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Conjugate prior

Concept in probability theoryIn Bayesian probability theory, if, given a likelihood functionp(x∣θ){\displaystyle p(x\mid \theta )}, the posterior distributionp(θ∣x){\displaystyle p(\theta \mid x)} is in the same probability distribution family as the prior probability distributionp(θ){\displaystyle p(\theta )}, the prior and posterior are then called conjugate distributions with respect to that likelihood function and the prior is called a conjugate prior for the likelihood function p(x∣θ){\displaystyle p(x\mid \theta )}.

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