A new Gaussian graphical modeling that is robustified against possible outliers is proposed. The likelihood function is weighted according to how the observation is deviated, where the deviation of the observation is measured based on its likelihood. Test statistics associated with the robustified estimators are developed. These include statistics for goodness of fit of a model. An outlying score, similar to but more robust than the Mahalanobis distance, is also proposed. The new scores make it easier to identify outlying observations. A Monte Carlo simulation and an analysis of a real data set show that the proposed method works better than ordinary Gaussian graphical modeling and some other robustified multivariate estimators.
