Springer Series in Statistics

Markov Bases in Algebraic Statistics

Authors: Aoki, Satoshi, Hara, Hisayuki, Takemura, Akimichi

  • Crucial guide for statisticians no matter previous exposure to algebra and algebraic statistics
  • Clear organization guides the reader through the 16 chapters with figures and tables
  • Shows topic in its broader context, beginning with introductory material
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About this book

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.

About the authors

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

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

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

Reviews

From the reviews:

“The book by Aoki, Hara, and Takemura presents a thorough introduction to Markov chain Monte Carlo tests for discrete exponential families, focusing on the concept of Markov bases. It is an authoritative and highly readable account of this field. … This text is the definitive reference on the subject, aimed principally at statisticians interested in Markov chain algorithms for sampling from discrete exponential families and its various applications … . It could also be used as a textbook for an advanced seminar on the subject.” (Luis David García-Puente, Mathematical Reviews, December, 2013)

Table of contents (16 chapters)

  • Exact Tests for Contingency Tables and Discrete Exponential Families

    Aoki, Satoshi (et al.)

    Pages 3-21

  • Markov Chain Monte Carlo Methods over Discrete Sample Space

    Aoki, Satoshi (et al.)

    Pages 23-31

  • Toric Ideals and Their Gröbner Bases

    Aoki, Satoshi (et al.)

    Pages 33-43

  • Definition of Markov Bases and Other Bases

    Aoki, Satoshi (et al.)

    Pages 47-63

  • Structure of Minimal Markov Bases

    Aoki, Satoshi (et al.)

    Pages 65-78

Buy this book

eBook $109.00
price for USA (gross)
  • ISBN 978-1-4614-3719-2
  • Digitally watermarked, DRM-free
  • Included format: PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Hardcover $149.00
price for USA
  • ISBN 978-1-4614-3718-5
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
Softcover $149.00
price for USA
  • ISBN 978-1-4899-9909-2
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
Rent the ebook  
  • Rental duration: 1 or 6 month
  • low-cost access
  • online reader with highlighting and note-making option
  • can be used across all devices
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Bibliographic Information

Bibliographic Information
Book Title
Markov Bases in Algebraic Statistics
Authors
Series Title
Springer Series in Statistics
Series Volume
199
Copyright
2012
Publisher
Springer-Verlag New York
Copyright Holder
Springer Science+Business Media New York
eBook ISBN
978-1-4614-3719-2
DOI
10.1007/978-1-4614-3719-2
Hardcover ISBN
978-1-4614-3718-5
Softcover ISBN
978-1-4899-9909-2
Series ISSN
0172-7397
Edition Number
1
Number of Pages
XII, 300
Topics