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Cyan comments on Are calibration and rational decisions mutually exclusive? (Part one) - Less Wrong
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Comments (19)
The ideas of the post are: calibration seems to me to be equivalent to confidence coverage (second and third paragraphs); in general, Bayesian posterior intervals do not have valid confidence coverage (fourth paragraph). The sentence you quote above follows from these two ideas.
Okay, that helps. My problem is that, on re-reading, I still don't know what the 4th paragraph means.
Why would anybody want non-informative distributions?
I don't know what it means for a confidence interval to be asymptotically valid, or why posterior intervals have this effect. This seems like an important point that should be justified.
You lost me entirely.
To have a prior distribution to use when very little is known about the estimand. It's meant to somehow capture the notion of minimal prior knowledge contributing to the posterior distribution, so that the data drive the conclusions, not the prior.
The confidence coverage of a posterior interval is equal to the posterior probability mass of the interval plus a term which goes to zero as the amount of data increases without bound.
E.g., a regression with more than one predictor. Each predictor has its own coefficient, so the model of the data-generating process contains more than one scalar parameter.