Statistical Inference for Networks - Professor Gesine Reinert, University of Oxford

Explore statistical inference for networks in this comprehensive lecture by Professor Gesine Reinert from the University of Oxford. Delve into the fascinating world of network analysis, covering topics such as the six degrees of separation hypothesis, network statistics, and various mathematical models. Learn about key concepts including degree distribution, clustering coefficients, shortest distances, and motifs. Examine different network types, from marriage networks to the London network, and understand research questions surrounding network analysis. Discover mathematical models like power law, preferential attachment, and stochastic block models. Gain insights into estimation techniques such as maximum likelihood and method of moments. Investigate model testing, complications in network analysis, and explore additional topics like sampling. This lecture provides a thorough introduction to the field of network statistics and its applications in various contexts, including computational biology and social interactions.

Introduction
Outline
Reading list
What are networks
Marriage network
London network
Example networks
Research questions
Network summaries
Degree distribution
Local clustering coefficient
Global clustering coefficient
Expected clustering coefficient
Shortest distance
Motifs
Other measures
Mathematical models
Via networks
Power law
preferential attachment
stochastic block model
degrees
special models
maximum likelihood
maximum likelihood estimator
method of moments
duplication divergence model
log log plot
log plot example
Markov chain
Testing the model
Complications
General framework
Other topics
Sampling