Statistics Based on Dirichlet Processes and Related Topics

Hajime Yamato

ISBN 10: 9811569746 / ISBN 13: 9789811569746

Published by Springer, Springer, 2020

About this Item

Druck auf Anfrage Neuware - Printed after ordering - 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' samplingformula. 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.

Seller Inventory # 9789811569746

Bibliographic Details

• Title: Statistics Based on Dirichlet Processes and Related Topics
• Publisher: Springer, Springer
• Publication Date: 2020
• Language: English
• ISBN 10: 9811569746
• ISBN 13: 9789811569746
• Binding: Taschenbuch
• Condition: Neu
• Dimensions: 235W x 155H x 6D millimeters 235 millimeters width by 155 millimeters height by 6 millimeters depth
• Weight: 143 grams

About this title

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.

About the Author

Hajime Yamato, Professor Emeritus of Kagoshima University.