The exchange algorithm enables Bayesian posterior inference for models with intractable likelihoods, such as Ising, Potts, or exponential random graph models (ERGM). Crucially, this algorithm relies on an auxiliary Markov chain to obtain an unbiased sample from the generative distribution of the model. It was originally proposed to use coupling from the past (CFTP) for this purpose, but this requires the Markov chain to be uniformly ergodic. In the case of the Ising model, coupling time increases super-exponentially for parameter values larger than the critical point. Alternatives to CFTP, such as perfect slice sampling or bounding chains for Swendsen-Wang, have been proposed for the Ising model. However, there are currently no suitable alternatives for ERGM, which also features a phase transition that can cause problems with convergence. This talk will review some recent work on simulation algorithms for ERGM and discuss how this problem might be addressed.
This is joint work with Kerrie Mengersen and Chris Drovandi (QUT, Australia), Antonietta Mira (USI Lugano, Switzerland), and Alberto Caimo (Dublin Inst. Tech., Ireland).