Dynamic stochastic block models: parameter estimation and detection of changes in community structure

The stochastic block model (SBM) is widely used for modelling network data by assigning individuals (nodes) to communities (blocks) with the probability of an edge existing between individuals depending upon community membership. In this paper, we introduce an autoregressive extension of the SBM, based on continuous-time Markovian edge dynamics. The model is appropriate for networks evolving over time and allows for edges to turn on and off. Moreover, we allow for the movement of individuals between communities. An effective reversible-jump Markov chain Monte Carlo algorithm is introduced for sampling jointly from the posterior distribution of the community parameters and the number and location of changes in community membership. The algorithm is successfully applied to a network of mice.