Statistics Based on Dirichlet Processes and Related Topics (eBook)
VIII, 74 Seiten
Springer Singapore (Verlag)
978-981-15-6975-3 (ISBN)
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' sampling formula. 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.
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-Tavare-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.
| Erscheint lt. Verlag | 17.7.2020 |
|---|---|
| Reihe/Serie | JSS Research Series in Statistics |
| JSS Research Series in Statistics | |
| SpringerBriefs in Statistics | SpringerBriefs in Statistics |
| Zusatzinfo | VIII, 74 p. 7 illus. |
| Sprache | englisch |
| Themenwelt | Mathematik / Informatik ► Mathematik ► Angewandte Mathematik |
| Mathematik / Informatik ► Mathematik ► Statistik | |
| Mathematik / Informatik ► Mathematik ► Wahrscheinlichkeit / Kombinatorik | |
| Schlagworte | Dirichlet process • Ewens Sampling Formula • Nonparametric Bayesian Inference • Random Partition • Shifted Binomial Distribution • Shifted Poisson Distribution • U-statistics • V-statistics |
| ISBN-10 | 981-15-6975-4 / 9811569754 |
| ISBN-13 | 978-981-15-6975-3 / 9789811569753 |
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