Overview
- 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
- Includes supplementary material: sn.pub/extras
Part of the book series: Springer Series in Statistics (SSS, volume 199)
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Table of contents (16 chapters)
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Front Matter
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Introduction and Some Relevant Preliminary Material
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Front Matter
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Introduction and some relevant preliminary material
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Properties of Markov Bases
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Front Matter
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Markov Bases for Specific Models
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Front Matter
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Markov bases for specific models
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Some Other Topics of Algebraic Statistics
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Front Matter
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Some other topics of algebraic statistics
Keywords
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.
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)Authors and Affiliations
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.
Bibliographic Information
Book Title: Markov Bases in Algebraic Statistics
Authors: Satoshi Aoki, Hisayuki Hara, Akimichi Takemura
Series Title: Springer Series in Statistics
DOI: https://doi.org/10.1007/978-1-4614-3719-2
Publisher: Springer New York, NY
eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)
Copyright Information: Springer Science+Business Media New York 2012
Hardcover ISBN: 978-1-4614-3718-5Published: 24 July 2012
Softcover ISBN: 978-1-4899-9909-2Published: 08 August 2014
eBook ISBN: 978-1-4614-3719-2Published: 25 July 2012
Series ISSN: 0172-7397
Series E-ISSN: 2197-568X
Edition Number: 1
Number of Pages: XII, 300
Topics: Statistics, general, Statistical Theory and Methods, General Algebraic Systems, Applications of Mathematics