The Observation Theory EncyclopediaFrom TSKAboutBy kindBy chapterBy Lean fileLedgerProvenance

Monte Carlo concept

DefinitionEstimating a probability or an expectation as the fraction or average over many simulated runs, a sample proportion with standard error the square root of p(1 minus p) over N. A null model run many times is one. Primer S, equation S.21.
Example17 of 100 runs show the event, so the estimate is 0.17 with standard error the square root of 0.17 times 0.83 over 100, which is 0.038.
BookData Mining as Observation, draft 0.2, commit f3914f0; entry id monte-carlo, kind concept.
Statusno ledger row names this entry. Corrections: none recorded.
Defining equation

Book equation S.21.

Assumptions and scopenone
Prior artnone recorded
Evidencenone
Reviewedsemantic review 2026-09-09; generated 2026-09-10 from records at the commits on the provenance page.

Equation

Book equation S.21.

\[\hat p=\frac{\#\text{runs with the event}}{N},\qquad \operatorname{SE}(\hat p)=\sqrt{\frac{\hat p(1-\hat p)}{N}}.\]

Conditions

none

Ledger

none

First stated

Primer S section S.11 of Data Mining as Observation, added in draft 0.3 (2026-09-09) for the ECE 514 readers whose first courses are far behind. The idea is standard and TSK Appendix C covers it at length.

Measurements

none

Failures and corrections

none

Invariance envelope

none declared

Machine checked

none

Used in

Data Mining as Observation primer S.

Related

pseudo-random generator; null model; standard error; permutation test.

See also

none

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.

← Monotone Invariance Theoremmultiple comparisons →