{GeneTS}R Documentation

Graphical Gaussian Models: Fit Mixture Distribution to Sample Correlation Coefficients

Description fits a mixture model

f(r) = eta0 dcor0(r, kappa) + etaA dunif(r, -1, 1)

to a vector of empirical partial correlation coefficients using likelihood maximization. This allows to estimates both the degree of freedom kappa in the null-distribution and the proportion eta0 of null r-values (note that etaA = 1-eta0).

cor.prob.nonzero computes

etaA dunif(r, -1, 1)/f(r),

i.e. the posterior probability that the true correlation is non-zero given the empirical correlation r, the degree of freedom of the null-distribution kappa, and the prior eta0 for the null-distribution.

Usage, MAXKAPPA=5000)
cor.prob.nonzero(r, kappa, eta0)


r vector of sample correlations
kappa the degree of freedom of the null distribution
eta0 the proportion of true null r-values (=the prior)
MAXKAPPA upper bound for the estimated kappa (default: MAXKAPPA=5000)


The above functions are useful to determine the null-distribution of edges in a sparse graphical Gaussian model, see Schaefer and Strimmer (2004) for more details and an application to infer genetic networks from microarray data.


A list object with the following components:

kappa the degree of freedom of the null distribution
eta0 the prior for the null distribution, i.e. the proportion of null r-values
logL the maximized log-likelihood


Juliane Schaefer ( and Korbinian Strimmer (


Schaefer, J., and Strimmer, K. (2004). An empirical Bayes approach to inferring large-scale gene association networks. Bioinformatics in press.

See Also

dcor0, cor0.estimate.kappa, kappa2N, fdr.estimate.eta0.


# load GeneTS library

# simulate mixture distribution
r <- rcor0(700, kappa=10)
u <- runif(200, min=-1, max=1)
rc <- c(r,u)

# estimate kappa and eta0 (=7/9) 

# for comparison

# posterior probabilities
r <- seq(-1,1, .01)
post.prob <- cor.prob.nonzero(r,kappa=10,eta0=7/9)
plot(r, post.prob, type="l")

[Package GeneTS version 2.3 Index]