Strategies for Graphical Model Selection

We consider the problem of model selection for Bayesian graphical models, and embed it in the larger context of accounting for model uncertainty. Data analysts typically select a single model from some class of models, and then condition all subsequent inference on this model. However, this approach ignores model uncertainty, leading to poorly calibrated predictions: it will often be seen in retrospect that one’s uncertainty bands were not wide enough. The Bayesian analyst solves this problem by averaging over all plausible models when making inferences about quantities of interest. In many applications, however, because of the size of the model space and awkward integrals, this averaging will not be a practical proposition, and approximations are required. Here we examine the predictive performance of two recently proposed model averaging schemes. In the examples considered, both schemes outperform any single model that might reasonably have been selected.