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Networks出版済み 3-5週間でお届けいたします。
Title: Networks Subtitle: Probability and Statistics Series: Cambridge Series in Statistical and Probabilistic Mathematics Author: Barbour, A. D. (Universitat Zurich) / Reinert, Gesine (University of Oxford) Publisher: Cambridge University Press ISBN: 9781009651721 Cover: HARDCOVER Date: 2026年06月 DESCRIPTION ネットワーク：確率と統計 このテキストは、ランダムネットワークのもっともらしいモデルを構築して分析する方法、およびそのようなモデルを検証し、データの特異な特徴を検出し、予測を行うために統計を使用する方法について説明します。数学的厳密性と分かりやすさの独自のバランスを保ちながら、広範囲に応用できるトピックを読者に紹介しています。 From social networks to biological systems, networks are a fundamental part of modern life. Network analysis is increasingly popular across the mathematical, physical, life and social sciences, offering insights into a range of phenomena, from developing new drugs based on intracellular interactions, to understanding the influence of social interactions on behaviour patterns. This book provides a toolkit for analyzing random networks, together with theoretical justification of the methods proposed. It combines methods from both probability and statistics, teaching how to build and analyze plausible models for random networks, and how to validate such models, to detect unusual features in the data, and to make predictions. Theoretical results are motivated by applications across a range of fields, and classical data sets are used for illustration throughout the book. This book offers a comprehensive introduction to the field for graduate students and researchers. Provides a comprehensive look at both probabilistic and statistical methods for network analysis Motivates the theoretical results with a large range of examples, from a wide range of disciplines including linguistics, engineering and biology Includes detailed exercises suitable for course use or self-study TABLE OF CONTENTS 1. Introduction Part I. Basic Setting: 2. Network data sets 3. Network summaries 4. Models for networks Part II. Probability Preliminaries: 5. Branching processes 6. Some birth and death processes 7. Poisson approximation 8. Ramifications of Poisson approximation 9. Normal approximation 10. Multivariate normal approximation Part III. Network Models: 11. The Bernoulli random graph 12. Models related to the Bernoulli random graph 13. The Chung-Lu model 14. The configuration and GPDS models 15. Random geometric graphs 16. Small world graphs 17. Preferential attachment models 18. Dense graph limits and graphon models 19. Random processes on networks 20. Summary of Chapters 5-19 Part IV. Network Inference: 21. Sampling from networks 22. Estimation: fitting a network model 23. Assessing model fit 24. Community detection 25. Using networks for inference 26. Some further topics
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