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Encyclopedia > Cromwell's rule

Cromwell's rule, named by statistician D. Lindley, states that one should avoid using prior probabilities of 0 or 1.

As Lindley puts it, if a coherent Bayesian attaches a prior probability of zero to the hypothesis that the Moon is made of green cheese, then even whole armies of astronauts coming back bearing green cheese cannot convince him. Setting the prior probability (what is known about a variable in the absence of some evidence) to 0 (or 1), then, by Bayes' theorem, the posterior probability (probability of the variable, given the evidence) is forced to be 0 (or 1) as well. Bayesian refers to probability and statistics methods associated with the Reverend Thomas Bayes (c. ... A prior probability is a marginal probability, interpreted as a description of what is known about a variable in the absence of some evidence. ... Bayes theorem is a result in probability theory, which gives the conditional probability distribution of a random variable A given B in terms of the conditional probability distribution of variable B given A and the marginal probability distribution of A alone. ... In Bayesian probability theory, the posterior probability is the conditional probability of some event or proposition, taking empirical data into account. ...

It is not inconceivable for something to have probability 0, but in the real world, virtually nothing does.

The reference is to Oliver Cromwell, who famously wrote to the synod of the Church of Scotland on August 5th, 1650 saying Unfinished portrait miniature of Oliver Cromwell by Samuel Cooper, 1657. ... A synod (also known as a council) is a council of a church, usually a Christian church, convened to decide an issue of doctrine or administration. ... The Church of Scotland is the national (established) church in Scotland. ... August 5 is the 217th day of the year in the Gregorian Calendar (218th in leap years), with 148 days remaining. ... Events June 23 - Claimant King Charles II of England, Scotland and Ireland arrives in Scotland, the only of the three Kingdoms that has accepted him as ruler. ...

I beseech you, in the bowels of Christ, consider it possible that you are mistaken.

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