1 - specificity) plot".