Bayes' rule concept
| Definition | The probability of a cause given an observation, equal to the probability of the observation given the cause times the base rate, divided by the overall probability of the observation. Precision is Bayes' rule with a classifier as the test. Primer S, equation S.3. Also Bayes. |
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| Example | Base rate one percent, detection ninety percent, false report five percent, so a positive report means the condition with probability 0.009 over 0.0585, about 0.154. |
| Book | Data Mining as Observation, draft 0.2, commit f3914f0; entry id bayes-rule, kind concept. |
| Status | no ledger row names this entry. Corrections: none recorded. |
| Defining equation | Book equation S.3. |
| Assumptions and scope | none |
| Prior art | none recorded |
| Evidence | none |
| Reviewed | semantic review 2026-09-09; generated 2026-09-10 from records at the commits on the provenance page. |
Equation
Book equation S.3.
\[\Pr[A\mid B]=\frac{\Pr[B\mid A]\,\Pr[A]}{\Pr[B]},\qquad \Pr[B]=\Pr[B\mid A]\Pr[A]+\Pr[B\mid A^{c}]\Pr[A^{c}].\]
Conditions
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Ledger
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First stated
Primer S section S.1 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
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Failures and corrections
none
Invariance envelope
none declared
Machine checked
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Used in
Data Mining as Observation primer S, chapters 6, 7.
Related
conditional probability; base rate; precision, recall; naive Bayes.
See also
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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.