# Definition of Bayes' theorem in US English:

## Bayes' theorem

Statistics
• 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.

/ˈbāz ˌTHēərəm/