# rgwish: Sampling from G-Wishart distribution In BDgraph: Bayesian Structure Learning in Graphical Models using Birth-Death MCMC

## Description

Generates random matrices, distributed according to the G-Wishart distribution with parameters b and D, W_G(b, D) with respect to the graph structure G. Note this fuction works for both non-decomposable and decomposable graphs.

## Usage

 1 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 which can be non-decomposable or decomposable. 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.

## Details

Sampling from G-Wishart distribution, K \sim W_G(b, D), with density:

Pr(K) \propto |K| ^ {(b - 2) / 2} \exp ≤ft\{- \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.

## 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). Note, for the case n=1, the output is a 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

  1 2 3 4 5 6 7 8 9 10 11 12 13 ## Not run: # Generating a 'circle' graph as a non-decomposable graph adj.g <- graph.sim( p = 5, graph = "circle" ) adj.g # adjacency of graph with 5 nodes sample <- rgwish( n = 1, adj.g = adj.g, b = 3, D = diag( 5 ) ) round( sample, 2 ) sample <- rgwish( n = 5, adj.g = adj.g, b = 3, D = diag( 5 ) ) round( sample, 2 ) ## End(Not run) 

BDgraph documentation built on May 20, 2018, 5:03 p.m.