02387nmm a2200313 u 4500001001200000003002700012005001700039007002400056008004100080020001800121100001900139245010600158250001700264260005300281300004100334505016000375653002800535653003500563653002800598653001700626653002300643041001900666989003600685490003800721028003000759856007200789082000800861520120400869EB001899127EBX0100000000000000106203600000000000000.0cr|||||||||||||||||||||200810 ||| eng a97898115697531 aYamato, Hajime00aStatistics Based on Dirichlet Processes and Related TopicshElektronische Ressourcecby Hajime Yamato a1st ed. 2020 aSingaporebSpringer Nature Singaporec2020, 2020 aVIII, 74 p. 7 illusbonline resource0 aIntroduction -- Dirichlet process and Chinese restaurant process -- Nonparametric estimation of estimable parameter -- Random partition of positive integer aMathematical statistics aStatistical Theory and Methods aMathematical Statistics aStatistics aApplied Statistics07aeng2ISO 639-2 bSpringeraSpringer eBooks 2005-0 aJSS Research Series in Statistics50a10.1007/978-981-15-6975-340uhttps://doi.org/10.1007/978-981-15-6975-3?nosfx=yxVerlag3Volltext0 a519 aThis 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