False-positive and false-negative costs are asymmetric

What it is

When a sensor cuts a continuous signal into “happened / did not,” it can err in two ways. A false positive treats a non-event as an event; a false negative treats an event as nothing. The two costs are almost never equal: a lamp that lights by mistake is annoyance; a fall alarm that stays silent can be harm. Asymmetry is a loss structure, not symmetric error inside an accuracy formula.

Why it happens

Expected loss is each error probability times its own cost, summed. Accuracy and F1 count the two errors as the same species, which silently assumes equal cost. That assumption is especially false on physiological channels: one extra “too stressed” intervention from EDA costs a nuisance; missing a real clinical event lives in another unit. An ROC curve only lists achievable tradeoffs; it does not pick the operating point—the loss matrix does. User-side asymmetry also has direction: false positives spend attention and trust, false negatives spend safety or task success, and a single “error rate” cannot net them.

Studying it

Signal detection theory plots false-alarm and miss rates separately and chooses the operating point with a payoff matrix rather than a lone correctness score. Factors: event base rate, and both errors priced in money or time. Outcomes: expected cost under a given loss, disablement rate, and task failures from misses. A lab score that fines each error one point flattens the asymmetry. Field work must also measure base rate: even with high specificity, positive predictive value can be poor for rare events, and the absolute count of false positives is inflated by that rate.

Where it stops holding

The two costs are occasionally close: decorative adaptation in a game, a preview that undoes immediately. As soon as the outcome is irreversible or someone else’s safety is involved, asymmetry widens. The same error is also asymmetric across roles—a missed alarm costs a caregiver more than an extra shout costs the person being watched. Treating accuracy on a balanced laboratory set as the product metric is a refusal to admit field base rates and the loss matrix.

Applying it

• Write two loss lines for every sensor decision: what one false alarm does, what one miss does; do not accept on accuracy alone.
• For rare safety events, accept on positive predictive value and miss cost, not overall accuracy.
• Reversible false positives can be allowed a little more; irreversible false positives should be treated like false negatives.
• Verify by replaying a week of logs at the true base rate, summing minutes of false-alarm interruption and counts of missed events, and seeing which side dominates loss.

Related

• Same group: C9.06.2 Threshold choice is a product decision, not an algorithm decision · C9.06.3 High-consequence actions must not be decided by a single sensor · C9.06.4 Medical alarms usually prefer false positives over false negatives; consumer settings often reverse that · C9.06.5 Cost asymmetry should appear as a concrete classification threshold, not only as a stated principle · C9.06.6 Reusing one sensor across functions may require different false-positive tolerances · C9.06.7 Evaluating false-positive cost must include long-term trust loss, not only the harm of a single error
• Adjacent: C7.08 False Wakes · C4.02 The Midas Touch Problem
• Search: loss matrix · false positive cost · signal detection