BDgraph (version 2.43)

rgwish: Sampling from G-Wishart distribution

Description

Generates random matrices, distributed according to the G-Wishart distribution with parameters b and D, \(W_G(b, D)\).

Usage

rgwish( n = 1, adj.g = NULL, b = 3, D = NULL )

Arguments

n

The number of samples required.

adj.g

The adjacency matrix corresponding to the graph structure. It should be 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, \(W_G(b, D)\).

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 distribution, \(K \sim W_G(b, D)\), with density:

$$Pr(K) \propto |K| ^ {(b - 2) / 2} \exp \left\{- \frac{1}{2} \mbox{trace}(K \times D)\right\},$$

which \(b > 2\) is the degree of freedom and D is a symmetric positive definite matrix.

References

Lenkoski, A. (2013). A direct sampler for G-Wishart variates, Stat, 2:119-128

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

Mohammadi, A. and E. Wit (2015). BDgraph: An R Package for Bayesian Structure Learning in Graphical Models, arXiv preprint arXiv:1501.05108

Mohammadi, A. et al (2017). Bayesian modelling of Dupuytren disease by using Gaussian copula graphical models, Journal of the Royal Statistical Society: Series C

Mohammadi, A., Massam H., and G. Letac (2017). The Ratio of Normalizing Constants for Bayesian Graphical Gaussian Model Selection, arXiv preprint arXiv:1706.04416

Examples

# NOT RUN {
graph.sim <- bdgraph.sim( p = 5, graph = "cycle" )
adj.g     <- graph.sim $ G
adj.g    # adjacency of graph with 5 nodes and 4 links
   
sample <- rgwish( n = 3, adj.g = adj.g, b = 3, D = diag(5) )
round( sample, 2 )  
# }