# MultivariateNormalInverseGamma

final class MultivariateNormalInverseGamma(μ:Expression<Real[_]>, Σ:Expression<Real[_,_]>, α:Expression<Real>, β:Expression<Real>) < Distribution<Real[_]>

Multivariate normal-inverse-gamma distribution.

This represents the joint distribution:

which may be denoted:

and is a conjugate prior of a Gaussian distribution with both unknown mean and variance. The variance scaling is independent and identical in the sense that all components of $x$ share the same $\sigma^2$.

In model code, it is not usual to use this final class directly. Instead, establish the conjugate relationship via code such as the following:

σ2 ~ InverseGamma(α, β);
x ~ Gaussian(μ, Σ*σ2);
y ~ Gaussian(x, σ2);


where the last argument in the distribution of y must appear in the last argument of the distribution of x. The operation of Σ on σ2 may be multiplication on the left (as above) or the right, or division on the right.

### Member Variables

Name Description
μ:Expression<Real[_]> Mean.
Σ:Expression<Real[_,_]> Covariance scale.
σ2:InverseGamma Covariance.