Approximate Bayesian inference for Exponential Random Graph Models

Exponential Random Graph Models (ERGM) are a powerful and flexible tool for modeling networks, but their inference faces the issue of the intractability of the normalizing constant, which renders traditional methods impossible to apply. Previous research on the subject focuses on Monte Carlo Maximum Likelihood Estimation (MC-MLE) for the frequentist approach, and augmented distribution sampling for the Bayesian approach. This thesis proposes the application of Approximate Bayesian Computation (ABC) to fit ERGMs, and it does so by implementing an ABC algorithm with Partial Rejection Control. The efficiency of the sampling step is aided by employing a multivariate Gaussian kernel on the model’s parameters. The performance of this algorithm is demonstrated by application on two well-known network datasets and on a third network of international trade, and tested through a Goodness of Fit procedure. Results show that the algorithm is able to fit data accurately and consistently when applied to social networks.