Exponential random graph models are a class of widely used exponential family
models for social networks. The topological structure of an observed network is
modeled by the relative prevalence of a set of local sub-graph configurations
termed network statistics. One of the key tasks in the application of these
models is which network statistics to include in the model. This can be thought
of as statistical model selection problem.
Exponential random graph models are extremely difficult models to handle from
a statistical viewpoint, since their normalising constant, which depends on
model parameters, is available only in very trivial cases. We show how
inference can be carried out in a Bayesian framework using a MCMC algorithm,
which circumvents the need to calculate the normalising constants. We use a
population MCMC approach which accelerates convergence and improves mixing of
the Markov chain.