extendedBIC function

Extended bayesian information criteria for gaussian graphical models

extendedBIC(gamma,omegahat,S,n)

Arguments

• gamma: a tuning parameter taking a scalar in [0,1] and leading to stronger penalization of large graphs
• omegahat: a p x p matrix indicating an estimates of precision (inverse covariance) matrix
• S: a p x p matrix indicating sample covariance matrix
• n: a scalar indicating sample size

Returns

Extended BIC penalized by the size of graphs

References

Foygel, R. and Drton, M. (2010). Extended bayesian information criteria for gaussian graphical models. arXiv preprint arXiv:1011.6640 .

Author(s)

Min Jin Ha mjha@mdanderson.org

Examples

library(glasso)
data(gbm)
x = gbm[,1]
Y = gbm[,-1]

# Estimating inverse covariance matrix using GLasso #
S = cov(Y)

rhoarray = exp(seq(log(0.001),log(1),length=100))
BIC = rep(0,length(rhoarray))
for (rh in 1:length(rhoarray)) {
    fit.gl1 = glasso(S,rho=rhoarray[rh])
    BIC[rh] = extendedBIC(gamma=0,omegahat=fit.gl1$wi,S=S,n=nrow(Y))
}
rho = rhoarray[which.min(BIC)]
fit.gl2 = glasso(S,rho=rho)
Omega = fit.gl2$wi