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I'm comparing two classification models by computing the area under ROC and Precision-Recall curves.
However sometimes one model is better with AU-ROC but worse in AU-PR, and other times it's better in AU-PR but worse in AU-ROC. (Outdated sentence, please see edit)
Based on that I made a conclusion based on my understanding on the AU-ROC and AU-PR, and I just want to make sure that my understanding/conclusions are corrects.
If one method is better in AU-ROC but worse in AU-PR, then the method is better in Recall but worse in Precision. So you should use this method when you want high recall.
If one method is better in AU-PR but worse in AU-ROC, then the method is better in Precision but worse in Recall. So you should use this method when you want high precision.
Are my understanding/conclusions correct? Precision-Recall tradeoff.
The case is the following: one model is always better in AU-ROC. While the other is always better in AU-PR.
So if my conclusions are incorrect, then what conclusion/s can one make from such a result? I'm interested in the conclusions of this because it allows me to make a rule to select each method. So if one method is always better in AU-ROC, then I would like to say that one should select the method if his priority is a high recall for example.