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The Resource Markov bases in algebraic statistics, by Satoshi Aoki, Hisayuki Hara, Akimichi Takemura

Markov bases in algebraic statistics, by Satoshi Aoki, Hisayuki Hara, Akimichi Takemura

Creator
Contributor
Summary
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
Language
eng
Work
Publication
Extent
1 online resource (xi, 298 pages)
Contents
  • Structure of Minimal Markov Bases
  • Method of Distance Reduction
  • Symmetry of Markov Bases--
  • Part 3.
  • Markov bases for specific models
  • Decomposable Models of Contingency Tables
  • Markov Basis for No-Three-Factor Interaction Models and Some Other Hierarchical Models
  • Two-Way Tables with Structural Zeros and Fixed Subtable Sums
  • Regular Factorial Designs with Discrete Response Variables
  • Groupwise Selection Models
  • Part 1.
  • The Set of Moves Connecting Specific Fibers--
  • Part 4.
  • Some other topics of algebraic statistics
  • Disclosure Limitation Problem and Markov Basis
  • Gröbner Basis Techniques for Design of Experiments
  • Running Markov Chain Without Markov Bases
  • Introduction and some relevant preliminary material
  • Exact Tests for Contingency Tables and Discrete Exponential Families
  • Markov Chain Monte Carlo Methods over Discrete Sample Space
  • Toric Ideals and Their Gröbner Bases--
  • Part 2.
  • Properties of Markov bases
  • Definition of Markov Bases and Other Bases
Isbn
9781461437192
Instance
Label
Markov bases in algebraic statistics
Title
Markov bases in algebraic statistics
Statement of responsibility
by Satoshi Aoki, Hisayuki Hara, Akimichi Takemura
Creator
Contributor
Subject
Language
eng
Summary
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
Member of
Cataloging source
GW5XE
http://library.link/vocab/creatorName
Aoki, Satoshi
Dewey number
519.5
Illustrations
illustrations
Index
index present
LC call number
QA276
LC item number
.A55 2012
Literary form
non fiction
Nature of contents
  • dictionaries
  • bibliography
http://library.link/vocab/relatedWorkOrContributorName
  • Hara, Hisayuki
  • Takemura, Akimichi
Series statement
Springer series in statistics
Series volume
v. 199
http://library.link/vocab/subjectName
  • Mathematical statistics
  • Markov processes
  • Gröbner bases
  • Markov Chains
  • Mathematics
  • Statistics
  • MATHEMATICS
  • Gröbner bases
  • Markov processes
  • Mathematical statistics
Label
Markov bases in algebraic statistics, by Satoshi Aoki, Hisayuki Hara, Akimichi Takemura
Instantiates
Publication
Antecedent source
unknown
Bibliography note
Includes bibliographical references (pages 287-293) and index
Carrier category
online resource
Carrier category code
  • cr
Carrier MARC source
rdacarrier
Color
multicolored
Content category
text
Content type code
  • txt
Content type MARC source
rdacontent
Contents
  • Structure of Minimal Markov Bases
  • Method of Distance Reduction
  • Symmetry of Markov Bases--
  • Part 3.
  • Markov bases for specific models
  • Decomposable Models of Contingency Tables
  • Markov Basis for No-Three-Factor Interaction Models and Some Other Hierarchical Models
  • Two-Way Tables with Structural Zeros and Fixed Subtable Sums
  • Regular Factorial Designs with Discrete Response Variables
  • Groupwise Selection Models
  • Part 1.
  • The Set of Moves Connecting Specific Fibers--
  • Part 4.
  • Some other topics of algebraic statistics
  • Disclosure Limitation Problem and Markov Basis
  • Gröbner Basis Techniques for Design of Experiments
  • Running Markov Chain Without Markov Bases
  • Introduction and some relevant preliminary material
  • Exact Tests for Contingency Tables and Discrete Exponential Families
  • Markov Chain Monte Carlo Methods over Discrete Sample Space
  • Toric Ideals and Their Gröbner Bases--
  • Part 2.
  • Properties of Markov bases
  • Definition of Markov Bases and Other Bases
Control code
802337870
Dimensions
unknown
Extent
1 online resource (xi, 298 pages)
File format
unknown
Form of item
online
Isbn
9781461437192
Level of compression
unknown
Media category
computer
Media MARC source
rdamedia
Media type code
  • c
Other control number
10.1007/978-1-4614-3719-2
Other physical details
illustrations
Quality assurance targets
not applicable
Reformatting quality
unknown
Sound
unknown sound
Specific material designation
remote
System control number
(OCoLC)802337870
Label
Markov bases in algebraic statistics, by Satoshi Aoki, Hisayuki Hara, Akimichi Takemura
Publication
Antecedent source
unknown
Bibliography note
Includes bibliographical references (pages 287-293) and index
Carrier category
online resource
Carrier category code
  • cr
Carrier MARC source
rdacarrier
Color
multicolored
Content category
text
Content type code
  • txt
Content type MARC source
rdacontent
Contents
  • Structure of Minimal Markov Bases
  • Method of Distance Reduction
  • Symmetry of Markov Bases--
  • Part 3.
  • Markov bases for specific models
  • Decomposable Models of Contingency Tables
  • Markov Basis for No-Three-Factor Interaction Models and Some Other Hierarchical Models
  • Two-Way Tables with Structural Zeros and Fixed Subtable Sums
  • Regular Factorial Designs with Discrete Response Variables
  • Groupwise Selection Models
  • Part 1.
  • The Set of Moves Connecting Specific Fibers--
  • Part 4.
  • Some other topics of algebraic statistics
  • Disclosure Limitation Problem and Markov Basis
  • Gröbner Basis Techniques for Design of Experiments
  • Running Markov Chain Without Markov Bases
  • Introduction and some relevant preliminary material
  • Exact Tests for Contingency Tables and Discrete Exponential Families
  • Markov Chain Monte Carlo Methods over Discrete Sample Space
  • Toric Ideals and Their Gröbner Bases--
  • Part 2.
  • Properties of Markov bases
  • Definition of Markov Bases and Other Bases
Control code
802337870
Dimensions
unknown
Extent
1 online resource (xi, 298 pages)
File format
unknown
Form of item
online
Isbn
9781461437192
Level of compression
unknown
Media category
computer
Media MARC source
rdamedia
Media type code
  • c
Other control number
10.1007/978-1-4614-3719-2
Other physical details
illustrations
Quality assurance targets
not applicable
Reformatting quality
unknown
Sound
unknown sound
Specific material designation
remote
System control number
(OCoLC)802337870

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