My point is that various observations appear "independent" (i.e. uncorrelated) only because of uncertainty in our map. (You could point to quantum randomness b

My point is that various observations appear "independent" (i.e. uncorrelated) only because of uncertainty in our map. (You could point to quantum randomness but it doesn't seem likely that this matters for most of the questions we're trying to answer, but even if it did there'd be no problem modeling it with Bayes.) It's possible I'm misunderstanding your objection, though.