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A theorem describing how the conditional probability of each of a set of possible causes for a given observed outcome can be computed from knowledge of the probability of each cause and the conditional probability of the outcome of each cause.

‘A follower of Clifford might object if there was no philosophical discussion of rival explanations or of the application here of Bayes' theorem in the theory of probability.’

‘To summarize the principle of our approach, we used Bayes' theorem to rewrite the posterior pdf as a function of a prior and a likelihood.’

‘Once these parameters have been estimated, Bayes' theorem is used to estimate the posterior probability that a given site came from the class of positively selected sites.’

‘The projections of the four individual submodels were integrated into a single prediction based upon Bayes' theorem.’

‘Following Bayes' theorem, the posterior distribution over the parameter space is proportional to the likelihood times the prior distribution.’

Origin

Mid 19th century: named after Thomas Bayes (1702–61), English mathematician.