rinvwishart {matrixsampling}

Inverse-Wishart sampler

Description

Samples the inverse-Wishart distribution.

Usage

rinvwishart(n, nu, Omega, epsilon = 0, checkSymmetry = TRUE)

Arguments

n

sample size, a positive integer

nu

degrees of freedom, must satisfy nu > p-1, where p is the dimension (the order of Omega)

Omega

scale matrix, a positive definite real matrix

epsilon

threshold to force invertibility in the algorithm; see Details

checkSymmetry

logical, whether to check the symmetry of Omega; if FALSE, only the upper triangular part of Omega is used

Details

The inverse-Wishart distribution with scale matrix Ω is defined as the inverse of the Wishart distribution with scale matrix Ω^-1 and same number of degrees of freedom. The argument epsilon is a threshold whose role is to guarantee the invertibility of the sampled Wishart distributions. See Details in rwishart.

Value

A numeric three-dimensional array; simulations are stacked along the third dimension (see example).

Examples

nu <- 6
p <- 3
Omega <- toeplitz(p:1)
IWsims <- rinvwishart(10000, nu, Omega)
dim(IWsims) # 3 3 10000
apply(IWsims, 1:2, mean) # approximately Omega/(nu-p-1)
# the epsilon argument:
IWsims <- tryCatch(rinvwishart(10000, nu=p+0.001, Omega),
                   error=function(e) e)
IWsims <- tryCatch(rinvwishart(10000, nu=p+0.001, Omega, epsilon=1e-8),
                   error=function(e) e)