Graphical Modelling with Large Numbers of Variables: An Application of Principal Components

Certain issues concerned with graphical modelling with large numbers of variables are discussed. A rudimentary form of initial model selection and testing is proposed in the context of covariance selection models, similar in spirit to the screening procedure of Kreiner (1987), which avoids the explicit fitting of any graphical model. It is conjectured that a useful guide to assess the performance of the model is to compare its predictive power against that of principal components. This is illustrated by an example from a data set with 30 continuous variables.