I understand precision at k and recall at k.  It is a more useful metric for evaluating the success of a binary classifier when the positive class is overwhelmingly out-weighed by the negative class.I'm wondering how to choose an appropriate k value.  According to resources like this the recall at k is bounded by the number of positive examples, so it is not a useful metric to use when evaluating the success of severely imbalanced classes.  It also seem to me like this:  Precision at K is also limited by the number of positive examples at K.  Saw we have 100 examples total, and only 3 are positive examples.  Say we rank these   Scenario 1: we choose k=10.  Then, the precision at K can at most be 3/10 = 0.3. And, the recall at k will be 0.03 because there are 3 in the entire dataset of 100.Scenario 2: we choose k=3.  Then, the precision at K would be 3/3 = 1.0 !!!And, the recall at k will STILL be 3/100 = 0.03.Even though our binary classifier is performing perfectly, it's perfect performance only is reflected when we choose k=3?  So, my question how do I choose K correctly?
How do I pick K for precision at K and recall at K?
accuracy;binary;classifier