BDgraph (version 2.41)

rwish: 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.

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 \(W(b, D)\).

Details

Sampling from Wishart distribution, \(K \sim W(b, D)\), 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

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 {
p      <- 5
sample <- rwish( n = 3, p = p, b = 3, D = diag(p) )
round( sample, 2 )  
# }