Effectiveness of combinations of Gaussian graphical models for model building

Combining statistical models is an useful approach in all the research area where a global picture of the problem needs to be constructed by binding together evidence from different sources [M.S. Massa and S.L. Lauritzen Combining Statistical Models, M. Viana and H. Wynn, eds., American Mathematical Society, Providence, RI, 2010, pp. 239-259]. In this paper, we investigate the effectiveness of combining a fixed number of Gaussian graphical models respecting some consistency assumptions in problems of model building. In particular, we use the meta-Markov combination of Gaussian graphical models as detailed in Massa and Lauritzen and compare model selection results obtained by combining selections over smaller sets of variables with selection results over all variables of interest. In order to do so, we carry out some simulation studies in which different criteria are considered for the selection procedures. We conclude that the combination performs, generally, better than global estimation, is computationally simpler by virtue of having fewer and simpler models to work on, and has an intuitive appeal to a wide variety of contexts.