I have come across two different terms regarding Area Under Curve (AUC):
Are they talking about the same things?
ROC AUC is the area under the curve where x is false positive rate (FPR) and y is true positive rate (TPR).
PR AUC is the area under the curve where x is recall and y is precision.
recall = TPR = sensitivity. However precision=PPV $\neq$ FPR.
So these are very different curves.
Are they talking about the same things?
Not really. Both are technically evaluating "discrimination" as opposed to "calibration".
If not, do they share similar values for all possible datasets?
No
If still not, an example of dataset where ROC AUC and AUPRC strongly disagrees would be great.
An example would be most imbalanced datasets. PPV depends on the prevalence, so it would disagree with the TPR/FPR of the ROC curve in instances, for example, with low prevalence.
This might help (I think the numbers add up, but not certain, but it should show the difference between PPV and FPR):
Consider FPR = 1-specificity = $1 - \dfrac{TN}{TN+FP}$
The False positive rate might be low. In other words, relative to the TN, there are few FP. Consider a dataset with 1000 TN and 50 TP. Even if the algorithm misclassifies 50 FP, the FPR is just 1 - 1000/(1000+50). So the area under the ROC will be high, assuming good sensitivity.
However, now consider
PPV = $\dfrac{TP}{TP+FP}$
Assume we get every positive case correct, but also have the FP from above. In the case above, we have PPV = 50/ (50+50) = 0.5!
Hence the area under the precision recall would be very low. So in a sense PPV is affected by the absolute number of FP. FPR is affected just by the number of FP relative to the number of TN.
