R: Sampling from G-Wishart distribution

rgwish {BDgraph} | R Documentation

## 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) with respect to the graph structure G. Note this fuction works for both non-decomposable and decomposable graphs.

### Usage

     rgwish( n = 1, adj = NULL, b = 3, D = NULL, threshold = 1e-8 )

### Arguments

`n` | The number of samples required.
`adj` | 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. `adj` could be an object of class `"graph"`, from function `graph.sim`. It also could be an object of class `"sim"`, from function `bdgraph.sim`. It also could be an object of class `"bdgraph"`, from functions `bdgraph.mpl` or `bdgraph`.
`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.
`threshold` | The threshold value for the convergence of sampling algorithm from G-Wishart.

### 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.

### Author(s)

Reza Mohammadi a.mohammadi@uva.nl

### References

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

Mohammadi, R. and Wit, E. C. (2019). BDgraph: An `R` Package for Bayesian Structure Learning in Graphical Models, Journal of Statistical Software, 89(3):1-30

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

Letac, G., Massam, H. and Mohammadi, R. (2018). The Ratio of Normalizing Constants for Bayesian Graphical Gaussian Model Selection, arXiv preprint arXiv:1706.04416v2

Mohammadi, A. et al (2017). Bayesian modelling of Dupuytren disease by using Gaussian copula graphical models, Journal of the Royal Statistical Society: Series C, 66(3):629-645

### See Also

`gnorm`, `rwish`

### Examples

    # Generating a 'circle' graph as a non-decomposable graph
    adj <- graph.sim( p = 5, graph = "circle" )
    adj    # adjacency of graph with 5 nodes

    sample <- rgwish( n = 1, adj = adj, b = 3, D = diag( 5 ) )
    round( sample, 2 )

    sample <- rgwish( n = 5, adj = adj )
    round( sample, 2 )

[Package BDgraph version 2.62 Index]