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MichaelBishop comments on Why (and why not) Bayesian Updating? - Less Wrong
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Comments (26)
A and B are correlated if P(A ∩ B) != P(A) * P(B).
The idea is that you'd represent the prior using a data structure which allows you to easily determine which beliefs are correlated with a given evidence. I'm not an expert here, but I think this is what Bayesian networks are all about.
Considering all the different combinations of things you might condition on, the task does not sound trivial.