Comparison of Bayesian Inference Methods for Probit Network Models

Abstract

This thesis explores and compares Bayesian inference procedures for probit network models. Network data typically exhibit high dyadic correlation due to reciprocity. For binary network data, presence of dyadic correlation often leads to inefficiency of a basic implementation of Markov chain Monte Carlo (MCMC). We first explore variational inference as a fast approximation to the posterior distribution. Aware of its insufficiency in quantifying posterior uncertainties, we propose an alternative MCMC algorithm which is more efficient and accurate. In particular, we propose to update the dyadic correlation parameter $\rho$ using the marginal likelihood unconditional of the latent relations $Z$. This reduces autocorrelations in the posterior samples of $\rho$ and hence improves mixing. Simulation study and real data examples are provided to compare the performance of these Bayesian inference methods.