Definition: Conjugate and non-conjugate prior distribution

Index: The Book of Statistical Proofs ▷ General Theorems ▷ Bayesian statistics ▷ Prior distributions ▷ Conjugate vs. non-conjugate

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 “non-conjugate”, if this is not the case.

 

Sources:

• Wikipedia (2020): "Conjugate prior"; in: Wikipedia, the free encyclopedia, retrieved on 2020-12-02; URL: https://en.wikipedia.org/wiki/Conjugate_prior.

Metadata: ID: D120 | shortcut: prior-conj | author: JoramSoch | date: 2020-12-02, 17:55.