Bayes is definitely about statistical correlation.
No, I strongly disagree.
it’s still all probabilities—and you need correlations for those
I do not need correlations for probabilities—where did you get that strange idea?
To make a simple observation, “correlation” is a linear relationship and there are many things in this world that are dependent in more complex ways. Are you familiar with the Anscombe’s quartet, by the way?
I do not need correlations for probabilities—where did you get that strange idea?
In that case, I’ll repeat my earlier question:
if you don’t know how much phenomenon A correlates with phenomenon B, how are you supposed to calculate the conditional probabilities P(A|B) and P(B|A)?
There is no general answer—this question goes to why do you consider a particular data point to be evidence suitable for updating your prior. Ideally you have causal (structural) knowledge about the relationship between A & B, but lacking that you probably should have some model (implicit or explicit) about that relationship. The relationship does not have to be linear and does not have to show up as correlation (though it, of course, might).
No, I strongly disagree.
I do not need correlations for probabilities—where did you get that strange idea?
To make a simple observation, “correlation” is a linear relationship and there are many things in this world that are dependent in more complex ways. Are you familiar with the Anscombe’s quartet, by the way?
In that case, I’ll repeat my earlier question:
There is no general answer—this question goes to why do you consider a particular data point to be evidence suitable for updating your prior. Ideally you have causal (structural) knowledge about the relationship between A & B, but lacking that you probably should have some model (implicit or explicit) about that relationship. The relationship does not have to be linear and does not have to show up as correlation (though it, of course, might).