## Bayesian probability banned?

This post on Understanding Uncertainty bears the amusing, alarming and somewhat over-stated title “Court of Appeal bans Bayesian probability (and Sherlock Holmes)”. It’s not unusual for people to experience a little intellectual indigestion when first faced with the Bayesian probabilistic paradigm; it is particularly prevalent among people whose point of view is roughly speaking “frequentist”, even though they may have had no formal education in probability in their lives. Personally, I think that the judge’s criticisms, and Understanding Uncertainty‘s criticisms of those criticisms, are somewhat overblown.

However, I will advance one criticism of Bayesian probability as applied to practical situations. The basic axiom of the Bayesian paradigm is that one’s state of knowledge (or uncertainty) can be encapsulated in a unique, well-defined probability measure ℙ (the “prior”) on some sample space. Having done this, the only sensible way to update your probability measure (to produce a “posterior”) in light of new evidence is to condition it using Bayes’ rule — and I have no bone of contention with that theorem. My issue is with specifying a unique prior. If I believe that a coin is perfectly balanced, then I might be willing to commit to the prior ℙ for which