Probabilistic Foundations of Statistical Network Analysis (Chapman & Hall/CRC Monographs on Statistics & Applied Probability)

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.

《統計網絡分析的概率基礎》提供了對現代網絡分析的基本原則和主要挑戰的新鮮而深入的觀點。其清晰的闡述為理解可交換和動態網絡模型、網絡抽樣以及稀疏性和冪律等網絡統計概念提供了必要的背景，這些概念在當代數據科學和機器學習應用中起著核心作用。該書通過對統計推斷的基本原則、網絡數據的實證特性以及概率理論的技術概念之間微妙的相互作用的清晰而直觀的理解，回報讀者。其在數學上嚴謹但非技術性的闡述使得該書對專業的數據科學家、統計學家和計算機科學家以及實踐者和研究人員都具有可讀性。對於新手和非量化研究人員來說，其概念方法對於發展對統計和概率技術思想的直覺非常有價值，而對於專家和研究生來說，該書是一個方便的參考資料，涵蓋了一系列新的主題，包括邊緣可交換性、相對可交換性、圖模型和圖值李維過程以及用於動態網絡的重連模型。

作者的深入評論補充了這些核心概念，挑戰讀者超越這一新興學科的現有限制。本書以易於理解的闡述和50多個帶有解答的開放性研究問題和練習題，非常適合對現代網絡分析、數據科學、機器學習和統計感興趣的高年級本科生和研究生。

Harry Crane是羅格斯大學統計學和生物統計學研究生課程的副教授和聯合主任，也是哲學研究生教師團隊的副成員。Crane教授的研究興趣涵蓋了網絡科學、概率論、統計推斷和數學邏輯等領域的一系列數學和應用主題。除了他在邊緣和關聯可交換性、相對可交換性和圖值馬爾可夫過程方面的技術工作外，Crane教授的方法還應用於外交政策研究所和蘭德公司項目空軍的特定領域的網絡安全和反恐問題。