Bayesian inference for exponential random graph models

TL;DR

This paper introduces a Bayesian MCMC method for exponential random graph models that bypasses the challenging normalising constant calculation, improving inference efficiency and convergence.

Contribution

It presents a novel Bayesian inference approach using population MCMC for ERGMs, enhancing performance over existing Monte Carlo maximum likelihood methods.

Findings

Efficient Bayesian inference for ERGMs without normalising constants

Population MCMC accelerates convergence and improves mixing

Outperforms traditional Monte Carlo maximum likelihood methods

Abstract

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).