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In this note I study how the precision of a classifier depends on the ratio$r$ of positive to negative cases in the test set, as well as the classifier'strue and false positive rates. This relationship allows prediction of how theprecision-recall curve will change with $r$, which seems not to be well known.It also allows prediction of how $F_{\beta}$ and the Precision Gain and RecallGain measures of Flach and Kull (2015) vary with $r$.

The Effect of Class Imbalance on Precision-Recall Curves