Bayesian Inference for Longitudinal Social Networks

A natural approach for modeling stochastic processes on social net-works is by using continuous-time Markov chains, examples of which have beengiven by Wasserman (1977, 1980b,a) and Leenders (1995b,a). Snijders (1996)proposed a class of models that allow for greater flexibility in defining the dy-namic components, relaxing the restrictions on the type of dependence struc-tures that could be modeled. Previously, estimation of the parameters in suchmodels has been based on a Markov chain Monte Carlo (MCMC) implementa-tion of the method of moments. In this paper we generalize the class of stochasticactor-oriented models, and propose an MCMC algorithm for exploring the pos-terior distribution of the parameters. The generalized class of stochastic actororiented models can handle un-directed, bipartite and valued social networksin addition to the dichotomous directed networks of the stochastic actor ori-ented models. The MCMC procedure explicitly models the changes in-betweenobservations as latent variables.