Bayesian model selection for exponential random graph models

TL;DR

This paper introduces a Bayesian model selection approach for exponential random graph models, addressing the challenge of intractable likelihoods by extending reversible jump MCMC to estimate posterior model probabilities.

Contribution

It develops a fully Bayesian model selection method for ERGMs using an extended reversible jump MCMC algorithm, handling doubly intractable posteriors.

Findings

Successfully estimates posterior probabilities for competing models

Addresses intractability in likelihood and evidence calculations

Provides a practical Bayesian framework for ERGM model selection

Abstract

Exponential random graph models are a class of widely used exponential family models for social networks. The topological structure of an observed network is modelled 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. This is a very challenging problem---the posterior distribution for each model is often termed "doubly intractable" since computation of the likelihood is rarely available, but also, the evidence of the posterior is, as usual, intractable. The contribution of this paper is the development of a fully Bayesian model selection method based on a reversible jump Markov chain Monte Carlo algorithm extension of Caimo and Friel (2011) which estimates the posterior probability for each competing model.