| mniw-package {mniw} | R Documentation |
Tools for the Matrix-Normal Inverse-Wishart distribution.
Description
Density evaluation and random number generation for the Matrix-Normal Inverse-Wishart (MNIW) distribution, as well as its constituent distributions, i.e., the Matrix-Normal, Matrix-T, Wishart, and Inverse-Wishart distributions.
Details
The Matrix-Normal Inverse-Wishart (MNIW) distribution (\boldsymbol{X}, \boldsymbol{V}) \sim \textrm{MNIW}(\boldsymbol{\Lambda}, \boldsymbol{\Sigma}, \boldsymbol{\Psi}, \nu) on random matrices \boldsymbol{X}_{p \times q} and symmetric positive-definite \boldsymbol{V}_{q\times q} is defined as
\begin{array}{rcl}
\boldsymbol{V} & \sim & \textrm{Inverse-Wishart}(\boldsymbol{\Psi}, \nu) \\
\boldsymbol{X} \mid \boldsymbol{V} & \sim & \textrm{Matrix-Normal}(\boldsymbol{\Lambda}, \boldsymbol{\Sigma}, \boldsymbol{V}),
\end{array}
where the Matrix-Normal distribution is defined as the multivariate normal
\textrm{vec}(\boldsymbol{X}) \sim \mathcal{N}(\textrm{vec}(\boldsymbol{\Lambda}), \boldsymbol{V} \otimes \boldsymbol{\Sigma}),
where \textrm{vec}(\boldsymbol{X}) is a vector stacking the columns of \boldsymbol{X}, and \boldsymbol{V} \otimes \boldsymbol{\Sigma} denotes the Kronecker product.
Author(s)
Maintainer: Martin Lysy mlysy@uwaterloo.ca
Authors:
Bryan Yates
See Also
Useful links: