Probabilistic Foundations of Statistical Network Analysis presents
a fresh and insightful perspective on the fundamental tenets and
major challenges of modern network analysis. Its lucid exposition
provides necessary background for understanding the essential ideas
behind exchangeable and dynamic network models, network sampling,
and network statistics such as sparsity and power law, all of which
play a central role in contemporary data science and machine
learning applications. The book rewards readers with a clear and
intuitive understanding of the subtle interplay between basic
principles of statistical inference, empirical properties of
network data, and technical concepts from probability theory. Its
mathematically rigorous, yet non-technical, exposition makes the
book accessible to professional data scientists, statisticians, and
computer scientists as well as practitioners and researchers in
substantive fields. Newcomers and non-quantitative researchers will
find its conceptual approach invaluable for developing intuition
about technical ideas from statistics and probability, while
experts and graduate students will find the book a handy reference
for a wide range of new topics, including edge exchangeability,
relative exchangeability, graphon and graphex models, and
graph-valued Levy process and rewiring models for dynamic networks.
The author's incisive commentary supplements these core concepts,
challenging the reader to push beyond the current limitations of
this emerging discipline. With an approachable exposition and more
than 50 open research problems and exercises with solutions, this
book is ideal for advanced undergraduate and graduate students
interested in modern network analysis, data science, machine
learning, and statistics. Harry Crane is Associate Professor and
Co-Director of the Graduate Program in Statistics and Biostatistics
and an Associate Member of the Graduate Faculty in Philosophy at
Rutgers University. Professor Crane's research interests cover a
range of mathematical and applied topics in network science,
probability theory, statistical inference, and mathematical logic.
In addition to his technical work on edge and relational
exchangeability, relative exchangeability, and graph-valued Markov
processes, Prof. Crane's methods have been applied to
domain-specific cybersecurity and counterterrorism problems at the
Foreign Policy Research Institute and RAND's Project AIR FORCE.
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