Close the boundary around exact threshold bookkeeping.
Compare the two threshold views
Threshold 1/2 marks A and B as positive. Threshold 3/4 marks only A as positive.
t = 1 / 2 ⇒ A , B ; t = 3 / 4 ⇒ A t=1/2\Rightarrow A,B;\quad t=3/4\Rightarrow A t = 1/2 ⇒ A , B ; t = 3/4 ⇒ A Decision Thresholds Exactly Exact score rows under two stated thresholds. same scored rows under two thresholds threshold 1/2 score line, threshold 1/2 0 1 t=1/2 A 4/5 B 3/5 C 2/5 D 1/5 predictions at 1/2 row y score pred A 1 4/5 1 B 0 3/5 1 C 1 2/5 0 D 0 1/5 0 confusion grid at 1/2 cell count TP 1 FP 1 FN 1 TN 1 threshold 3/4 score line, threshold 3/4 0 1 t=3/4 A 4/5 B 3/5 C 2/5 D 1/5 predictions at 3/4 row y score pred A 1 4/5 1 B 0 3/5 0 C 1 2/5 0 D 0 1/5 0 confusion grid at 3/4 cell count TP 1 FP 0 FN 1 TN 2 same four scored rows; rule is score at least threshold does not claim: NOT best threshold; NOT accuracy guarantee NOT future performance; NOT calibration; NOT fairness NOT safety; NOT generalization; NOT probability truth
No threshold winner claim
This comparison shows exact bookkeeping under two stated thresholds. It does not choose a threshold winner.
bookkeeping under stated thresholds \text{bookkeeping under stated thresholds} bookkeeping under stated thresholds Decision Thresholds Exactly Exact score rows under two stated thresholds. same scored rows under two thresholds threshold 1/2 score line, threshold 1/2 0 1 t=1/2 A 4/5 B 3/5 C 2/5 D 1/5 predictions at 1/2 row y score pred A 1 4/5 1 B 0 3/5 1 C 1 2/5 0 D 0 1/5 0 confusion grid at 1/2 cell count TP 1 FP 1 FN 1 TN 1 threshold 3/4 score line, threshold 3/4 0 1 t=3/4 A 4/5 B 3/5 C 2/5 D 1/5 predictions at 3/4 row y score pred A 1 4/5 1 B 0 3/5 0 C 1 2/5 0 D 0 1/5 0 confusion grid at 3/4 cell count TP 1 FP 0 FN 1 TN 2 same four scored rows; rule is score at least threshold does not claim: NOT best threshold; NOT accuracy guarantee NOT future performance; NOT calibration; NOT fairness NOT safety; NOT generalization; NOT probability truth
The honest boundary
This is exact threshold arithmetic only; it does not claim: NOT best threshold; NOT accuracy guarantee; NOT future performance; NOT calibration; NOT fairness; NOT safety; NOT generalization; NOT probability truth.
same rows; exact threshold bookkeeping \text{same rows; exact threshold bookkeeping} same rows; exact threshold bookkeeping Decision Thresholds Exactly Exact score rows under two stated thresholds. same scored rows under two thresholds threshold 1/2 score line, threshold 1/2 0 1 t=1/2 A 4/5 B 3/5 C 2/5 D 1/5 predictions at 1/2 row y score pred A 1 4/5 1 B 0 3/5 1 C 1 2/5 0 D 0 1/5 0 confusion grid at 1/2 cell count TP 1 FP 1 FN 1 TN 1 threshold 3/4 score line, threshold 3/4 0 1 t=3/4 A 4/5 B 3/5 C 2/5 D 1/5 predictions at 3/4 row y score pred A 1 4/5 1 B 0 3/5 0 C 1 2/5 0 D 0 1/5 0 confusion grid at 3/4 cell count TP 1 FP 0 FN 1 TN 2 same four scored rows; rule is score at least threshold does not claim: NOT best threshold; NOT accuracy guarantee NOT future performance; NOT calibration; NOT fairness NOT safety; NOT generalization; NOT probability truth