# matrix.normal: Matrix-Normal Distribution In MBSP: Multivariate Bayesian Model with Shrinkage Priors

## Description

This function provides a way to draw a sample from the matrix-normal distribution, given the mean matrix, the covariance structure of the rows, and the covariance structure of the columns.

## Usage

 1 matrix.normal(M, U, V) 

## Arguments

 M mean a \times b matrix U a \times a covariance matrix (covariance of rows). V b \times b covariance matrix (covariance of columns).

## Details

This function provides a way to draw a random a \times b matrix from the matrix-normal distribution,

MN(M, U, V),

where M is the a \times b mean matrix, U is an a \times a covariance matrix, and V is a b \times b covariance matrix.

## Value

A randomly drawn a \times b matrix from MN(M,U,V).

## Author(s)

Ray Bai and Malay Ghosh

## Examples

  1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 # Draw a random 50x20 matrix from MN(O,U,V), # where: # O = zero matrix of dimension 50x20 # U has AR(1) structure, # V has sigma^2*I structure # Specify Mean.mat p <- 50 q <- 20 Mean.mat <- matrix(0, nrow=p, ncol=q) # Construct U rho <- 0.5 times <- 1:p H <- abs(outer(times, times, "-")) U <- rho^H # Construct V sigma.sq <- 2 V <- sigma.sq*diag(q) # Draw from MN(Mean.mat, U, V) mn.draw <- matrix.normal(Mean.mat, U, V) 

MBSP documentation built on April 9, 2018, 5:05 p.m.