A nonparametric latent space model for dynamic relational networks

Recent years have seen a growing interest in the study of social networks and relational data and, in particular, of their evolution over time. In the context of static networks, a commonly used statistical model defines a latent social space and assumes the relationship between two actors to be determined by the distance between them in such latent space. In this manner, it is possible to introduce additionalinformation about each actor and to quantify the residual dependence through a row-column exchangeability assumption on the adjacency matrix associated to the error terms of the model. The present paper analyzes the behavior of the stochastic model given by changes in a ''global sociability'' parameter which describes the dispersion of the residuals of the positions of the actors in the latent space. This justifies the definition of a Bayesian model for dynamic networks which extends the latent space representation through an infinite hidden Markov model on such positions.