Definition: Conjugate and nonconjugate prior distribution
Index: The Book of Statistical Proofs ▷ General Theorems ▷ Bayesian statistics ▷ Prior distributions ▷ Conjugate vs. nonconjugate
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Metadata: ID: D120  shortcut: priorconj  author: JoramSoch  date: 20201202, 17:55.
Definition: Let $m$ be a generative model with likelihood function $p(y \vert \theta, m)$ and prior distribution $p(\theta \vert m)$. Then,

the prior distribution is called “conjugate”, if it, when combined with the likelihood function, leads to a posterior distribution that belongs to the same family of probability distributions;

the prior distribution is called “nonconjugate”, if this is not the case.
 Wikipedia (2020): "Conjugate prior"; in: Wikipedia, the free encyclopedia, retrieved on 20201202; URL: https://en.wikipedia.org/wiki/Conjugate_prior.
Metadata: ID: D120  shortcut: priorconj  author: JoramSoch  date: 20201202, 17:55.