rwish {BDgraph} R Documentation

## Sampling from Wishart distribution

### Description

Generates random matrices, distributed according to the Wishart distribution with parameters b and D, W(b, D).

### Usage

 rwish( n = 1, p = 2, b = 3, D = diag( p ) )

### Arguments

 n The number of samples required. p The number of variables (nodes). b The degree of freedom for Wishart distribution, W(b, D). D The positive definite (p \times p) "scale" matrix for Wishart distribution, W(b, D). The default is an identity matrix.

### Details

Sampling from Wishart distribution, K \sim W(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 Wishart distribution W(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 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, 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

gnorm, rgwish
sample <- rwish( n = 3, p = 5, b = 3, D = diag( 5 ) )