Cromwell's rule - Wikipedia

Abstraction: Bayesian principle against assigning zero or one prior probability to hypotheses

Key points:

• Named by Dennis Lindley after Oliver Cromwell's 1650 letter: "I beseech you, think it possible that you may be mistaken"
• If prior probability is exactly 0 or 1, Bayes' theorem cannot update it regardless of evidence — the posterior is forced to remain 0 or 1
• Lindley's example: leave at least 1-in-a-million probability for the moon being made of green cheese, or astronauts returning with samples will leave you unmoved
• Strengthened version restricts priors to strict interval (0, 1) even for mathematical truths
• Illustrated by Tim vs. Susan coin example: Susan's 0-probability prior for an unfair coin means no amount of heads can update her belief
• Nate Silver's "Signal and Noise" shows that investors starting from 10%, 50%, 90% priors converge to near-certainty given sufficient evidence — unlike the 0%/100% case

Connections: Dennis Lindley · Bayesian Inference · Prior Probability

Source: http://en.wikipedia.org/wiki/Cromwell%27s_rule