BDgraph (version 2.33)

gnorm: Log of the normalizing constant of G-Wishart distribution

Description

Calculates log of the normalizing constant of G-Wishart distribution based on the Monte Carlo method, developed by Atay-Kayis and Massam (2005).

Usage

gnorm( adj.g, b = 3, D = diag( ncol(adj.g) ), iter = 100 )

Arguments

adj.g

The adjacency matrix corresponding to the graph structure. It is an 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, \(W_G(b, D)\). The default value 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.

iter

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

Value

Log of the normalizing constant of G-Wishart distribution.

Details

Log of the normalizing constant approximation using Monte Carlo method for a G-Wishart distribution, \(K \sim W_G(b, D)\), with density: $$Pr(K) = \frac{1}{I(b, D)} |K| ^ {(b - 2) / 2} \exp \left\{- \frac{1}{2} \mbox{trace}(K \times D)\right\}.$$

References

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 Mohammadi, A. and E. Wit (2015). Bayesian Structure Learning in Sparse Gaussian Graphical Models, Bayesian Analysis, 10(1):109-138

Examples

adj.g <- matrix( c(0,0,1,
                   0,0,1,
		                   0,0,0), 3, 3, byrow = TRUE )		                
# adj.g: adjacency matrix of graph with 3 nodes and 2 links
   
gnorm( adj.g, b = 3, D = diag(3) )