While I can understand why probability textbooks present Bayes' Theorem as P(A|B) = [ P(B|A) * P(A) ] / P(B), I've always thought the following rewrite makes

While I can understand why probability textbooks present Bayes' Theorem as P(A|B) = [ P(B|A) * P(A) ] / P(B), I've always thought the following rewrite makes more sense when the probabilities represent degrees of belief: P(A|B) = P(A) * [ P(B|A) / P(B) ] In other words: (posterior belief) = (prior belief) * (evidence adjustment) Also, while Bayes' Theorem follows from probability axioms, Bayes' Rule for updating beliefs in light of new evidence (which has the same formulation) is justified by Cox's Theorem: http://en.wikipedia.org/wiki/Coxs_theorem http://en.wikipedia.org/wiki/Coxs_theorem