Cromwell's rule, named by statistician Dennis Lindley,[1] 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:[2] 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".
An example of Bayesian divergence of opinion is based on Appendix A of Sharon Bertsch McGrayne's 2011 book.
An example of Bayesian convergence of opinion is in Nate Silver's 2012 book The Signal and the Noise: Why so many predictions fail – but some don't.
By the end of the simulation (shown in a graph), "all of the investors conclude they are in a bull market with almost (although not exactly of course) 100 percent certainty".