I think you’re confusing the odds ratio (P(A)/P(¬A) * P(B|A)/P(B|¬A)), which ADT can’t touch, with the update on the odds ratio (P(B|A)/P(B|¬A)), which has to be used with a bit more creativity.
I think you’re confusing the odds ratio (P(A)/P(¬A) * P(B|A)/P(B|¬A)), which ADT can’t touch, with the update on the odds ratio (P(B|A)/P(B|¬A)), which has to be used with a bit more creativity.