Custom cover image
Custom cover image

Algebraic statistics / Seth Sullivant

By: Resource type: Ressourcentyp: Buch (Online)Book (Online)Language: English Series: Graduate studies in mathematics ; 194Publisher: Providence, Rhode Island : American Mathematical Society, 2018Description: 1 Online-RessourceISBN:
  • 1470449803
  • 978147044980
Subject(s): Additional physical formats: 1470435179 | 9781470435172 | Erscheint auch als: Algebraic statistics. Druck-Ausgabe Providence, Rhode Island : American Mathematical Society, 2018. xiii, 490 SeitenDDC classification:
  • 519.5
MSC: MSC: *62-01 | 62-02 | 62F03 | 62H17 | 14M12 | 14M25 | 13P15 | 60J10RVK: RVK: SK 830 | SK 240Online resources: Summary: 10.1. Motivating Applications10.2. Integer Programming and Gröbner Bases; 10.3. Quotient Rings and Gröbner Bases; 10.4. Linear Programming Relaxations; 10.5. Formulas for Bounds on Cell Entries; 10.6. Exercises; Chapter 11. Exponential Random Graph Models; 11.1. Basic Setup; 11.2. The Beta Model and Variants; 11.3. Models from Subgraphs Statistics; 11.4. Exercises; Chapter 12. Design of Experiments; 12.1. Designs; 12.2. Computations with the Ideal of Points; 12.3. The Gröbner Fan and Applications; 12.4. Two-level Designs and System Reliability; 12.5. Exercises; Chapter 13. Graphical ModelsSummary: 13.1. Conditional Independence Description of Graphical Models13.2. Parametrizations of Graphical Models; 13.3. Failure of the Hammersley-Clifford Theorem; 13.4. Examples of Graphical Models from Applications; 13.5. Exercises; Chapter 14. Hidden Variables; 14.1. Mixture Models; 14.2. Hidden Variable Graphical Models; 14.3. The EM Algorithm; 14.4. Exercises; Chapter 15. Phylogenetic Models; 15.1. Trees and Splits; 15.2. Types of Phylogenetic Models; 15.3. Group-based Phylogenetic Models; 15.4. The General Markov Model; 15.5. The Allman-Rhodes-Draisma-Kuttler Theorem; 15.6. ExercisesSummary: 7.1. Algebraic Solution of the Score Equations7.2. Likelihood Geometry; 7.3. Concave Likelihood Functions; 7.4. Likelihood Ratio Tests; 7.5. Exercises; Chapter 8. The Cone of Sufficient Statistics; 8.1. Polyhedral Geometry; 8.2. Discrete Exponential Families; 8.3. Gaussian Exponential Families; 8.4. Exercises; Chapter 9. Fisher's Exact Test; 9.1. Conditional Inference; 9.2. Markov Bases; 9.3. Markov Bases for Hierarchical Models; 9.4. Graver Bases and Applications; 9.5. Lattice Walks and Primary Decompositions; 9.6. Other Sampling Strategies; 9.7. Exercises; Chapter 10. Bounds on Cell EntriesSummary: 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 familPPN: PPN: 104548430XPackage identifier: Produktsigel: ZDB-4-NLEBK
No physical items for this record
KIT – The Research University in the Helmholtz Association                         Home | Impressum | Datenschutz | Barrierefreiheit | KIT