  This paper proposes a penalized composite likelihood method for model
selection in colored graphical Gaussian models. The method provides a sparse
and symmetry-constrained estimator of the precision matrix, and thus conducts
model selection and precision matrix estimation simultaneously. In particular,
the method uses penalty terms to constrain the elements of the precision
matrix, which enables us to transform the model selection problem into a
constrained optimization problem. Further, computer experiments are conducted
to illustrate the performance of the proposed new methodology. It is shown that
the proposed method performs well in both the selection of nonzero elements in
the precision matrix and the identification of symmetry structures in graphical
models. The feasibility and potential clinical application of the proposed
method are demonstrated on a microarray gene expression data set.
