MBSP (version 4.0)

matrix_normal: Matrix-Normal Distribution

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

matrix_normal(M, U, V)

Value

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

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).

Author

Ray Bai and Malay Ghosh

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.

Examples

# 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)