Feature-inclusion Stochastic Search for Gaussian Graphical Models

James G. Scott and Carlos M. Carvalho

DSS, Duke University and University of Chicago GSB

September 2007

Final version published in Journal of Computational and Graphical Statistics, 17 (2008) .

We describe a serial algorithm called feature-inclusion stochastic search, or FINCS, that uses online estimates of edge-inclusion probabilities to inform the process of model determination in Gaussian graphical models. FINCS is compared to Metropolis-based search methods and found to be superior along a variety of dimensions, leading to more accurate and less volatile estimates edge-inclusion probabilities, greater speed in finding good models, and better predictions in doing Bayesian model averaging over the top models discovered. We illustrate the use of FINCS by studying two questions of theoretical interest in Gaussian graphical models: the predictive power of the median probability graph, and the performance of empirical-Bayes vs. fully Bayes treatments of model hyperparameters.

Keywords: Gaussian graphical models; stochastic search; empirical Bayes.

The manuscript is available in PDF format.