I just finished reading this discussion. They argue that PR AUC is better than ROC AUC on imbalanced dataset.
For example, we have 10 samples in test dataset. 9 samples are positive and 1 is negative. We have a terrible model which predicts everything positive. Thus, we will have a metric that TP = 9, FP = 1, TN = 0, FN = 0.
Then, Precision = 0.9, Recall = 1.0. The precision and recall are both very high, but we have a poor classifier.
On the other hand, TPR = TP/(TP+FN) = 1.0, FPR = FP/(FP+TN) = 1.0. Because the FPR is very high, we can identify that this is not a good classifier.
Clearly, ROC is better than PR on imbalanced datasets. Can somebody explain why PR is better?