False Positive/False Negative

A false positive is an alert raised on a legitimate case. A false negative is a fraudulent case that went undetected. Both have a cost, but not of the same nature: the false negative costs a direct loss, the false positive costs a lost customer and analyst time, a friction that appears in no fraud figure. The essential point is that they move in opposite directions: tightening a threshold reduces false negatives and mechanically increases false positives. There is therefore no optimal setting in absolute terms, only a trade-off to be made explicitly, measured by precision and recall rather than by a detection rate on its own.