Bayesian inference of exponential random graph models for large social networks

This paper addresses the issue of sampling from the posterior distribution of exponential random graph (ERG) models and other statistical models with intractable normalizing constants. Existing methods based on exact sampling are either infeasible or require very long computing time. We propose and study a general framework of approximate MCMC sampling from these posterior distributions. We also develop a new Metropolis-Hastings kernel with improved mixing properties, to sample sparse large networks from ERG models. We illustrate the proposed methods on several examples. In particular, we combine both algorithms to fit the Faux Magnolia high school data set of Goodreau et al. (2008), a network data with 1, 461 nodes.