BDgraph (version 2.3)

I.g: Computing 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(A, b, D, MCiter = 500)

Arguments

A

upper triangular matrix in which $a_{ij}=1$ if there is a link between notes $i$ and $j$, otherwise $a_{ij}=0$.

b

the degree of freedom for G-Wishart distribution, $W_G(b,D)$.

D

the positive definite matrix for G-Wishart distribution, $W_G(b,D)$.

MCiter

the number of iterations for the Monte Carlo approximation.

Value

• the normalizing constant of G-Wishart distribution.

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 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

A <- matrix(c(0,1,1,
              0,0,1,
		              0,0,0), 3, 3, byrow = TRUE) 
# matrix A shows full graph with 3 nodes and 3 edges
I.g(A, b = 3, D = diag(3), MCiter = 50)