This book constitutes the thoroughly refereed post-proceedings of the International Workshop on Statistical Network Analysis: Models, Issues, and New Directions held in Pittsburgh, PA, USA in June 2006 as associated event of the 23rd International Conference on Machine Learning, ICML 2006. It covers probabilistic methods for network analysis, paying special attention to model design and computational issues of learning and inference.

Networks are ubiquitous in science and have become a focal point for discussion in everyday life. Formal statistical models for the analysis of network data have emerged as a major topic of interest in diverse areas of study, and most of these involve a form of graphical representation. Probability models on graphs date back to 1959. Along with empirical studies in social psychology and sociology from the 1960s, these early works generated an active network community and a substantial literature in the 1970s. This effort moved into the statistical literature in the late 1970s and 1980s, and the past decade has seen a burgeoning network literature in statistical physics and computer science. The growth of the World Wide Web and the emergence of online networking communities such as Facebook, MySpace, and LinkedIn, and a host of more specialized professional network communities has intensified interest in the study of networks and network data. Our goal in this review is to provide the reader with an entry point to this burgeoning literature. We begin with an overview of the historical development of statistical network modeling and then we introduce a number of examples that have been studied in the network literature. Our subsequent discussion focuses on a number of prominent static and dynamic network models and their interconnections. We emphasize formal model descriptions, and pay special attention to the interpretation of parameters and their estimation. We end with a description of some open problems and challenges for machine learning and statistics.

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.

Presents new models, methods, and techniques and considers important real-world applications in political science, sociology, economics, marketing, and finance Emphasizing interdisciplinary coverage, Bayesian Inference in the Social Sciences builds upon the recent growth in Bayesian methodology and examines an array of topics in model formulation, estimation, and applications. The book presents recent and trending developments in a diverse, yet closely integrated, set of research topics within the social sciences and facilitates the transmission of new ideas and methodology across disciplines while maintaining manageability, coherence, and a clear focus. Bayesian Inference in the Social Sciences features innovative methodology and novel applications in addition to new theoretical developments and modeling approaches, including the formulation and analysis of models with partial observability, sample selection, and incomplete data. Additional areas of inquiry include a Bayesian derivation of empirical likelihood and method of moment estimators, and the analysis of treatment effect models with endogeneity. The book emphasizes practical implementation, reviews and extends estimation algorithms, and examines innovative applications in a multitude of fields. Time series techniques and algorithms are discussed for stochastic volatility, dynamic factor, and time-varying parameter models. Additional features include: Real-world applications and case studies that highlight asset pricing under fat-tailed distributions, price indifference modeling and market segmentation, analysis of dynamic networks, ethnic minorities and civil war, school choice effects, and business cycles and macroeconomic performance State-of-the-art computational tools and Markov chain Monte Carlo algorithms with related materials available via the book’s supplemental website Interdisciplinary coverage from well-known international scholars and practitioners Bayesian Inference in the Social Sciences is an ideal reference for researchers in economics, political science, sociology, and business as well as an excellent resource for academic, government, and regulation agencies. The book is also useful for graduate-level courses in applied econometrics, statistics, mathematical modeling and simulation, numerical methods, computational analysis, and the social sciences.

Politics is intuitively about relationships, but until recently the network perspective has not been a dominant part of the methodological paradigm that political scientists use to study politics. This volume is a foundational statement about networks in the study of politics.

Pioneering introduction of unprecedented breadth and scope to inferential and statistical methods for network analysis.

In response to scientific needs for more diverse and structured explanations of statistical data, researchers have discovered how to model individual data points as belonging to multiple groups. Handbook of Mixed Membership Models and Their Applications shows you how to use these flexible modeling tools to uncover hidden patterns in modern high-dimensional multivariate data. It explores the use of the models in various application settings, including survey data, population genetics, text analysis, image processing and annotation, and molecular biology. Through examples using real data sets, you’ll discover how to characterize complex multivariate data in: Studies involving genetic databases Patterns in the progression of diseases and disabilities Combinations of topics covered by text documents Political ideology or electorate voting patterns Heterogeneous relationships in networks, and much more The handbook spans more than 20 years of the editors’ and contributors’ statistical work in the field. Top researchers compare partial and mixed membership models, explain how to interpret mixed membership, delve into factor analysis, and describe nonparametric mixed membership models. They also present extensions of the mixed membership model for text analysis, sequence and rank data, and network data as well as semi-supervised mixed membership models.