Cromwell’s rule

From Think Bayes–Bayesian statistics made simple (Allen Downey,  Green Tea Press)

“Also, notice that in a Bayesian update, we multiply each prior probability
by a likelihood, so if p(H) is 0, p(HjD) is also 0, regardless of D. In the
Euro problem, if you are convinced that x is less than 50%, and you assign
probability 0 to all other hypotheses, no amount of data will convince you
otherwise.

This observation is the basis of Cromwell’s rule, which is the recommendation
that you should avoid giving a prior probability of 0 to any hypothesis
that is even remotely possible (see http://en.wikipedia.org/wiki/
Cromwell’s_rule).
Cromwell’s rule is named after Oliver Cromwell, who wrote, “I beseech
you, in the bowels of Christ, think it possible that you may be mistaken.”
For Bayesians, this turns out to be good advice (even if it’s a little overwrought).”

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