Efficient Bayesian inference for exponential random graph models by correcting the pseudo-posterior distribution

TL;DR

This paper introduces a correction method for pseudo-posterior distributions in Bayesian inference of exponential random graph models, improving accuracy and efficiency over naive approaches.

Contribution

It proposes a practical correction technique for pseudo-posterior samples, enabling more accurate Bayesian inference in ERGMs despite intractable likelihoods.

Findings

Corrected pseudo-posterior samples closely match true posterior distributions.

The method improves computational efficiency over existing algorithms.

Application to real-world graphs demonstrates practical effectiveness.

Abstract

Exponential random graph models are an important tool in the statistical analysis of data. However, Bayesian parameter estimation for these models is extremely challenging, since evaluation of the posterior distribution typically involves the calculation of an intractable normalizing constant. This barrier motivates the consideration of tractable approximations to the likelihood function, such as the pseudolikelihood function, which offers an approach to constructing such an approximation. Naive implementation of what we term a pseudo-posterior resulting from replacing the likelihood function in the posterior distribution by the pseudolikelihood is likely to give misleading inferences. We provide practical guidelines to correct a sample from such a pseudo-posterior distribution so that it is approximately distributed from the target posterior distribution and discuss the computational and statistical efficiency that result from this approach. We illustrate our methodology through the analysis of real-world graphs. Comparisons against the approximate exchange algorithm of Caimo and Friel (2011) are provided, followed by concluding remarks.