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In Bayesian probability theory, if the posterior distribution is in the same probability distribution family as the prior probability distribution , the prior and posterior are then called conjugate distributions, and the prior is called a conjugate prior for the likelihood function .
|Part of a series on|
|Posterior = Likelihood × Prior ÷ Evidence|
A conjugate prior is an algebraic convenience, giving a closed-form expression for the posterior; otherwise, numerical integration may be necessary. Further, conjugate priors may give intuition by more transparently showing how a likelihood function updates a prior distribution.
The concept, as well as the term "conjugate prior", were introduced by Howard Raiffa and Robert Schlaifer in their work on Bayesian decision theory. A similar concept had been discovered independently by George Alfred Barnard.