BDgraph (version 2.13)

I.g: Normalizing constant of G-Wishart distribution

Description

Monte Carlo method for approximating the normalizing constant of G-Wishart distribution. The function uses the Monte Carlo method of Atay-Kayis and Massam (2005).

Usage

I.g( G, b = 3, D = diag( ncol(G) ), mc = 100 )

Arguments

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 identity matrix.

mc

The number of iteration for the Monte Carlo approximation. The default is 100.

Value

• the normalizing constant of G-Wishart distribution.

Details

Normalizing constant approximation using Monte Carlo method for a G-Wishart(b,D): $$p(K) = \frac{1}{I(b, D)} |K| ^ {(b - 2) / 2} exp(- \frac{1}{2} trace(K \times D))$$

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 Atay-Kayis, A. and H. Massam (2005). A monte carlo method for computing the marginal likelihood in nondecomposable Gaussian graphical models. Biometrika 92(2), 317-335.

Examples

G <- matrix( c(0,0,1,
               0,0,1,
		               0,0,0), 3, 3, byrow = TRUE )
		                
# matrix G shows a graph with 3 nodes and 2 links
I.g( G, b = 3, D = diag(3) )