Generate n random matrices, distributed according to the G-Wishart distribution with parameters b and D, $W_G(b, D)$.
Usage
rgwish( n = 1, G = NULL, b = 3, D = NULL )
Arguments
n
The number of samples required. The default is 1.
G
Adjacency matrix corresponding to 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 $G_{ij}=0$.
b
the degree of freedom for G-Wishart distribution, $W_G(b, D)$. The default is 3.
D
the positive definite $(p \times p)$ "scale" matrix for G-Wishart distribution, $W_G(b, D)$.
The default is an identity matrix.
Value
A numeric array, say A, of dimension $(p \times p \times n)$, where each $A[,,i]$ 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 Wit, E. C. (2014). Bayesian structure learning in sparse Gaussian
graphical models, Bayesian Analysis, acceped. http://arxiv.org/abs/1210.5371v6
Lenkoski, A. (2013). A direct sampler for G-Wishart variates, Stat 2, 119-128.