It is the conjugate prior of a normal distribution with unknown mean and variance. Definition · Characterization · Properties

8 февр. 2010 г. · 2.1 Posterior. Assuming µ is fixed, then the conjugate prior for σ2 is an inverse Gamma distribution: z | α, β ∼ IG(α, β). P(z | α, β) = βα. Γ(α).

7 мар. 2021 г. · and we use the Normal-inverse-Gamma as prior p(μ,σ2)=N(μ|μ0,σ2V0)IG(σ2|α0,b0)=1√2πV0bα00Γ(α0)1σ(σ2)−α0−1exp(−12σ2[V−10(μ−μ0)2+2b0]). Parameterization of inverse gamma prior in Bayesian methods Conjugate prior for inverse Gamma with known scale parameter Why do we use inverse Gamma as prior on variance, when ... Другие результаты с сайта stats.stackexchange.com

In this setting we analyze the conjugate normal-normal/inverse gamma model which is the workhorse in econometrics.

The normal-inverse-gamma distribution serves as a conjugate prior because it maintains the same family of distributions for the posterior when combined with a ...

Beta conjugate prior distribution · Gamma conjugate prior distribution · Normal-inverse-gamma prior distribution. Normal-normal-inverse-gamma conjugate model.

Продолжительность: 9:21
Опубликовано: 16 сент. 2015 г.

but the Gamma is not conjugate for normal likelihood. Thre Gamma is a conjugate for the precision, 1/σ2, in which case the prior for σ2 is inverse-Gamma.

8 мар. 2022 г. · The conjugate prior for a Gaussian distribution with unknown mean and variance is the Normal-inverse gamma (NIG) distribution, which has four parameters: m, V, ...

▷ The conjugate prior for σ2 is the inverse gamma distribution. ▷ If a r.v. Y ∼ gamma, then 1/Y ∼ inverse gamma (IG). ▷ The prior for σ2 is p(σ2) = βα. Γ(α).