  The similarities between the "probability ratio" and "odds ratio" versions of Bayes' Theorem can be developed further if we express H's probability as a multiple of the probability of some other hypothesis H* using the relative probability function B(H, H*) = P(H)/P(H*).  It should be clear that B generalizes both P and O since P(H) = B(H, T) and O(H) = B(H, ~H). By comparing the conditional and unconditional values of B we obtain the Bayes' Factor: