MultivariateNormalInverseGamma
final class MultivariateNormalInverseGamma(μ:Expression<Real[_]>, Σ:Expression<LLT>, σ2:InverseGamma) < 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 class directly. Instead, establish a 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.
Factory Functions
Name | Description |
---|---|
MultivariateNormalInverseGamma |
Member Variables
Name | Description |
---|---|
Λ:Expression<LLT> | Precision. |
ν:Expression<Real[_]> | Precision times mean. |
α:Expression<Real> | Variance shape. |
γ:Expression<Real> | Variance scale accumulator. |
σ2:InverseGamma | Variance scale. |
Factory Function Details
function MultivariateNormalInverseGamma(μ:Expression<Real[_]>, Σ:Expression<LLT>, σ2:InverseGamma) -> MultivariateNormalInverseGamma