The Effect of Class Imbalance on Precision-Recall Curves

In this note, I study how the precision of a binary classifier depends on the ratio $r$ of positive to negative cases in the test set, as well as the classifier's true and false-positive rates. This relationship allows prediction of how the precision-recall curve will change with $r$⁠, which seems not to be well known. It also allows prediction of how $Fβ$ and the precision gain and recall gain measures of Flach and Kull (2015) vary with $r$⁠.