Generate n random matrices, distributed according to the G-Wishart distribution with parameters b and D, $W_G(b, D)$.
Usage
rGWishart(n = 1, b = 3, D = diag(2), G = NULL, method = "block gibbs", start.K = NULL)
Arguments
n
integer sample size.
b
the degree of freedom for G-Wishart distribution, $W_G(b, D)$.
D
the positive definite $(p \times p)$ "scale" matrix for G-Wishart distribution, $W_G(b, D)$.
G
adjacency matrix which shows the graph structure. It is an upper triangular matrix in which $g_{ij}=1$
if there is a link between notes $i$ and $j$, otherwise $g_{ij}=0$.
method
a character with two options "block gibbs" and "accept-reject" to determine a type of sampling method. Option
"block gibbs" (default) determines a pair wise block gibbs sampling from G-Wishart distribution. Option
"accept-reject" determines a accept-r
start.K
starting point for "block gibbs" method.
Value
a numeric array, say R, of dimension $(p \times p \times n)$, where each $R[,,i]$ is a positive
definite matrix, a realization of the G-Wishart distribution $W_G(b, D)$.
Details
Sampling from G-Wishart(b,D) distribution with density:
$$p(K) \propto |K| ^ {(b - 2) / 2} exp(- \frac{1}{2} trace(K \times D))$$
which $b > 2$ is the degree of freedom and D is a symmetric positive definite matrix.
References
Mohammadi, A. and E. C. Wit (2012). Gaussian graphical model determination based on birth-death
MCMC inference, arXiv:1210.5371v4. http://arxiv.org/abs/1210.5371v4
Wang, H. and S.Z. Li (2012). Efficient Gaussian graphical model determination under G-Wishart prior distributions.
Electronic Journal of Statistics 6, 168-198.
Wang, H. and C. M. Carvalho (2010). Simulation of hyper-inverse Wishart distributions for non-decomposable graphs.
Electronic Journal of Statistics 4, 1470-1475.
G <- toeplitz(c(0, 1, rep(0, 3)))
G # graph with 5 nodes and 4 links sample <- rGWishart(n = 3, b = 3, D = diag(5), G = G, method = "block gibbs")
round(sample, 2)