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IlyaShpitser comments on Probability, knowledge, and meta-probability - Less Wrong
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I don't really understand what "being Bayesian about causal models" means. What makes the most sense (e.g. what people typicalliy do) is:
(a) "be Bayesian about statistical models", and
(b) Use additional assumptions to interpret the output of (a) causally.
(a) makes sense because I understand how evidence help me select among sets of statistical alternatives.
(b) also makes sense, but then no one will accept your answer without actually verifying the causal model by experiment -- because your assumptions linking the statistical model to a causal one may not be true. And this game of verifying these assumptions doesn't seem like a Bayesian kind of game at all.
I don't know what it means to use Bayes theorem to select among causal models directly.
It means that you figure out which causal models look more or less like what you observed.
More generally: There's a language of causal models which, we think, allows us to describe the actual universe, and many other universes besides. Some of these models are simpler than others. Any given sequence of experiences has some probability of being encountered in a given causal universe.