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>There's no fundamental ontological difference between "give me your likelihood ratios between drawing cards [a and b] as the next draw from this deck of cards"
by ouid 5y ago
>There's no fundamental ontological difference between "give me your likelihood ratios between drawing cards [a and b] as the next draw from this deck of cards" and "give me your likelihood ratios between finding and not finding a continent in an unexplored part of the world".
These are not the same, my observables being independent of each other is not the same thing as my not knowing about the correlated observable. In a practical sense, there are lots of ways that I could reason that there is a continent in the unexplored bit, and obviously no way to know which card will come up in a shuffle.
- comp_throw7 5y agoMy 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.
- ineedasername 5y ago>I could reason that there is a continent in the unexplored bit, and obviously no way to know which card will come up in a shuffle. You can reason the continent exists, but you can't know. You're using knowledge you already have. Similarly, knowledge accumulates as you run through a deck, which can be used to reason that a specific card will come up next. I'm not sure I see a difference.