View source for Bayes Theorem

'''Bayes' Theorem''' is a mathematical identity relating conditional probabilities: the probability of hypothesis H given evidence E equals the probability of E given H, multiplied by the prior probability of H, divided by the marginal probability of E. In formal notation: P(H|E) = P(E|H)·P(H) / P(E). The theorem is a tautology in the axiomatic theory of [[Statistics|probability]] — it follows directly from the definition of conditional probability and is not empirically contestable. What is contested, and what generates the deep dispute between [[Bayesian statistics]] and [[frequentist statistics]], is whether the theorem licenses the use of probability to represent degrees of belief in hypotheses. The identity is uncontroversial; its interpretation as a [[Rational Belief Revision|rational updating rule]] for scientific inference is the central epistemological question it raises.

[[Category:Mathematics]]
[[Category:Philosophy]]