ROC Curve and AUC: the Mass Above the Diagonal

A classifier gives every example a score. Here negative examples score like a standard normal, on the back wall in red, and positive examples score like a normal shifted by d, on the left wall in blue.

Pick a threshold tau and call everything above it positive. The blue tail beyond tau is the true positive rate; the red tail beyond tau is the false positive rate.

The rest of the narration is in the book's Companion.