Statistics Based on Dirichlet Processes and Related Topics - Hajime Yamato

Statistics Based on Dirichlet Processes and Related Topics

(Autor)

Buch | Softcover
74 Seiten
2020 | 1st ed. 2020
Springer Verlag, Singapore
978-981-15-6974-6 (ISBN)
58,84 inkl. MwSt
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.
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.

Hajime Yamato, Professor Emeritus of Kagoshima University.

Introduction.- Dirichlet process and Chinese restaurant process.- Nonparametric estimation of estimable parameter.- Random partition of positive integer.

Erscheinungsdatum
Reihe/Serie JSS Research Series in Statistics
SpringerBriefs in Statistics
Zusatzinfo 7 Illustrations, black and white; VIII, 74 p. 7 illus.
Verlagsort Singapore
Sprache englisch
Maße 155 x 235 mm
Themenwelt Mathematik / Informatik Mathematik Angewandte Mathematik
Mathematik / Informatik Mathematik Statistik
Mathematik / Informatik Mathematik Wahrscheinlichkeit / Kombinatorik
ISBN-10 981-15-6974-6 / 9811569746
ISBN-13 978-981-15-6974-6 / 9789811569746
Zustand Neuware
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