Precision and Recall
Two complementary metrics capturing how accurate a classifier's positive calls are and how many positives it finds.
Definition
Precision is the fraction of predicted positives that are truly positive: TP / (TP + FP). Recall (sensitivity) is the fraction of actual positives the model finds: TP / (TP + FN).
The F-beta score generalizes F1 by weighting recall more or less heavily than precision, letting the metric match the real cost balance of a task. Reporting a full precision-recall curve, rather than one operating point, gives a more complete picture under imbalance.
The choice of operating point is a business or safety decision, not a statistical one: a cancer screen favors recall to avoid missing disease, while a spam filter may favor precision to avoid discarding real mail. Because the trade-off is set by the decision threshold, reporting performance across the full range of thresholds, rather than at one point, gives decision-makers the information they actually need.
The F1 score is their harmonic mean, a single number balancing the two.
The trade-off
- Raising the decision threshold usually increases precision but lowers recall.
- Lowering it does the reverse.
- The right balance depends on the cost of false alarms versus misses.
Why it matters
Accuracy is misleading when classes are imbalanced; a detector for a rare event can score high accuracy by never predicting it. Precision and recall expose this, which is why they are preferred for rare-event detection.
Fusion connection
For flagging rare unstable states in simulated Hyperion discharges, Kronos favors high recall, accepting some false alarms so that genuine risks are not missed.