Estimation and prediction for stochastic blockstructures

A statistical approach to a posteriori blockmodeling for digraphs and value d digraphs is proposed, The probability model assumes that the vertices of the digraph are partitioned into several unobserved (latent) classes and th at the probability distribution of the relation between two vertices depend s only on the classes to which they belong. A Bayesian estimator based on G ibbs sampling is proposed. The basic model is not identified, because class labels are arbitrary. The resulting identifiability problems are solved by restricting inference to the posterior distributions of invariant function s of the parameters and the vertex class membership. In addition, models ar e considered where class labels are identified by prior distributions for t he class membership of some of the vertices. The model is illustrated by an example from the social networks literature (Kapferer's tailor shop).