Volume: 194; 2018; 490 pp; Hardcover
MSC: Primary 62; 14; 13; 52; 60; 90; 92;
Print ISBN: 978-1-4704-3517-2
Product Code: GSM/194
List Price: $83.00
AMS Member Price: $66.40
MAA Member Price: $74.70
Electronic ISBN: 978-1-4704-4980-3
Product Code: GSM/194.E
List Price: $83.00
AMS Member Price: $66.40
MAA Member Price: $74.70
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Supplemental Materials
Algebraic Statistics
Share this pageSeth Sullivant
Algebraic statistics uses tools from algebraic geometry, commutative algebra, combinatorics, and their computational sides to address problems in statistics and its applications. The starting point for this connection is the observation that many statistical models are semialgebraic sets. The algebra/statistics connection is now over twenty years old, and this book presents the first broad introductory treatment of the subject. Along with background material in probability, algebra, and statistics, this book covers a range of topics in algebraic statistics including algebraic exponential families, likelihood inference, Fisher's exact test, bounds on entries of contingency tables, design of experiments, identifiability of hidden variable models, phylogenetic models, and model selection. With numerous examples, references, and over 150 exercises, this book is suitable for both classroom use and independent study.
Readership
Graduate students and researchers interested in algebraic statistics and its applications.
Table of Contents
Table of Contents
Algebraic Statistics
- Cover Cover11
- Title page iii4
- Preface ix10
- Chapter 1. Introduction 116
- Chapter 2. Probability Primer 1126
- Chapter 3. Algebra Primer 4156
- Chapter 4. Conditional Independence 7186
- Chapter 5. Statistics Primer 99114
- Chapter 6. Exponential Families 117132
- Chapter 7. Likelihood Inference 137152
- Chapter 8. The Cone of Sufficient Statistics 169184
- Chapter 9. Fisher’s Exact Test 189204
- Chapter 10. Bounds on Cell Entries 227242
- Chapter 11. Exponential Random Graph Models 251266
- Chapter 12. Design of Experiments 265280
- Chapter 13. Graphical Models 287302
- Chapter 14. Hidden Variables 313328
- Chapter 15. Phylogenetic Models 335350
- Chapter 16. Identifiability 371386
- Chapter 17. Model Selection and Bayesian Integrals 399414
- Chapter 18. MAP Estimation and Parametric Inference 423438
- Chapter 19. Finite Metric Spaces 439454
- Bibliography 463478
- Index 481496
- Back Cover Back Cover1506