Bailey Fosdick (SAMSI): Bayesian Inference for Network Models with Additive and Multiplicative Effects

Latent variable network models with additive and multiplicative effects provide a parsimonious representation of the patterns in a network. These models have been shown to capture a variety of common network phenomena such as transitivity, clustering, and reciprocity. It is straightforward to construct a Markov chain Monte Carlo (MCMC) algorithm to estimate these models, however obtaining a reasonable approximation to the posterior distribution based on samples from this procedure can take an undesirable, and possibly impractical, amount of time due to poor mixing of the chain. We propose three key modifications to a traditional MCMC algorithm that significantly improve the efficiency of the sampler and accuracy of the posterior approximation. Two of these modifications involve group updates which simultaneously move sets of parameters along specific directions in the parameter space. We discuss a mean-field variational approach to estimation for this class of models and present a simulation study which suggests the variational approximation severely underestimates both the parameter uncertainty in the posterior distribution, as well as the magnitudes of the posterior means for many covariance parameters.