Statistics Based on Dirichlet Processes and Related Topics (SpringerBriefs in Statistics) - Softcover
Synopsis
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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About the Author
Hajime Yamato, Professor Emeritus of Kagoshima University.
From the Back Cover
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Statistics Based on Dirichlet Processes and Related Topics
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Springer Nature Singapore Jul 2020, 2020
ISBN 10: 9811569746
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Taschenbuch. Condition: Neu. This item is printed on demand - it takes 3-4 days longer - Neuware -This book focuses on the properties associated with the Dirichlet process, describing itsusea priorifor nonparametric inference and the Bayes estimateto obtain limitsfor the estimable parameter.It presentsthe limits and the well-knownU- andV-statistics as a convex combination ofU-statistics, and by investigating this convex combination, it demonstratesthese 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, whicharediscussed. 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 propertiesof the Griffiths-Engen-McCloskey distribution,which is related to theDirichlet process and the Ewens' sampling formula. 84 pp. Englisch. Seller Inventory # 9789811569746
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Kartoniert / Broschiert. Condition: New. Dieser Artikel ist ein Print on Demand Artikel und wird nach Ihrer Bestellung fuer Sie gedruckt. Describes the Bayes estimate of the estimable parameter by using the Dirichlet process as a priori distributionPresents the convex combination of U-statistics for the estimable parameterShows . Seller Inventory # 377136916
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Statistics Based on Dirichlet Processes and Related Topics
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Taschenbuch. Condition: Neu. This item is printed on demand - Print on Demand Titel. Neuware -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.Springer-Verlag KG, Sachsenplatz 4-6, 1201 Wien 84 pp. Englisch. Seller Inventory # 9789811569746