Deterministic Bayesian inference for the p* model

The p* model is widely used in social network analysis. The likelihood of a network under this model is impossible to calculate for all but trivially small networks. Various approximation have been presented in the literature, and the pseudolikelihood approximation is the most popular. The aim of this paper is to introduce two likelihood approximations which have the pseudolikelihood estimator as a special case. We show, for the examples that we have considered, that both approximations result in improved estimation of model parameters with respect to the standard methodological approaches. We provide a deterministic approach and also illustrate how Bayesian model choice can be carried out in this setting.