Cromwell's rule, named by statistician Dennis Lindley

Dennis Lindley

Dennis Victor Lindley is a British statistician, decision theorist and leading advocate of Bayesian statistics.Dennis Lindley grew up in the south-west London suburb of Surbiton. He was an only child and his father was a local building contractor...

, states that one should avoid using prior probabilities

Prior probability

In Bayesian statistical inference, a prior probability distribution, often called simply the prior, of an uncertain quantity p is the probability distribution that would express one's uncertainty about p before the "data"...

 of 0 or 1, except when applied to statements that are logically true or false. (For instance, Lindley would allow us to say that )

The reference is to Oliver Cromwell

Oliver Cromwell

Oliver Cromwell was an English military and political leader who overthrew the English monarchy and temporarily turned England into a republican Commonwealth, and served as Lord Protector of England, Scotland, and Ireland....

, who famously wrote to the synod

Synod

A synod historically is a council of a church, usually convened to decide an issue of doctrine, administration or application. In modern usage, the word often refers to the governing body of a particular church, whether its members are meeting or not...

 of the Church of Scotland

Church of Scotland

The Church of Scotland, known informally by its Scots language name, the Kirk, is a Presbyterian church, decisively shaped by the Scottish Reformation....

 on August 5, 1650 saying

I beseech you, in the bowels of Christ, think it possible that you may be mistaken.

As Lindley puts it, if a coherent Bayesian

Bayesian inference

In statistics, Bayesian inference is a method of statistical inference. It is often used in science and engineering to determine model parameters, make predictions about unknown variables, and to perform model selection...

 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

Bayes' theorem

In probability theory and applications, Bayes' theorem relates the conditional probabilities P and P. It is commonly used in science and engineering. The theorem is named for Thomas Bayes ....

, the posterior probability

Posterior probability

In Bayesian statistics, the posterior probability of a random event or an uncertain proposition is the conditional probability that is assigned after the relevant evidence is taken into account...

(probability of the variable, given the evidence) is forced to be 0 (or 1) as well.