Question

For the ROC curve of True positive rate vs False positive rate, which of the following are true?
The curve is always concave (negative convex).
The curve is never concave.
The curve may or may not be concave.

Answer 1

true false false is the answrr

Answer 2

Statement 1 and 2 are false. Statement 3 is true.

1. The curve is always concave (negative convex) - False

An ideal observer's receiver operating characteristic curve must be convex that means its slope must decrease monotonically.

2. The curve is never concave - False

It can be concave, for example, when raw classifier scores are used the ROC curve has a dent or concavity. ROC concavities demonstrate locally sub-optimal behaviour of a classifier.

3. The curve may or may not be concave - True

In statistics, a ROC curve or a receiver operating characteristic curve is a graphical plot which illustrates the diagnostic ability of a binary classifier system. It is created by plotting the true positive rate or TPR against the false positive rate or FPR at various threshold settings.