Eric A Vance
Assistant Research Professor & Director of LISA (Laboratory for Interdisciplinary Statistical Analysis)Virginia Tech, Department of Statistics
Statistical Methods for Dynamic Network Data
Motivated by questions involving three examples of dynamic network data, we apply, extend, and develop statistical methodology for the treatment of these data. Ranging from a handful of observations per week on African elephants, to 1,000 telephone calls per day in a calling network, to data streaming every five minutes from a server on a large AT&T network, our data are dynamic and the networks they induce—or are derived from—are constantly evolving, thus posing special challenges to the statisticians analyzing them. In this dissertation we demonstrate the usefulness of our statistical methodology by characterizing these dynamics and pinpointing their causes. Chapter 1 discusses the evolution of social network models and introduces the themes which guide the rest of the work. Chapter 2 answers questions about how and why wild African elephants interact through the use of a social network model. Chapter 3 explains this social network model in detail and develops novel interpretations and uses for it. Chapter 4 applies concepts from social network theory to discover fraud within a dynamic telephone calling network. Chapter 5 discusses the challenges faced when analyzing dynamic, streaming data and develops methodology for handling this type of data. The method of DataSpheres is applied to a real data example to show how this methodology can be useful to managers of such streaming data. Finally, we close, in Chapter 6, with some areas for future research that have opened up as a result of studying these models for dynamic network data.