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.

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

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

References

• Lindley, D. Making Decisions. John Wiley. Second Edition 1985. ISBN 0471908088