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    $\begingroup$ I believe the slide is correct. If you use two different decision procedures with two different thresholds and then take a randomized decision, you will get a convex combination which will give a point lying in between the two. This point may be above both (!) of the curves at the same false positive rate. This is because the threshold used for each procedure is different at that point. $\endgroup$ Commented May 15, 2012 at 18:54
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    $\begingroup$ So the A and B in the convex combination is different from the A and B that are chosen individually to at that false positive rate. I just think the diagram was confusing as I did not see that A and B were selected from a family of classifiers. $\endgroup$ Commented May 15, 2012 at 19:11
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    $\begingroup$ Yes, the diagram is a bit confusing, as is the surrounding text! It took me a few minutes to unravel it. You fix two decision procedures, from each curve, say at the lower "hump" for the $A$ curve and upper hump for $B$ curve. This defines a rule for each. Then, the randomized rule is to flip a coin and take the decision from the corresponding classifier. This yields a new rule with different TP and FP rates from both of them giving the convex combination shown. (NB: To get even a single ROC curve at all, one needs a parametrized family of classifiers.) $\endgroup$ Commented May 15, 2012 at 19:18
  • $\begingroup$ I believe that this answer is the correct, appended with cardinal's comment! Getting out of the intersection area might happen, but it's not a method. I've found the original paper from the guy who invented this method, and it explains it very well! bmva.org/bmvc/1998/pdf/p082.pdf $\endgroup$ Commented May 19, 2012 at 12:54
  • $\begingroup$ @zsero: I believe that even Michael will acknowledge that this answer was based on the understanding of the diagram at the time the answer was posted and his interpretation of it has changed since the comments and other answer appeared. Just as the figure depicts, one can achieve via randomization any point on any line between a point on the first curve and a point on the second even if the resulting true positive rate dominates the other two curves for a given false positive rate. $\endgroup$ Commented May 20, 2012 at 14:56