qpgraph (version 2.6.1)

qpRndWishart: Random Wishart distribution

Description

Random generation for the (n.var * n.var) Wishart distribution (see Press, 1972) with matrix parameter A=diag(delta)%*%P%*%diag(delta) and degrees of freedom df.

Usage

qpRndWishart(delta=1, P=0, df=NULL, n.var=NULL)

Arguments

delta

a numeric vector of n.var positive values. If a scalar is provided then this is extended to form a vector.

P

a (n.var * n.var) positive definite matrix with unit diagonal. If a scalar is provided then this number is used as constant off-diagonal entry for P.

df

degrees of freedom.

n.var

dimension of the Wishart matrix. It is required only when both delata and P are scalar.

Value

A list of two n.var * n.var matrices rW and meanW where rW is a random value from the Wishart and meanW is the expected value of the distribution.

Details

The degrees of freedom are df > n.var-1 and the expected value of the distribution is equal to df * A. The random generator is based on the algorithm of Odell and Feiveson (1966).

References

Odell, P.L. and Feiveson, A.G. A numerical procedure to generate a sample covariance matrix. J. Am. Statist. Assoc. 61, 199-203, 1966.

Press, S.J. Applied Multivariate Analysis: Using Bayesian and Frequentist Methods of Inference. New York: Holt, Rinehalt and Winston, 1972.

Tur, I., Roverato, A. and Castelo, R. Mapping eQTL networks with mixed graphical Markov models. Genetics, 198(4):1377-1393, 2014.

See Also

qpG2Sigma

Examples

## Construct an adjacency matrix for a graph on 6 vertices

nVar <- 6
A <- matrix(0, nVar, nVar)
A[1,2] <- A[2,3] <- A[3,4] <- A[3,5] <- A[4,6] <- A[5,6] <- 1
A=A + t(A)
A
set.seed(123)
M <- qpRndWishart(delta=sqrt(1/nVar), P=0.5, n.var=nVar)
M
set.seed(123)
d=1:6
M <- qpRndWishart(delta=d, P=0.7, df=20)
M