University of Washington - Department of Statistics
In this talk we review statistical and stochastic models for graphs that can be used to represent the structural characteristics of networks. To date, the use of graph models for networks has been limited by three interrelated factors: the complexity of realistic models, paucity of empirically relevant simulation studies, and a poor understanding of the properties of inferential methods. In this talk we discuss some proposed solutions to these limitations. We emphasize the important of likelihood-based inferential procedures and role of Markov Chain Monte Carlo (MCMC) algorithms for simulation and inference. A primary ongoing issue is the identification of classes of realistic and parsimonious models. In this regard we show the unsuitability of some commonly promoted Markov models classes because they can result in degenerate probability distributions. The ideas are motivated and illustrated by the study of sexual relations networks with the objective of understanding the social determinants of HIV spread. This area poses many challenging problem for statisticians, and we have much to offer. There will be time at the end for discussions of research opportunities and directions.