BDgraph (version 2.19)

rwish: Sampling from Wishart distribution

Description

Generate 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. The default value is 1.

p

The number of variables (nodes). The default value is 2.

b

The degree of freedom for Wishart distribution, $W(b, D)$. The default value is 3.

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:1501.05108v2 Mohammadi, A., F. Abegaz Yazew, E. van den Heuvel, and E. Wit (2015). Bayesian Modeling of Dupuytren Disease Using Gaussian Copula Graphical Models, Arxiv preprint arXiv:1501.04849v2

Examples

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