JSS Research Series in Statistics
cover

Partitions, Hypergeometric Systems, and Dirichlet Processes in Statistics

Authors: Mano, Shuhei

  • Discusses the intersection of three subjects that are generally studied independently from each other: partitions, hypergeometric systems, and Dirichlet processes
  • Explains the relationship between the above three subjects with simple problems that broaden readers’ mathematical horizons and statistical interests
  • Provides an interdisciplinary approach that appeals to a wide audience, including statisticians, mathematicians, and researchers working in various fields of data sciences
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eBook $54.99
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  • ISBN 978-4-431-55888-0
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Softcover $69.99
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  • Usually dispatched within 3 to 5 business days.
About this book

This book focuses on statistical inferences related to various combinatorial stochastic processes. Specifically, it discusses the intersection of three subjects that are generally studied independently of each other: partitions, hypergeometric systems, and Dirichlet processes. The Gibbs partition is a family of measures on integer partition, and several prior processes, such as the Dirichlet process, naturally appear in connection with infinite exchangeable Gibbs partitions. Examples include the distribution on a contingency table with fixed marginal sums and the conditional distribution of Gibbs partition given the length. The A-hypergeometric distribution is a class of discrete exponential families and appears as the conditional distribution of a multinomial sample from log-affine models. The normalizing constant is the A-hypergeometric polynomial, which is a solution of a system of linear differential equations of multiple variables determined by a matrix A, called A-hypergeometric system. The book presents inference methods based on the algebraic nature of the A-hypergeometric system, and introduces the holonomic gradient methods, which numerically solve holonomic systems without combinatorial enumeration, to compute the normalizing constant. Furher, it discusses Markov chain Monte Carlo and direct samplers from A-hypergeometric distribution, as well as the maximum likelihood estimation of the A-hypergeometric distribution of two-row matrix using properties of polytopes and information geometry. The topics discussed are simple problems, but the interdisciplinary approach of this book appeals to a wide audience with an interest in statistical inference on combinatorial stochastic processes, including statisticians who are developing statistical theories and methodologies, mathematicians wanting to discover applications of their theoretical results, and researchers working in various fields of data sciences.

About the authors

Shuhei Mano, Associate Professor, The Institute of Statistical Mathematics,smano@ism.ac.jp
10-3, Midori-cho, Tachikawa, Tokyo 190-8562, Japan

Table of contents (5 chapters)

Table of contents (5 chapters)
  • Introduction

    Mano, Shuhei

    Pages 1-9

  • Measures on Partitions

    Mano, Shuhei

    Pages 11-43

  • A-Hypergeometric Systems

    Mano, Shuhei

    Pages 45-70

  • Dirichlet Processes

    Mano, Shuhei

    Pages 71-103

  • Methods for Inferences

    Mano, Shuhei

    Pages 105-122

Buy this book

eBook $54.99
price for USA in USD (gross)
  • ISBN 978-4-431-55888-0
  • Digitally watermarked, DRM-free
  • Included format: EPUB, PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Softcover $69.99
price for USA in USD
  • ISBN 978-4-431-55886-6
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
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Bibliographic Information

Bibliographic Information
Book Title
Partitions, Hypergeometric Systems, and Dirichlet Processes in Statistics
Authors
Series Title
JSS Research Series in Statistics
Copyright
2018
Publisher
Springer Japan
Copyright Holder
The Author(s)
eBook ISBN
978-4-431-55888-0
DOI
10.1007/978-4-431-55888-0
Softcover ISBN
978-4-431-55886-6
Series ISSN
2364-0057
Edition Number
1
Number of Pages
VIII, 135
Number of Illustrations
9 b/w illustrations
Topics