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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. This approach improves performance with respect to the Monte Carlo maximum likelihood method of Geyer and Thompson (1992).
Caimo, A. and Friel, N. (2011), Bayesian Inference for Exponential Random Graph Models. Social Networks, 33(1), 41 – 55, 2011. doi: 10.1016/j.socnet.2010.09.004