rwish {BDgraph}

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

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:

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.

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.

Author(s)

Reza Mohammadi [e-mail]

References

Lenkoski, A. (2013). A direct sampler for G-Wishart variates, Stat, 2:119-128, 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, 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 )