Imagine an AI reading 100 chest X-rays. For each one it answers a yes/no question ("is there an effusion?") and reports how sure it is. One forward pass, one confidence number per case. This page builds four reliability concepts from that single object: a queue of 100 cases sorted by entropy. Every section is a different way of reading the same queue. Drag things.
100 X-rays, sorted confident → uncertain · ■ right · ■ wrong · faded = deferred by conformal
cut
q̂
low entropyhigh entropy
1
Accuracy: the whole-table number
Definition. correct ÷ all cases. It divides by everything, so it cannot see where the errors sit or how sure the model felt about them.
Accuracy, current model
…
(TP+TN) / 100
Accuracy, other model
…
identical on purpose
Always-yes baseline
…
= prevalence of "yes"
truth: yes
truth: no
model: yes
… TP
… FP
model: no
… FN
… TN
Toggle the model above: accuracy does not move. Both models are wrong on the same 12 of 100 X-rays. Only where those errors sit in the confidence queue differs. Everything below exists because that difference, invisible to accuracy, decides deployment fate. And note the baseline trap: this set is 70% positive, so a model that answers yes to every X-ray without looking already scores 70%.
2
Selective prediction: act on the confident slice
Definition. Sort by entropy, auto-commit the most confident fraction c (the cut), defer the rest to a radiologist. Then measure two risks: selective risk = wrong admitted ÷ admitted, and generalized risk = wrong admitted ÷ all 100, the silent-failure mass: cases nobody double-checked and the model botched. Identity: generalized = c × selective.
40%
Admitted
…
of 100 X-rays
Selective risk
…
wrong ÷ admitted
Generalized risk
…
wrong ÷ 100 (silent failures)
Slide the cut and watch the dashed blue line on the queue. On Model A, risk stays near zero until the cut reaches deep into the uncertain tail: its errors are the cases it already distrusts. Switch to Model B: an error sits near the very front of the queue, so silent failures exist at almost every cut. A confidence gate can only protect you from mistakes the model is unsure about.
3
AUGRC: grade the whole curve, not one cut
Definition. Sweep the cut from 0% to 100%, plot generalized risk at every setting, and take the average height. AUGRC = the expected fraction of the caseload silently failed, averaged over every possible workload choice. Lower is better. It blends ranking quality with accuracy, deliberately.
Model A · AUGRC …Model B · AUGRC …your current cut
Same accuracy, yet a several-fold gap in average silent harm. The gap is carried entirely by where the errors sit. Model B is the dangerous kind: its mistakes arrive with high confidence, and confident errors walk straight through any gate, at any threshold. The curve is destiny: if it sits high everywhere, no cut, hand-picked or calibrated, has a good place to land.
4
Conformal prediction: run the map backwards, with a warranty
Definition. Choose the tolerable miscoverage α first. Calibrate a threshold q̂ on held-out X-rays so that committed-and-wrong stayed ≤ α there. At test time, emit {yes} or {no} when confidence clears q̂, and {yes, no}, a principled deferral to the radiologist, when it does not. If test data is exchangeable with calibration data, math guarantees the truth lands in the emitted set ≥ 1 − α of the time, for any model, however miscalibrated. In binary, miscoverage is the generalized risk at the cut q̂ induces.
10%
0
Empirical coverage
…
truth ∈ set / 100
Committed (singletons)
…
automation kept
Deferred {yes, no}
…
the drift alarm
exchangeability holds · guarantee active
Raise corruption with blur, noise, or a new scanner, and entropy rises everywhere. Fewer cases clear the clean-calibrated q̂, so the purple line retreats left and the faded (deferred) region grows. Coverage barely moves: the promise is defended by doing less, which is why the deferral rate, not coverage, is the first thing that shifts. And watch the badge: from severity 1 on, the guarantee is void even while the number stays good. Same coverage, different status: a promise became a diary entry.
The weld. All four concepts read one quantity, silent-failure mass, off one entropy-sorted queue. Accuracy averages over the whole queue and sees nothing. Selective prediction picks a cut and reads the mass there. AUGRC integrates it over every possible cut. Conformal bounds it by promise, deriving the cut from the budget. And all four trust whatever confidence selects, so a separate audit of what the model actually looked at still gets the last word.