  Graphical Gaussian models have proven to be useful tools for exploring
network structures based on multivariate data. Applications to studies of gene
expression have generated substantial interest in these models, and resulting
recent progress includes the development of fitting methodology involving
penalization of the likelihood function. In this paper we advocate the use of
the multivariate t and related distributions for more robust inference of
graphs. In particular, we demonstrate that penalized likelihood inference
combined with an application of the EM algorithm provides a simple and
computationally efficient approach to model selection in the t-distribution
case.
