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Markov Bases in Algebraic Statistics

  • Satoshi Aoki
  • Hisayuki Hara
  • Akimichi Takemura

Part of the Springer Series in Statistics book series (SSS, volume 199)

Table of contents

  1. Front Matter
    Pages i-xi
  2. Introduction and Some Relevant Preliminary Material

    1. Front Matter
      Pages 1-1
    2. Satoshi Aoki, Hisayuki Hara, Akimichi Takemura
      Pages 3-21
    3. Satoshi Aoki, Hisayuki Hara, Akimichi Takemura
      Pages 23-31
    4. Satoshi Aoki, Hisayuki Hara, Akimichi Takemura
      Pages 33-43
  3. Properties of Markov Bases

    1. Front Matter
      Pages 45-45
    2. Satoshi Aoki, Hisayuki Hara, Akimichi Takemura
      Pages 47-63
    3. Satoshi Aoki, Hisayuki Hara, Akimichi Takemura
      Pages 65-78
    4. Satoshi Aoki, Hisayuki Hara, Akimichi Takemura
      Pages 79-89
    5. Satoshi Aoki, Hisayuki Hara, Akimichi Takemura
      Pages 91-105
  4. Markov Bases for Specific Models

    1. Front Matter
      Pages 107-107
    2. Satoshi Aoki, Hisayuki Hara, Akimichi Takemura
      Pages 109-128
    3. Satoshi Aoki, Hisayuki Hara, Akimichi Takemura
      Pages 129-157
    4. Satoshi Aoki, Hisayuki Hara, Akimichi Takemura
      Pages 159-179
    5. Satoshi Aoki, Hisayuki Hara, Akimichi Takemura
      Pages 181-208
    6. Satoshi Aoki, Hisayuki Hara, Akimichi Takemura
      Pages 209-227
    7. Satoshi Aoki, Hisayuki Hara, Akimichi Takemura
      Pages 229-247
  5. Some Other Topics of Algebraic Statistics

    1. Front Matter
      Pages 249-249
    2. Satoshi Aoki, Hisayuki Hara, Akimichi Takemura
      Pages 251-259
    3. Satoshi Aoki, Hisayuki Hara, Akimichi Takemura
      Pages 261-273
    4. Satoshi Aoki, Hisayuki Hara, Akimichi Takemura
      Pages 275-286
  6. Back Matter
    Pages 287-298

About this book

Introduction

Algebraic statistics is a rapidly developing field, where ideas from statistics and algebra meet and stimulate new research directions. One of the origins of algebraic statistics is the work by Diaconis and Sturmfels in 1998 on the use of Gröbner bases for constructing a connected Markov chain for performing conditional tests of a discrete exponential family. In this book we take up this topic and present a detailed summary of developments following the seminal work of Diaconis and Sturmfels.

This book is intended for statisticians with minimal backgrounds in algebra. As we ourselves learned algebraic notions through working on statistical problems and collaborating with notable algebraists, we hope that this book with many practical statistical problems is useful for statisticians to start working on the field.

Satoshi Aoki obtained his doctoral degree from University of Tokyo in 2004 and is currently an associate professor in Graduate school of Science and Engineering, Kagoshima University.

Hisayuki Hara obtained his doctoral degree from University of Tokyo in 1999 and is currently an associate professor in Faculty of Economics, Niigata University.

Akimichi Takemura obtained his doctoral degree from Stanford University in 1982 and is currently a professor in Graduate School of Information Science and Technology, University of Tokyo.

Keywords

Algebra Algebraic Statistics Markov Bases Monte Carlo Toric Ideals

Authors and affiliations

  • Satoshi Aoki
    • 1
  • Hisayuki Hara
    • 2
  • Akimichi Takemura
    • 3
  1. 1.Dept. Mathematics & Computer ScienceKagoshima UniversityKagoshimaJapan
  2. 2.Faculty of EconomicsNiigata UniversityNiigataJapan
  3. 3.University of TokyoTokyoJapan

Bibliographic information

  • DOI https://doi.org/10.1007/978-1-4614-3719-2
  • Copyright Information Springer Science+Business Media New York 2012
  • Publisher Name Springer, New York, NY
  • eBook Packages Mathematics and Statistics
  • Print ISBN 978-1-4614-3718-5
  • Online ISBN 978-1-4614-3719-2
  • Series Print ISSN 0172-7397
  • Buy this book on publisher's site