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In a Gaussian graphical model, the conditional independence between twovariables are characterized by the corresponding zero entries in the inversecovariance matrix. Maximum likelihood method using the smoothly clippedabsolute deviation (SCAD) penalty (Fan and Li, 2001) and the adaptive LASSOpenalty (Zou, 2006) have been proposed in literature. In this article, weestablish the result that using Bayesian information criterion (BIC) to selectthe tuning parameter in penalized likelihood estimation with both types ofpenalties can lead to consistent graphical model selection. We compare theempirical performance of BIC with cross validation method and demonstrate theadvantageous performance of BIC criterion for tuning parameter selectionthrough simulation studies.

Tuning parameter selection for penalized likelihood estimation of inverse covariance matrix