Probabilistic foundations of statistical network analysis

Probabilistic foundations of statistical network analysis /

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Bibliographic Details
Main Author: Crane, Harry (Statistics professor) (Author)
Corporate Author: ProQuest (Firm)
Format: Electronic eBook
Language:English
Published: Boca Raton, FL : CRC Press, Taylor & Francis Group, [2018]
Series:Monographs on statistics and applied probability (Series) ; 157.
Subjects:
System analysis > Mathematical models.
Network analysis (Planning)
Online Access:Connect to this title online (unlimited simultaneous users allowed; 325 uses per year)

MARC

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020 |z 9781138585997 
020 |z 1138585998 
020 |z 9781138630154 
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100 1 |a Crane, Harry  |c (Statistics professor),  |e author. 
245 1 0 |a Probabilistic foundations of statistical network analysis /  |c Harry Crane. 
264 1 |a Boca Raton, FL :  |b CRC Press, Taylor & Francis Group,  |c [2018] 
300 |a 1 online resource (xx, 236 pages.) 
336 |a text  |b txt  |2 rdacontent 
337 |a computer  |b c  |2 rdamedia 
338 |a online resource  |b cr  |2 rdacarrier 
490 1 |a Monographs on statistics and applied probability ;  |v 157 
504 |a Includes bibliographical references and index. 
505 0 0 |a Machine generated contents note:   |g 1.  |t Orientation --   |g 1.1.  |t Analogy: Bernoulli trials --   |g 1.2.  |t What it is: Graphs vs. Networks --   |g 1.3.  |t How to look at it: Labeling and representation --   |g 1.4.  |t Where it comes from: Context --   |g 1.5.  |t Making sense of it all: Coherence --   |g 1.6.  |t What we're talking about: Examples of network data --   |g 1.6.1.  |t Internet --   |g 1.6.2.  |t Social networks --   |g 1.6.3.  |t Karate club --   |g 1.6.4.  |t Enron email corpus --   |g 1.6.5.  |t Collaboration networks --   |g 1.6.6.  |t Blockchain and cryptocurrency networks --   |g 1.6.7.  |t Other networks --   |g 1.6.8.  |t Some common scenarios --   |g 1.7.  |t Major open questions --   |g 1.7.1.  |t Sparsity --   |g 1.7.2.  |t Modeling network complexity --   |g 1.7.3.  |t Sampling issues --   |g 1.7.4.  |t Modeling network dynamics --   |g 1.8.  |t Toward a Probabilistic Foundation for Statistical Network Analysis --   |g 2.  |t Binary relational data --   |g 2.1.  |t Scenario: Patterns in international trade --   |g 2.1.1.  |t Summarizing network structure --   |g 2.2.  |t Dyad independence model --   |g 2.3.  |t Exponential random graph models (ERGMs) --   |g 2.4.  |t Scenario: Friendships in a high school --   |g 2.5.  |t Network inference under sampling --   |g 2.6.  |t Further reading --   |g 3.  |t Network sampling --   |g 3.1.  |t Opening Example --   |g 3.2.  |t Consistency under selection --   |g 3.2.1.  |t Consistency of the p1 model --   |g 3.3.  |t Significance of sampling consistency --   |g 3.3.1.  |t Toward a coherent framework for network modeling --   |g 3.4.  |t Selection from sparse networks --   |g 3.5.  |t Scenario: Ego networks in high school friendships --   |g 3.6.  |t Network sampling schemes --   |g 3.6.1.  |t Relational sampling --   |g 3.6.1.1.  |t Edge sampling --   |g 3.6.1.2.  |t Hyperedge sampling --   |g 3.6.1.3.  |t Path sampling --   |g 3.6.2.  |t Snowball sampling --   |g 3.7.  |t Units of observation --   |g 3.8.  |t What is the sample size? --   |g 3.9.  |t Consistency under subsampling --   |g 3.10.  |t Further reading --   |g 3.11.  |t Solutions to exercises --   |g 3.11.1.  |t Exercise 3.1 --   |g 3.11.2.  |t Exercise 3.2 --   |g 3.11.3.  |t Exercise 3.3 --   |g 3.11.4.  |t Exercise 3.4 --   |g 4.  |t Generative models --   |g 4.1.  |t Specification of generative models --   |g 4.2.  |t Generative model 1: Preferential attachment model --   |g 4.3.  |t Generative model 2: Random walk models --   |g 4.4.  |t Generative model 3: Erdos--Renyi--Gilbert model --   |g 4.5.  |t Generative model 4: General sequential construction --   |g 4.6.  |t Further reading --   |g 5.  |t Statistical modeling paradigm --   |g 5.1.  |t quest for coherence --   |g 5.2.  |t incoherent model --   |g 5.3.  |t What is a statistical model? --   |g 5.3.1.  |t Population model --   |g 5.3.2.  |t Finite sample models --   |g 5.4.  |t Coherence --   |g 5.4.1.  |t Coherence in sampling models --   |g 5.4.2.  |t Coherence in generative models --   |g 5.5.  |t Statistical implications of coherence --   |g 5.6.  |t Examples --   |g 5.6.1.  |t Example 1: Erdos--Renyi--Gilbert model under selection sampling --   |g 5.6.2.  |t Example 2: ERGM under selection sampling --   |g 5.6.3.  |t Example 3: Erdos--Renyi--Gilbert model under edge sampling --   |g 5.7.  |t Invariance principles --   |g 5.8.  |t Further reading --   |g 5.9.  |t Solutions to exercises --   |g 5.9.1.  |t Exercise 5.1 --   |g 6.  |t Vertex exchangeable models --   |g 6.1.  |t Preliminaries: Formal definition of exchangeability --   |g 6.2.  |t Implications of exchangeability --   |g 6.3.  |t Finite exchangeable random graphs --   |g 6.3.1.  |t Exchangeable ERGMs --   |g 6.4.  |t Countable exchangeable models --   |g 6.4.1.  |t Graphon models --   |g 6.4.1.1.  |t Generative model --   |g 6.4.2.  |t Aldous--Hoover theorem --   |g 6.4.3.  |t Graphons and vertex exchangeability --   |g 6.4.4.  |t Subsampling description --   |g 6.5.  |t Viability of graphon models --   |g 6.5.1.  |t Implication 1: Dense structure --   |g 6.5.2.  |t Implication 2: Representative sampling --   |g 6.5.3.  |t emergence of graphons --   |g 6.6.  |t Potential benefits of graphon models --   |g 6.6.1.  |t Connection to de Finetti's theorem --   |g 6.6.2.  |t Graphon estimation --   |g 6.7.  |t Further reading --   |g 6.8.  |t Solutions to exercises --   |g 6.8.1.  |t Exercise 6.1 --   |g 6.8.2.  |t Exercise 6.2 --   |g 6.8.3.  |t Exercise 6.3 --   |g 6.8.4.  |t Exercise 6.4 --   |g 6.8.5.  |t Exercise 6.5 --   |g 6.8.6.  |t Exercise 6.6 --   |g 6.8.7.  |t Exercise 6.7 --   |g 6.8.8.  |t Exercise 6.8 --   |g 7.  |t Getting beyond graphons --   |g 7.1.  |t Something must go --   |g 7.2.  |t Sparse graphon models --   |g 7.3.  |t Completely random measures and graphex models --   |g 7.3.1.  |t Scenario: Formation of Facebook friendships --   |g 7.3.2.  |t Network representation --   |g 7.3.3.  |t Interpretation of vertex labels --   |g 7.3.4.  |t Exchangeable point process models --   |g 7.3.5.  |t Oxymoron: `Sparse exchangeable graphs' --   |g 7.3.6.  |t Graphex representation --   |g 7.3.7.  |t Sampling context --   |g 7.3.8.  |t Further discussion --   |g 7.4.  |t Variants of invariance --   |g 7.4.1.  |t Relatively exchangeable models (Chapter 8) --   |g 7.4.2.  |t Edge exchangeable models (Chapter 9) --   |g 7.4.3.  |t Relationally exchangeable models (Chapter 10) --   |g 7.5.  |t Solutions to exercises --   |g 7.5.1.  |t Exercise 7.1 --   |g 7.5.2.  |t Exercise 7.2 --   |g 7.5.3.  |t Exercise 7.3 --   |g 7.5.4.  |t Exercise 7.4 --   |g 8.  |t Relatively exchangeable models --   |g 8.1.  |t Scenario: Heterogeneity in social networks --   |g 8.2.  |t Stochastic blockmodels --   |g 8.2.1.  |t Generalized blockmodels --   |g 8.2.2.  |t Community detection and Bayesian versions of SBM --   |g 8.2.3.  |t Beyond SBMs and community detection --   |g 8.3.  |t Exchangeability relative to another network --   |g 8.3.1.  |t Scenario: High school social network revisited --   |g 8.3.2.  |t Exchangeability relative to a social network --   |g 8.3.3.  |t Lack of interference --   |g 8.3.4.  |t Label equivariance --   |g 8.4.  |t Latent space models --   |g 8.5.  |t Relatively exchangeable random graphs --   |g 8.5.1.  |t Relatively exchangeable φ-processes --   |g 8.6.  |t Relative exchangeability under arbitrary sampling --   |g 8.7.  |t Relatively invariant graphex models --   |g 8.8.  |t Final remarks and further reading --   |g 8.9.  |t Solutions to exercises --   |g 8.9.1.  |t Exercise 8.1 --   |g 8.9.2.  |t Exercise 8.2 --   |g 8.9.3.  |t Exercise 8.3 --   |g 8.9.4.  |t Exercise 8.4 --   |g 9.  |t Edge exchangeable models --   |g 9.1.  |t Scenario: Monitoring phone calls --   |g 9.2.  |t Edge-centric view --   |g 9.3.  |t Edge exchangeability --   |g 9.4.  |t Interaction propensity processes --   |g 9.5.  |t Characterizing edge exchangeable random graphs --   |g 9.6.  |t Vertex components models --   |g 19.6.1.  |t Stick-breaking constructions for vertex components --   |g 9.7.  |t Holly wood model --   |g 9.7.1.  |t Hollywood process --   |g 9.7.2.  |t Role of parameters in the Holly wood model --   |g 9.7.3.  |t Statistical properties of the Hollywood model --   |g 9.7.4.  |t Prediction from the Hollywood model --   |g 9.8.  |t Contexts for edge sampling --   |g 9.9.  |t Relative edge exchangeability --   |g 9.10.  |t Thresholding --   |g 9.11.  |t Comparison: Edge exchangeability v. graphex --   |g 9.12.  |t Further reading --   |g 9.13.  |t Solutions to exercises --   |g 9.13.1.  |t Exercise 9.1 --   |g 9.13.2.  |t Exercise 9.2 --   |g 9.13.3.  |t Exercise 9.3 --   |g 9.13.4.  |t Exercise 9.4 --   |g 9.13.5.  |t Exercise 9.5 --   |g 9.13.6.  |t Exercise 9.6 --   |g 9.13.7.  |t Exercise 9.7 --   |g 9.13.8.  |t Exercise 9.8 --   |g 10.  |t Relationally exchangeable models --   |g 10.1.  |t Sampling multiway interactions (hyperedges) --   |g 10.1.1.  |t Collaboration networks --   |g 10.1.2.  |t Coauthorship networks --   |g 10.2.  |t Representing multiway interaction networks --   |g 10.3.  |t Hyperedge exchangeability --   |g 10.3.1.  |t Interaction propensity process --   |g 10.3.2.  |t Characterization of hyperedge exchangeable network models --   |g 10.4.  |t Scenario: Traceroute sampling of Internet topology --   |g 10.4.1.  |t Representing the data --   |g 10.4.2.  |t Path exchangeability --   |g 10.4.3.  |t Relational exchangeability --   |g 10.5.  |t General Hollywood model --   |g 10.6.  |t Markovian vertex components models --   |g 10.7.  |t Contexts for relational sampling --   |g 10.8.  |t Concluding remarks and further reading --   |g 11.  |t Dynamic network models --   |g 11.1.  |t Scenario: Dynamics in social media activity --   |g 11.2.  |t Modeling considerations --   |g 11.2.1.  |t Network dynamics: Markov property --   |g 11.2.1.1.  |t Modeling the initial state --   |g 11.2.1.2.  |t Is the Markov property a good assumption? --   |g 11.2.1.3.  |t Temporal Exponential Random Graph Model (TERGM) --   |g 11.2.2.  |t Projectivity and sampling --   |g 11.2.2.1.  |t Example: A TERGM for triangle counts --   |g 11.2.2.2.  |t Projective Markov property --   |g 11.3.  |t Rewiring chains and Markovian graphons --   |g 11.3.1.  |t Exchangeable rewiring processes (Markovian graphons) --   |g 11.4.  |t Graph-valued Levy processes --   |g 11.4.1.  |t Inference from graph-valued Levy processes --   |g 11.5.  |t Continuous time processes --   |g 11.5.1.  |t Poissonian construction --   |g 11.6.  |t Further reading --   |g 11.7.  |t Solutions to exercises --   |g 11.7.1.  |t Exercise 11.1. 
533 |a Electronic reproduction.  |b Ann Arbor, MI  |n Available via World Wide Web. 
588 |a Description based on print version record. 
650 0 |a System analysis  |x Mathematical models. 
650 0 |a Network analysis (Planning) 
710 2 |a ProQuest (Firm) 
776 0 8 |c Original  |z 9781138585997  |z 1138585998  |z 9781138630154  |z 1138630152  |w (DLC) 2018006902 
830 0 |a Monographs on statistics and applied probability (Series) ;  |v 157. 
856 4 0 |u https://ebookcentral.proquest.com/lib/santaclara/detail.action?docID=5352298  |z Connect to this title online (unlimited simultaneous users allowed; 325 uses per year)  |t 0 
907 |a .b31647327  |b 200401  |c 180529 
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919 |a .ulebk  |b 2017-02-14 
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