Tuesday, September 15, 2009

 

Cromwell's Rule

AJ refers me to Wikipedia's article on Cromwell's Rule:

Cromwell's rule, named by statistician Dennis Lindley, states that one should avoid using prior probabilities of 0 or 1, except when applied to statements that are logically true or false. (For instance, Lindley would allow us to say that \Pr(2+2 = 4) = 1.)

The reference is to Oliver Cromwell, who famously wrote to the synod of the Church of Scotland 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 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.

This seems reasonable. But is there a psychological problem if we are sure of nothing in the world? We might be haunted by having to always to do a substantive Bayes's Rule calculation. Maybe not, though. The substance of Lindley's idea is the story of the astronauts bringing green cheese-- we will throw away our heuristic solid belief if that happens.

 

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