I don’t think “are generally” applies “no matter the the direction or even existence of causal relations”.
If A causes E and B independently causes E, then there will be correlation between A and E and between B and E, but no reason to expect correlation between A and B.
You’re right, and I really should have known better. This is one of the examples used in Judea Pearl’s Casaulity, about how to assign plausible causation structures given only correlations.
You’re right. I should have said “are generally”, rather “are”.
I don’t think “are generally” applies “no matter the the direction or even existence of causal relations”.
If A causes E and B independently causes E, then there will be correlation between A and E and between B and E, but no reason to expect correlation between A and B.
You’re right, and I really should have known better. This is one of the examples used in Judea Pearl’s Casaulity, about how to assign plausible causation structures given only correlations.
A pair of correlations between A and B, and between B and C, is correlated with a correlation between A and C. :P