Okay, Cyan, I have parsed your posts. I don't know any statistics whatsoever except what I've learned over the last ten hours, but pretty much everything you say seems to be correct, except maybe the last paragraph of this post which still looks foggy to me. The Jean Perrin example in the other comments section was especially illuminating. Let me rephrase it here for the benefit of future readers:

Suppose you're Jean Perrin trying to determine the value of the Avogadro number. This means you have a family of probability distributions depending on a single parameter, and some numbers that you know were sampled from the distribution with the true parameter value. Now estimate it.

• If you're a frequentist, you calculate a 90% confidence interval for the parameter. Briefly, this means you calculate a couple numbers ("statistics") from the data - like, y'know, average them and stuff - in such a way that, for any given value of the parameter, if you'd imagined calculating those statistics from random values sampled under this parameter, they'd have a 90% chance of lying on different sides of it. If a billion statisticians do the same, about 90% of them will be right - not much more and not much less. This is, presumably, good calibration.

• On the other hand, if you're a Bayesian, you pick an uninformative prior, then use your samples to morph it into a posterior and get a credible interval. Different priors lead to different intervals and God only knows what proportion out of a billion people like you is going to actually catch the actual Avogadro number with their interval, even though all of you used the credence value of 90%. This is, presumably, poor calibration.

This sounds like an opportune moment to pull a Jaynes and demonstrate conclusively why one side is utterly dumb and the other is forever right, but I don't yet feel the power. Let's someone else do that, please? (Eliezer, are you listening?)