How about this for a precise definition: A is evidence about B if p(A | B) != p(A | ~B).
Of course, by this definition, almost everything is evidence about almost everything else. So we’d like to talk about the strength of evidence. A good candidate is log p(A | B) - log p(A | ~B). This is the number that gets added to your log odds for B when you observe A.
How about this for a precise definition: A is evidence about B if p(A | B) != p(A | ~B).
Of course, by this definition, almost everything is evidence about almost everything else. So we’d like to talk about the strength of evidence. A good candidate is log p(A | B) - log p(A | ~B). This is the number that gets added to your log odds for B when you observe A.