InverseWishart
final class InverseWishart(Ψ:Expression<LLT>, k:Expression<Real>) < Distribution<LLT>
Inverse Wishart distribution.
This is typically used to establish a conjugate prior for a Bayesian multivariate linear regression:
where \mathbf{X} are inputs and \mathbf{Y} are outputs.
The relationship is established in code as follows:
V:Random<Real[_,_]>;
Ψ:LLT;
k:Real;
W:Random<Real[_,_]>;
M:Real[_,_];
U:Real[_,_];
Y:Random<LLT>;
X:Real[_,_];
V ~ InverseWishart(Ψ, k);
W ~ Gaussian(M, U, V);
Y ~ Gaussian(X*W, V);
Factory Functions
Name | Description |
---|---|
InverseWishart | Create inverse-Wishart distribution. |
InverseWishart | Create inverse-Wishart distribution. |
InverseWishart | Create inverse-Wishart distribution. |
InverseWishart | Create inverse-Wishart distribution. |
InverseWishart | Create inverse-Wishart distribution. |
InverseWishart | Create inverse-Wishart distribution. |
InverseWishart | Create inverse-Wishart distribution. |
InverseWishart | Create inverse-Wishart distribution. |
Member Variables
Name | Description |
---|---|
Ψ:Expression<LLT> | Scale. |
k:Expression<Real> | Degrees of freedom. |
Factory Function Details
function InverseWishart(Ψ:Expression<LLT>, k:Expression<Real>) -> InverseWishart
Create inverse-Wishart distribution.
function InverseWishart(Ψ:Expression<LLT>, k:Real) -> InverseWishart
Create inverse-Wishart distribution.
function InverseWishart(Ψ:LLT, k:Expression<Real>) -> InverseWishart
Create inverse-Wishart distribution.
function InverseWishart(Ψ:LLT, k:Real) -> InverseWishart
Create inverse-Wishart distribution.
function InverseWishart(Ψ:Expression<Real[_,_]>, k:Expression<Real>) -> InverseWishart
Create inverse-Wishart distribution.
function InverseWishart(Ψ:Expression<Real[_,_]>, k:Real) -> InverseWishart
Create inverse-Wishart distribution.
function InverseWishart(Ψ:Real[_,_], k:Expression<Real>) -> InverseWishart
Create inverse-Wishart distribution.
function InverseWishart(Ψ:Real[_,_], k:Real) -> InverseWishart
Create inverse-Wishart distribution.