UID:
almahu_9949728655502882
Format:
1 online resource :
,
text file, PDF
Edition:
First edition.
ISBN:
9781315209661
,
1315209667
,
9781351807333
,
1351807331
,
9781351807319
,
1351807315
Series Statement:
Monographs on statistics and applied probability ; 157
Content:
"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 authors 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 Cranes 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. Cranes methods have been applied to domain-specific cybersecurity and counterterrorism problems at the Foreign Policy Research Institute and RANDs Project AIR FORCE.??????"--Provided by publisher.
Note:
Cover; Half Title; Monographs On Statistics Andapplied Probability; Title; Copyright; Dedication; Contents; Preface; Acknowledgments; Chapter 1 Orientation; 1.1 Analogy: Bernoulli Trials; 1.2 What It Is: Graphs Vs. Networks; 1.3 How To Look At It: Labeling And Representation; 1.4 Where It Comes From: Context; 1.5 Making Sense Of It All: Coherence; 1.6 What We're Talking About: Examples Of Network Data; 1.6.1 Internet; 1.6.2 Social Networks; 1.6.3 Karate Club; 1.6.4 Enron Email Corpus; 1.6.6 Blockchain And Cryptocurrency Networks; 1.6.5 Collaboration Networks; 1.6.7 Other Networks.
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1.6.8 Some Common Scenarios1.7 Major Open Questions; 1.7.1 Sparsity; 1.7.2 Modeling Network Complexity; 1.7.3 Sampling Issues; 1.7.4 Modeling Network Dynamics; 1.8 Toward A Probabilistic Foundation For Statistical Network Analysis; Chapter 2 Binary Relational Data; 2.1 Scenario: Patterns In International Trade; 2.1.1 Summarizing Network Structure; 2.2 Dyad Independence Model; 2.3 Exponential Random Graph Models (ergms; 2.4 Scenario: Friendships In A High School; 2.5 Network Inference Under Sampling; 2.6 Further Reading; Chapter 3 Network Sampling; 3.1 Opening Example.
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3.2 Consistency Under Selection3.2.1 Consistency Of The P1 Model; 3.3 Significance Of Sampling Consistency; 3.3.1 Toward A Coherent Framework For Network Modeling; 3.4 Selection From Sparse Networks; 3.5 Scenario: Ego Networks In High School Friendships; 3.6 Network Sampling Schemes; 3.6.1 Relational Sampling; 3.6.1.1 Edge Sampling; 3.6.1.2 Hyperedge Sampling; 3.6.1.3 Path Sampling; 3.6.2 Snowball Sampling; 3.7 Units Of Observation; 3.8 What Is The Sample Size; 3.9 Consistency Under Subsampling; 3.10 Further Reading; 3.11 Solutions To Exercises; 3.11.1 Exercise 3.1; 3.11.2 Exercise 3.2.
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3.11.3 Exercise 3.33.11.4 Exercise 3.4; Chapter 4 Generative Models; 4.1 Specification Of Generative Models; 4.2 Generative Model 1: Preferential Attachment Model; 4.3 Generative Model 2: Random Walk Models; 4.4 Generative Model 3: Erd.os-rényi-gilbert Model; 4.5 Generative Model 4: General Sequential Construction; 4.6 Further Reading; Chapter 5 Statistical Modeling Paradigm; 5.1 The Quest For Coherence; 5.2 An Incoherent Model; 5.3 What Is A Statistical Model; 5.3.1 Population Model; 5.3.2 Finite Sample Models; 5.4 Coherence; 5.4.1 Coherence In Sampling Models.
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5.4.2 Coherence In Generative Models5.5 Statistical Implications Of Coherence; 5.6 Examples; 5.6.1 Example 1: Erd.os-rényi-gilbert Model Under Selection Sampling; 5.6.2 Example 2: Ergm Under Selection Sampling; 5.6.3 Example 3: Erd.os-rényi-gilbert Model Under Edge Sampling 72 5.7 Invariance Principles; 5.7 Invariance Principles; 5.8 Further Reading; 5.9 Solutions To Exercises; 5.9.1 Exercise 5.1; Chapter 6 Vertex Exchangeable Models; 6.1 Preliminaries: Formal Definition Of Exchangeability; 6.2 Implications Of Exchangeability; 6.3 Finite Exchangeable Random Graphs.
Additional Edition:
ISBN 9781351807333
Additional Edition:
ISBN 9781351807326
Language:
English
Keywords:
Electronic books.
;
Electronic books.
URL:
https://www.taylorfrancis.com/books/9781315209661
URL:
https://www.taylorfrancis.com/books/9781315209661
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