國立高雄大學圖資館 |

Language: English

Back

Statistics based on Dirichlet proces...

SpringerLink (Online service)

Statistics based on Dirichlet processes and related topics

Record Type:	Electronic resources : Monograph/item
Title/Author:	Statistics based on Dirichlet processes and related topicsby Hajime Yamato.
Author:	Yamato, Hajime.
Published:	Singapore :Springer Singapore :2020.
Description:	viii, 74 p. :ill., digital ;24 cm.
Contained By:	Springer Nature eBook
Subject:	Nonparametric statistics.
Online resource:	https://doi.org/10.1007/978-981-15-6975-3
ISBN:	9789811569753$q(electronic bk.)

Statistics based on Dirichlet processes and related topics
Yamato, Hajime.

Statistics based on Dirichlet processes and related topics[electronic resource] /by Hajime Yamato. - Singapore :Springer Singapore :2020. - viii, 74 p. :ill., digital ;24 cm. - SpringerBriefs in statistics, JSS research series in statistics. - SpringerBriefs in statistics.JSS research series in statistics..

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

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' 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.

ISBN: 9789811569753$q(electronic bk.)

Standard No.: 10.1007/978-981-15-6975-3doiSubjects--Topical Terms:

182700
Nonparametric statistics.

LC Class. No.: QA278.8 / .Y363 2020

Dewey Class. No.: 519.54

Statistics based on Dirichlet processes and related topics
LDR:02415nmm a2200337 a 4500 001 583752
003 DE-He213
005 20201116172135.0
006 m d
007 cr nn 008maaau
008 210202s2020 si s 0 eng d
020 $a 9789811569753$q(electronic bk.)
020 $a 9789811569746$q(paper)
024 7 $a 10.1007/978-981-15-6975-3 $2 doi
035 $a 978-981-15-6975-3
040 $a GP $c GP
041 0 $a eng
050 4 $a QA278.8 $b .Y363 2020
072 7 $a PBT $2 bicssc
072 7 $a MAT029000 $2 bisacsh
072 7 $a PBT $2 thema
082 0 4 $a 519.54 $2 23
090 $a QA278.8 $b .Y19 2020
100 1 $a Yamato, Hajime. $3 874465
245 1 0 $a Statistics based on Dirichlet processes and related topics $h [electronic resource] / $c by Hajime Yamato.
260 $a Singapore : $b Springer Singapore : $b Imprint: Springer, $c 2020.
300 $a viii, 74 p. : $b ill., digital ; $c 24 cm.
490 1 $a SpringerBriefs in statistics, JSS research series in statistics
505 0 $a Introduction -- Dirichlet process and Chinese restaurant process -- Nonparametric estimation of estimable parameter -- Random partition of positive integer.
520 $a 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' 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.
650 0 $a Nonparametric statistics. $3 182700
650 0 $a Dirichlet problem. $3 456146
650 1 4 $a Applied Statistics. $3 805583
650 2 4 $a Statistical Theory and Methods. $3 274054
650 2 4 $a Probability Theory and Stochastic Processes. $3 274061
650 2 4 $a Applications of Mathematics. $3 273744
710 2 $a SpringerLink (Online service) $3 273601
773 0 $t Springer Nature eBook
830 0 $a SpringerBriefs in statistics. $p JSS research series in statistics. $3 829180
856 4 0 $u https://doi.org/10.1007/978-981-15-6975-3
950 $a Mathematics and Statistics (SpringerNature-11649)