Conjugate Prior
- a conjugate prior is an algebraic convenience, giving a closed-form expression for the posterior; otherwise, numerical integration may be necessary
Conjugate Prior - Definition
- 𝐏(𝜃|𝑋1, …, 𝑋𝑛) ∝ 𝐏(𝑋1, …, 𝑋𝑛|𝜃) 𝐏(𝜃) # bayes theorem
where:
- 𝑋1, …, 𝑋𝑛 - observed data
- 𝜃 - parameter(s) and its value(s) of a distribution model
Prior 𝐏(𝜃) is the CONJUGATE PRIOR of the likelihood function 𝐏(𝑋|𝜃), if the resulting posterior 𝐏(𝜃|𝑋) has the same distribution model as 𝐏(𝜃)
Conjugate Prior - Why Use Them?
- helpful in computing Maximum a Posteriori (MAP)
Conjugate Prior - Examples
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Likelihood Distribution |
Conjugate Prior Distribution |
Proof |
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