We begin with a discussion of multivariate power laws of in- and out-degree in a preferential attachment model. The problem can be approached in a variety of ways: (i) Multivariate Tauberian theory; (ii) Direct approaches via asymptotic to get a limit measure; (iii) proving multivariate regular variation of the limiting mass function of normalized in- and out-degree. Each method has its own surprises. We then turn to model calibration comparing various information sources and methods. If a full history of network growth is available, full MLE implementation is possible and performs well on simulated data. If a single snapshot in time is all that is available, then approximate MLE can be used. Comparison with MLE and use of asymptotic methods relying on heavy tail estimators can also be made and predictably there is a trade-off between robustness and accuracy. Methods generally perform well on simulated data but real data creates problems with model error and we illustrate this with wikipedia data obtained from Konect. Obvious model error can suggest other directions.
Professor Sidney Resnick joined the Cornell faculty in 1987 after nine years at Colorado State University, six years at Stanford University, and two years at the Technion, in Haifa, Israel. He has held visiting appointments at the University of Amsterdam and the Amsterdam Mathematics Center; the Australian National University and CSIRO, in Canberra, Australia; the Technion in Israel (as a Lady Davis Fellow); Sussex University, in Brighton, UK, Erasmus University Rotterdam, ETH Zurich, Department of Statistics, UNC, Chapel Hill; Columbia University; Samsi, Research Triangle Park, NC; Technical University Munich (as John Von Neuman Visiting Professor). Resnick is a fellow of the Institute of Mathematical Statistics, and while at Colorado State was an Oliver Pennock Distinguished Service Award winner. He is a founding associate editor of Annals of Applied Probability, and a current associate editor of Stochastic Models, Extremes, Stochastic Processes and their Applications and The Mathematical Scientist. He is a former associate editor of Journal of Applied Probability. He served a three-year term on the Council of the Institute of Mathematical Statistics and served on their ad hoc committee on electronic publishing. He is currently an editor for Birkhauser, Boston serving on the boards of the Progress in Probability and Progress in Probability and Its Applications series and also serves on the editorial board of the Springer series Operations Research and Financial Engineering. His BS is from Queens College, NYC and his PhD is from Purdue. Resnick concluded a five year term as Director of Cornell’s School of Operations Research and Information Engineering in June 2004. Professor Resnick has authored or coauthored 160 papers and four books.
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