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

Description Usage Arguments Details Value Author(s) Examples

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.

1	matrix.normal(M, U, V)

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

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.

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

Ray Bai and Malay Ghosh

# 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)