coverage concept
| Definition | The fraction of decisions a certificate clears, reported beside its false-clear rate, since a certificate that clears nothing has a false-clear rate of zero and no use. Equation 0.26. |
|---|---|
| Example | A certificate that clears 500 of 1000 decisions has coverage one half. |
| Book | Data Mining as Observation, draft 0.2, commit f3914f0; entry id coverage, kind concept. |
| Status | no ledger row names this entry. Corrections: none recorded. |
| Defining equation | Book equation 0.26. |
| Assumptions and scope |
|
| Prior art | none recorded |
| Evidence | lean/DataMiningAsObservation/Certificate.lean |
| Reviewed | not yet reviewed; generated 2026-09-10 from records at the commits on the provenance page. |
Equation
Book equation 0.26.
\[\mathrm{FC}=\Pr\big[W\ \text{refutes}\ \big|\ \mathcal C_t\ \text{clears}\big],\qquad \text{coverage}=\Pr\big[\mathcal C_t\ \text{clears}\big].\]
Conditions
- A naive certificate clears every decision, so its coverage is one and its conditional and joint false-clear rates coincide.
- A witnessed certificate clears fewer decisions, and its false-clear rate is read beside its coverage, never alone.
- The word also names, in chapter 14, what a moderation instrument can read of the signal its inputs carry, which is a different quantity and is not this entry.
Conditions are curated in entries.toml rather than read
from a record.
Ledger
none
First stated
Data Mining as Observation, chapter 0 section 0.13 and chapter 13, introduced on 2026-09-03 when the false-clear rate was restated as a conditional rate, and Volume 14 chapter 19 at geometric-observation 7d91883.
Measurements
none
Failures and corrections
none
Invariance envelope
none declared
Machine checked
lean/DataMiningAsObservation/Certificate.lean,
theorems falseClear_mul_coverage,
coverage_empty, falseClear_mem_unit,
minOverStrata_passes_iff,
minOverStrata_le_weighted_mean, at observation-data-mining
f3914f0; what the check covers is stated in the book’s appendix
C.
Used in
Data Mining as Observation chapters 0, 10, 12, 13, 14.
Related
false-clear rate; certificate; witness.
See also
Sources-table rows that share a record with the entry without naming it: chapter 12 section 12.6, chapter 13 section 13.3.
Status
Generated 2026-09-10 by encyclopedia/generate.py; book
at observation-data-mining f3914f0; the commit of every record is listed
in the encyclopedia’s provenance.