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＜電子ブック＞
Statistics Based on Dirichlet Processes and Related Topics / by Hajime Yamato
(JSS Research Series in Statistics. ISSN:23640065)

版	1st ed. 2020.
出版者	(Singapore : Springer Nature Singapore : Imprint: Springer)
出版年	2020
本文言語	英語
大きさ	VIII, 74 p. 7 illus : online resource
著者標目	*Yamato, Hajime author SpringerLink (Online service)
件　名	LCSH:Statistics  LCSH:Mathematical statistics FREE:Applied Statistics FREE:Statistical Theory and Methods FREE:Mathematical Statistics
一般注記	Introduction -- Dirichlet process and Chinese restaurant process -- Nonparametric estimation of estimable parameter -- Random partition of positive integer 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 HTTP:URL=https://doi.org/10.1007/978-981-15-6975-3

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