Bayesian perspectives on exponential random graph models

2026-05-25

AI Summary

This study addresses the dual intractability problem in Bayesian inference for exponential random graph models (ERGMs), where the likelihood normalizing constant depends on unknown parameters and lacks a closed-form expression. The work provides the first systematic review and classification of existing approaches, organizing them into three dominant paradigms: auxiliary variable Markov chain Monte Carlo (MCMC), corrected pseudolikelihood, and variational inference. It further integrates model selection strategies and extends the framework to handle realistic scenarios such as missing data, longitudinal dynamics, network populations, and weighted networks. By unifying these components into a coherent Bayesian ERGM framework, the study enables principled prior incorporation and rigorous uncertainty quantification, thereby advancing both theoretical foundations and practical applicability across multiple disciplines.

Abstract

Exponential random graph models (ERGMs) are a widely used framework for network data, enabling hypothesis testing on the structural mechanisms underlying observed networks. Bayesian ERGMs provide principled uncertainty quantification and enable the incorporation of prior knowledge through fully probabilistic modelling. However, computation remains challenging because the posterior is doubly intractable, with a likelihood normalising constant that depends on unknown parameters. This paper reviews Bayesian approaches to ERGM inference, categorising inference methods into three broad classes: auxiliary variable MCMC methods, adjusted pseudo-likelihood approaches, and variational methods, alongside dedicated treatment of model selection. We also discuss modelling extensions for missing data, longitudinal dynamics, populations of networks, weighted networks, highlighting applications across various scientific disciplines.

Problem

• Bayesian inference
• exponential random graph models
• doubly intractable posterior
• normalising constant
• network data

Innovation

• Bayesian ERGM
• doubly intractable posterior
• auxiliary variable MCMC
• adjusted pseudo-likelihood
• variational inference