Topic status: We're looking for students to study this topic.
Network models are useful for dealing with the kinds of statistical dependence induced by a variety of relationships between entities, varying from social relationships between people to proteins. Much recent effort has been focused on inference for social network models and applications are in fields such as epidemiology, with the spread of diseases, business and political science. The key idea is to represent complex relationships and interactions between objects of interest (e.g. people, regions, proteins) by a network graph comprising nodes connected via edges representative of node relationships. This can result in extremely complex graphs, the advantage being that typically complex real-world settings can be better represented. The standard statistical models for random network structure are exponential random graph models (ERGMs), which are in the exponential family and have a long history in the networks literature. This project will review current maximum likelihood and Bayesian methods for finding estimates of the ERGM parameters given an observed network and apply them to network data.