Muutke küpsiste eelistusi

Graphical Models for Categorical Data [Pehme köide]

(Università di Bologna)
  • Formaat: Paperback / softback, 178 pages, kõrgus x laius x paksus: 230x155x10 mm, kaal: 240 g, Worked examples or Exercises
  • Sari: SemStat Elements
  • Ilmumisaeg: 24-Aug-2017
  • Kirjastus: Cambridge University Press
  • ISBN-10: 1108404960
  • ISBN-13: 9781108404969
Teised raamatud teemal:
Graphical Models for Categorical DataSuurem pilt
  • Formaat: Paperback / softback, 178 pages, kõrgus x laius x paksus: 230x155x10 mm, kaal: 240 g, Worked examples or Exercises
  • Sari: SemStat Elements
  • Ilmumisaeg: 24-Aug-2017
  • Kirjastus: Cambridge University Press
  • ISBN-10: 1108404960
  • ISBN-13: 9781108404969
Teised raamatud teemal:
Püsilink: https://www.kriso.ee/db/9781108404969.html
Märksõnad:
For advanced students of network data science, this compact account covers both well-established methodology and the theory of models recently introduced in the graphical model literature. It focuses on the discrete case where all variables involved are categorical and, in this context, it achieves a unified presentation of classical and recent results.

Arvustused

'Graphical Models for Categorical Data is a concise introduction to the theory of graphical models. The book is a perfect read for those who want better grasp of the basics of graphical models for discrete data. The main strength of the book is the unified notation, which helps the reader draw links between various approaches to graphical models for discrete data. The book also exploits the link between the theory of graphical models and the more general theory of statistical exponential families. This makes it an extremely valuable addition to the current literature and a useful tool for future research.' Piotr Zwiernik, Mathematical Reviews

Muu info

This compact account covers both well-established methodology and the theory of models recently introduced in the graphical model literature.
Preface vii
1 Introduction
1(3)
1.1 Graphical Models
1(1)
1.2 Outline of the Book
2(2)
1.2.1 Discrete Graphical Models and Their Parameterization
2(1)
1.2.2 Binary vs Non-binary Variables
3(1)
2 Conditional Independence and Cross-product Ratios
4(17)
2.1 Notation and Terminology
4(4)
2.1.1 Cross-classified Tables
5(3)
2.2 Conditional Independence
8(1)
2.3 Establishing Independence Relationships
9(12)
3 Mobius Inversion
21(13)
3.1 Preliminaries
21(3)
3.1.1 Notation and Terminology
21(1)
3.1.2 The Zeta and the Mobius Matrices
22(2)
3.2 The Mobius Inversion Formula
24(3)
3.2.1 Two Basic Lemmas
25(2)
3.3 Mobius Inversion and Partially Ordered Sets
27(7)
4 Undirected Graph Models
34(58)
4.1 Graphs
34(2)
4.2 Markov Properties for Undirected Graphs
36(3)
4.3 The Log-linear Parameterization
39(5)
4.4 Hierarchical Log-linear Models
44(4)
4.5 Log-linear Graphical Models
48(1)
4.6 Data, Estimation and Testing
49(7)
4.7 Graph Decomposition and Decomposable Graphs
56(4)
4.8 Local Computation Properties
60(6)
4.9 Models for Decomposable Graphs
66(4)
4.10 Log-linear Models and the Exponential Family
70(8)
4.10.1 Basic Facts on the Theory of the Exponential Family
70(1)
4.10.2 The Cross-classified Bernoulli Distribution
71(1)
4.10.3 Exponential Family Representations of the Saturated Model
72(2)
4.10.4 Exponential Family Representation of Hierarchical Log-linear Models
74(4)
4.11 Modular Structure of the Asymptotic Variance of ML Estimates
78(14)
4.11.1 The Variance Function and the Asymptotic Variance of ML Estimates
79(3)
4.11.2 Variances in the Saturated Model
82(3)
4.11.3 Variances in Hierarchical Log-linear Models
85(2)
4.11.4 Decompositions and Decomposable Models
87(5)
5 Bidirected Graph Models
92(24)
5.1 Bidirected Graphs
93(1)
5.2 Markov Properties for Bidirected Graphs
94(4)
5.3 The Log-mean Linear Parameterization
98(6)
5.4 Log-mean Linear Graphical Models
104(3)
5.5 Example: Symptoms in Psychiatric Patients
107(3)
5.6 Parsimonious Graphical Modeling
110(6)
6 Directed Acyclic and Regression Graph Models
116(30)
6.1 Directed Acyclic Graphs
117(2)
6.2 Markov Properties for Directed Acyclic Graphs
119(5)
6.3 Regression Graphs
124(1)
6.4 Markov Properties for Regression Graphs
125(1)
6.5 On the Interpretation of Models defined by Regression Graphs
126(2)
6.6 The Log-hybrid Linear Parameterization
128(12)
6.7 Log-hybrid Linear Graphical Models
140(3)
6.8 Inference in Regression Graph Models
143(3)
Bibliography 146
Alberto Roverato is Professor of Statistics at Università di Bologna.