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JSS Research Series in Statistics

Statistics Based on Dirichlet Processes and Related Topics

Authors: Yamato, Hajime

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  • Describes the Bayes estimate of the estimable parameter by using the Dirichlet process as a priori distribution
  • Presents the convex combination of U-statistics for the estimable parameter
  • Shows convergence to shifted Poisson distribution for the number of distinct components of Ewens’ sampling formula
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  • ISBN 978-981-15-6975-3
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About this book

This book focuses on the properties associated with the Dirichlet process, describing its use a priori for nonparametric inference and the Bayes estimate to obtain limits for the estimable parameter. It presents the limits and the well-known U- and V-statistics as a convex combination of U-statistics, and by investigating this convex combination, it demonstrates  these three statistics. Next, the book notes that the Dirichlet process gives the discrete distribution with probability one, even if the parameter of the process is continuous. Therefore, there are duplications among the sample from the distribution, which are discussed. Because sampling from the Dirichlet process is described sequentially, it can be described equivalently by the Chinese restaurant process. Using this process, the Donnelly–Tavaré–Griffiths formulas I and II are obtained, both of which give the Ewens’ sampling formula. The book then shows the convergence and approximation of the distribution for its number of distinct components. Lastly, it explains the interesting properties of the Griffiths–Engen–McCloskey distribution, which is related to the Dirichlet process and the Ewens’ sampling formula.

About the authors

Hajime Yamato, Professor Emeritus of Kagoshima University.

Table of contents (4 chapters)

Table of contents (4 chapters)

Buy this book

eBook $44.99
price for USA in USD
  • ISBN 978-981-15-6975-3
  • Digitally watermarked, DRM-free
  • Included format: PDF, EPUB
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Softcover $59.99
price for USA in USD
  • ISBN 978-981-15-6974-6
  • Free shipping for individuals worldwide
  • Immediate ebook access, if available*, with your print order
  • Usually dispatched within 3 to 5 business days.
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Bibliographic Information

Bibliographic Information
Book Title
Statistics Based on Dirichlet Processes and Related Topics
Authors
Series Title
JSS Research Series in Statistics
Copyright
2020
Publisher
Springer Singapore
Copyright Holder
The Editor(s) (if applicable) and The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd.
eBook ISBN
978-981-15-6975-3
DOI
10.1007/978-981-15-6975-3
Softcover ISBN
978-981-15-6974-6
Series ISSN
2364-0057
Edition Number
1
Number of Pages
VIII, 74
Number of Illustrations
7 b/w illustrations
Topics

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