To whom it may concern:
This thread is for the discussion of Less Wrong topics that have not appeared in recent posts. If a discussion gets unwieldy, celebrate by turning it into a top-level post.
(After the critical success of part II, and the strong box office sales of part III in spite of mixed reviews, will part IV finally see the June Open Thread jump the shark?)
Do you (or anyone else reading this) know of any attempts to give a precise non-frequentist interpretation of the exact numerical values of Bayesian probabilities? What I mean is someone trying to give a precise meaning to the claim that the "degree of plausibility" of a hypothesis (or prediction or whatever) is, say, 0.98, which wouldn't boil down to the frequentist observation that relative to some reference class, it would be right 98/100 of the time, as in the above quoted example.
Or to put it in a way that might perhaps be clearer, suppose we're dealing with the claim that the "degree of plausibility" of a hypothesis is 0.2. Not 0.19, or 0.21, or even 0.1999 or 0.2001, but exactly that specific value. Now, I have no intuition whatsoever for what it might mean that the "degree of plausibility" I assign to some proposition is equal to one of these numbers and not any of the other mentioned ones -- except if I can conceive of an experiment or observation (or at least a thought-experiment) that would yield that particular exact number via a frequentist ratio.
I'm not trying to open the whole Bayesian vs. frequentist can of worms at this moment; I'd just like to find out if I've missed any significant references that discuss this particular question.
Have you seen my What Are Probabilities, Anyway? post?