The Book of Why: The New Science of Cause and Effect

by Judea Pearl

But epistemologically, it is far from elementary. It acts, in fact, as a normative rule for updating beliefs in response to evidence. In other words, we should view Bayes’s rule not just as a convenient definition of the new concept of “conditional probability” but as an empirical claim to faithfully represent the English expression “given that I know.” It asserts, among other things, that the belief a person attributes to S after discovering T is never lower than the degree of belief that person attributes to S AND T before discovering T. Also, it implies that the more surprising the evidence T—that is, the smaller P(T) is—the more convinced one should become of its cause S.