gnorm: Normalizing constant for G-Wishart

In BDgraph: Bayesian Structure Learning in Graphical Models using Birth-Death MCMC

Normalizing constant for G-Wishart

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

Arguments

adj	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	degree of freedom for G-Wishart distribution, W_G(b, D).
D	positive definite (p \times p) "scale" matrix for G-Wishart distribution, W_G(b,D). The default is an identity matrix.
iter	number of iteration for the Monte Carlo approximation.

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\}.

Value

Log of the normalizing constant of G-Wishart distribution.

Author(s)

Reza Mohammadi [e-mail]

References

Atay-Kayis, A. and Massam, H. (2005). A monte carlo method for computing the marginal likelihood in nondecomposable Gaussian graphical models, Biometrika, 92(2):317-335, \Sexpr[results=rd]{tools:::Rd_expr_doi("10.1093/biomet/92.2.317")}

Mohammadi, R., Massam, H. and Letac, G. (2023). Accelerating Bayesian Structure Learning in Sparse Gaussian Graphical Models, Journal of the American Statistical Association, \Sexpr[results=rd]{tools:::Rd_expr_doi("10.1080/01621459.2021.1996377")}

Uhler, C., et al (2018) Exact formulas for the normalizing constants of Wishart distributions for graphical models, The Annals of Statistics 46(1):90-118, \Sexpr[results=rd]{tools:::Rd_expr_doi("10.1214/17-AOS1543")}

See Also

rgwish, rwish

Examples

## Not run: 
# adj: adjacency matrix of graph with 3 nodes and 2 links
adj <- matrix( c( 0, 0, 1,
                  0, 0, 1,
                  0, 0, 0 ), 3, 3, byrow = TRUE )		                
   
gnorm( adj, b = 3, D = diag( 3 ) )

## End(Not run)

BDgraph documentation built on Sept. 11, 2024, 5:30 p.m.