Markov Bases in Algebraic Statistics

Authors:

ISBN: 978-1-4614-3718-5 (Print) 978-1-4614-3719-2 (Online)

Table of contents (16 chapters)

  1. Front Matter

    Pages i-xi

  2. Introduction and some relevant preliminary material

    1. Front Matter

      Pages 1-1

    2. No Access

      Book Chapter

      Pages 3-21

      Exact Tests for Contingency Tables and Discrete Exponential Families

    3. No Access

      Book Chapter

      Pages 23-31

      Markov Chain Monte Carlo Methods over Discrete Sample Space

    4. No Access

      Book Chapter

      Pages 33-43

      Toric Ideals and Their Gröbner Bases

  3. Properties of Markov bases

    1. Front Matter

      Pages 45-45

    2. No Access

      Book Chapter

      Pages 47-63

      Definition of Markov Bases and Other Bases

    3. No Access

      Book Chapter

      Pages 65-78

      Structure of Minimal Markov Bases

    4. No Access

      Book Chapter

      Pages 79-89

      Method of Distance Reduction

    5. No Access

      Book Chapter

      Pages 91-105

      Symmetry of Markov Bases

  4. Markov bases for specific models

    1. Front Matter

      Pages 107-107

    2. No Access

      Book Chapter

      Pages 109-128

      Decomposable Models of Contingency Tables

    3. No Access

      Book Chapter

      Pages 129-157

      Markov Basis for No-Three-Factor Interaction Models and Some Other Hierarchical Models

    4. No Access

      Book Chapter

      Pages 159-179

      Two-Way Tables with Structural Zeros and Fixed Subtable Sums

    5. No Access

      Book Chapter

      Pages 181-208

      Regular Factorial Designs with Discrete Response Variables

    6. No Access

      Book Chapter

      Pages 209-227

      Groupwise Selection Models

    7. No Access

      Book Chapter

      Pages 229-247

      The Set of Moves Connecting Specific Fibers

  5. Some other topics of algebraic statistics

    1. Front Matter

      Pages 249-249

    2. No Access

      Book Chapter

      Pages 251-259

      Disclosure Limitation Problem and Markov Basis

    3. No Access

      Book Chapter

      Pages 261-273

      Gröbner Basis Techniques for Design of Experiments

    4. No Access

      Book Chapter

      Pages 275-286

      Running Markov Chain Without Markov Bases

  6. Back Matter

    Pages 287-298