rwish function

Sampling from Wishart distribution

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

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

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.

Details

Sampling from Wishart distribution, $K \sim W(b, D)$, with density:

which $b > 2$ is the degree of freedom and $D$ is a symmetric positive definite matrix.

Returns

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, tools:::Rd_expr_doi("10.1002/sta4.23")

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")

Author(s)

Reza Mohammadi a.mohammadi@uva.nl

See Also

gnorm, rgwish

Examples

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

round( sample, 2 )