Overview
- 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
Part of the book series: SpringerBriefs in Statistics (BRIEFSSTATIST)
Part of the book sub series: JSS Research Series in Statistics (JSSRES)
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Table of contents (4 chapters)
Keywords
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’ samplingformula. 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.
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Bibliographic Information
Book Title: Statistics Based on Dirichlet Processes and Related Topics
Authors: Hajime Yamato
Series Title: SpringerBriefs in Statistics
DOI: https://doi.org/10.1007/978-981-15-6975-3
Publisher: Springer Singapore
eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)
Copyright Information: The Editor(s) (if applicable) and The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2020
Softcover ISBN: 978-981-15-6974-6Published: 18 July 2020
eBook ISBN: 978-981-15-6975-3Published: 17 July 2020
Series ISSN: 2191-544X
Series E-ISSN: 2191-5458
Edition Number: 1
Number of Pages: VIII, 74
Number of Illustrations: 7 b/w illustrations
Topics: Applied Statistics, Statistical Theory and Methods, Probability Theory and Stochastic Processes, Applications of Mathematics