BDgraph (version 2.70)

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 ) )

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.

Arguments

n

number of samples required.

p

number of variables (nodes).

b

degree of freedom for Wishart distribution, \(W(b, D)\).

D

positive definite \((p \times p)\) "scale" matrix for Wishart distribution, \(W(b, D)\). The default is an identity matrix.

Author

Reza Mohammadi

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

Lenkoski, A. (2013). A direct sampler for G-Wishart variates, Stat, 2:119-128, tools:::Rd_expr_doi("10.1002/sta4.23")

Mohammadi, A. and Wit, E. C. (2015). Bayesian Structure Learning in Sparse Gaussian Graphical Models, Bayesian Analysis, 10(1):109-138, tools:::Rd_expr_doi("10.1214/14-BA889")

Mohammadi, R., Massam, H. and Letac, G. (2021). Accelerating Bayesian Structure Learning in Sparse Gaussian Graphical Models, Journal of the American Statistical Association, tools:::Rd_expr_doi("10.1080/01621459.2021.1996377")

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, tools:::Rd_expr_doi("10.18637/jss.v089.i03")

See Also

gnorm, rgwish

Examples

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

round( sample, 2 )