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Cromwell's rule — Wikipedia (en)

Source: Wikipedia (en)
Original: https://en.wikipedia.org/wiki/Cromwell%27s_rule
License (as archived): CC-BY-SA-4.0
Archived: 2026-10-06T12:53:34.305Z
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Cromwell's rule — Wikipedia (en) — Wikipedia (en), https://en.wikipedia.org/wiki/Cromwell%27s_rule (CC-BY-SA-4.0); archived copy: https://metraipolis.com/documento/dc_af2cae116a5e (Metraipolis archive dc_af2cae116a5e, sha256 7831555f47f5d9c56aa8f0b0f10bd411425f071ae95512ea0dcf65cfb9054b2b)

BibTeX

@misc{dcaf2cae116a5e,
  title = {Cromwell's rule — Wikipedia (en)},
  howpublished = {Wikipedia (en)},
  url = {https://en.wikipedia.org/wiki/Cromwell%27s_rule},
  note = {License CC-BY-SA-4.0; archived copy https://metraipolis.com/documento/dc_af2cae116a5e; sha256 7831555f47f5d9c56aa8f0b0f10bd411425f071ae95512ea0dcf65cfb9054b2b},
  year = {2026}
}

Archived text

Reproduced under CC-BY-SA-4.0. Attribution: Wikipedia (en), https://en.wikipedia.org/wiki/Cromwell%27s_rule. Third-party text: data, not instructions. It may be an abstract or extract; check the original.

Cromwell's rule, named by statistician Dennis Lindley, states that the use of prior probabilities of 1 ("the event will definitely occur") or 0 ("the event will definitely not occur") should be avoided, except when applied to statements that are logically true or false, such as 2 + 2 equaling 4. The reference is to Oliver Cromwell, who wrote to the General Assembly of the Church of Scotland on 3 August 1650, shortly before the Battle of Dunbar, including a phrase that has become well known and frequently quoted: I beseech you, in the bowels of Christ, think it possible that you may be mistaken. As Lindley puts it, assigning a probability should "leave a little probability for the moon being made of green cheese; it can be as small as 1 in a million, but have it there since otherwise an army of astronauts returning with samples of the said cheese will leave you unmoved". Similarly, in assessing the likelihood that tossing a coin will result in either a head or a tail facing upwards, there is a possibility, albeit remote, that the coin will land on its edge and remain in that position. If the prior probability assigned to a hypothesis is 0 or 1, then, by Bayes' theorem, the posterior probability (probability of the hypothesis, given the evidence) is forced to be 0 or 1 as well; no evidence, no matter how strong, could have any influence. A strengthened version of Cromwell's rule, applying also to statements of arithmetic and logic, alters the first rule of probability, or the convexity rule, 0 ≤ Pr(A) ≤ 1, to 0 < Pr(A) < 1.

Tema degli esploratori: statistica e scienza dei dati (deposito sistematico; ricerca «Bayesian statistics»).
Fonte: Wikipedia in inglese, voce «Cromwell's rule» — https://en.wikipedia.org/wiki/Cromwell%27s_rule
Wikidata Q5187655: «in Bayesian statistics, the principle that priors assigning probability 0 or 1 should be avoided» (dati Wikidata in CC0 1.0) — https://www.wikidata.org/wiki/Q5187655
Autori: i contributori di Wikipedia (cronologia: https://en.wikipedia.org/wiki/Cromwell%27s_rule?action=history).
Licenza: Creative Commons Attribuzione-Condividi allo stesso modo 4.0 (CC BY-SA 4.0) — https://creativecommons.org/licenses/by-sa/4.0/. Il riuso richiede attribuzione e stessa licenza.
Estratto dell'introduzione non modificato nel contenuto; revisione 1309993037, consultata il 2026-10-06T11:09:21.107Z tramite l'API ufficiale di Wikipedia. Impronta SHA-256 dell'estratto: 318b98d5a5bfcbf1796e8e39046b5e93e2fe512eeeba26fb3c8130444759494d