Networks are a form of "relational data". Relational data arise in many social science fields and graph models are a natural approach to representing the structure of these relations. This framework has many applications including, for example, the structure of social networks, the behavior of epidemics, the interconnectedness of the WWW, and long-distance telephone calling patterns.
We review stochastic models for such graphs, with particular focus on sexual and drug use networks. Commonly used Markov models were introduced by Frank and Strauss (1986) and were derived from developments in spatial statistics (Besag 1974). These models recognize the complex dependencies within relational data structures.
To date, the use of graph models for networks has been limited by three interrelated factors: the complexity of realistic models, lack of use of simulation studies, and a poor understanding of the properties of inferential methods. In this talk we discuss these factors and the degeneracy of commonly promoted models. We also review the role of Markov Chain Monte Carlo (MCMC) algorithms for simulation and likelihood-based inference.
These ideas are applied to a sexual relations and IV drug networks from Colorado Springs with the objective of understanding the social determinants of HIV spread.
