Why clinicians are natural bayesians: Authors' reply

EDITOR—Hutchon is correct that Bayes's original theorem concerned probabilities rather than odds. We should have stated more clearly that expressing this is an application of Bayes's theorem expressed as odds. Odds and probabilities are interchangeable quantities [P = 1/(1 - odds); and Odds = (1 - P)/(P)]. This can be expressed more precisely by using Bayes's original equations as follows, although these are cumbersome and not as intuitively useful as the version that we presented in the paper. Posterior odds are P(D|data)/P(not D|data) (where P = probability and D = having the disease). By Bayes's rule, the numerator is P(D)P(data|D)/P(data) …