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Ordered and size-biased frequencies in GEM and Gibbs’ models for species sampling. / Pitman, Jim; Yakubovich, Yuri.

в: Annals of Applied Probability, Том 28, № 3, 01.06.2018, стр. 1793-1820.

Результаты исследований: Научные публикации в периодических изданиях › статья › Рецензирование

Harvard

Pitman, J & Yakubovich, Y 2018, 'Ordered and size-biased frequencies in GEM and Gibbs’ models for species sampling', Annals of Applied Probability, Том. 28, № 3, стр. 1793-1820. https://doi.org/10.1214/17-AAP1343

APA

Pitman, J., & Yakubovich, Y. (2018). Ordered and size-biased frequencies in GEM and Gibbs’ models for species sampling. Annals of Applied Probability, 28(3), 1793-1820. https://doi.org/10.1214/17-AAP1343

Vancouver

Pitman J, Yakubovich Y. Ordered and size-biased frequencies in GEM and Gibbs’ models for species sampling. Annals of Applied Probability. 2018 Июнь 1;28(3):1793-1820. https://doi.org/10.1214/17-AAP1343

Author

Pitman, Jim ; Yakubovich, Yuri. / Ordered and size-biased frequencies in GEM and Gibbs’ models for species sampling. в: Annals of Applied Probability. 2018 ; Том 28, № 3. стр. 1793-1820.

BibTeX

@article{3a2fe87d2b8f4f5291a561ba9a555d55,
title = "Ordered and size-biased frequencies in GEM and Gibbs{\textquoteright} models for species sampling",
abstract = "We describe the distribution of frequencies ordered by sample values in a random sample of size n from the two parameter GEM(a, ?) random discrete distribution on the positive integers. These frequencies are a (size-a)-biased random permutation of the sample frequencies in either ranked order, or in the order of appearance of values in the sampling process. This generalizes a well-known identity in distribution due to Donnelly and Tavar{\'e} [Adv. in Appl. Probab. 18 (1986) 1–19] for a = 0 to the case 0 = a < 1. This description extends to sampling from Gibbs(a) frequencies obtained by suitable conditioning of the GEM(a, ?) model, and yields a value-ordered version of the Chinese restaurant construction of GEM(a, ?) and Gibbs(a) frequencies in the more usual size-biased order of their appearance. The proofs are based on a general construction of a finite sample (X1, . . ., Xn) from any random frequencies in size-biased order from the associated exchangeable random partition 8 of N which they generate.",
keywords = "Chinese restaurant construction, GEM distribution, Gibbs{\textquoteright} partitions, Random exchangeable partition, Size-biased order, Species sampling, PRIORS, ALLELES, REPRESENTATION, EXCHANGEABLE RANDOM PARTITIONS, DISTRIBUTIONS, Gibbs' partitions, random exchangeable partition, REVERSIBILITY, DIFFUSION, size-biased order, AGE",
author = "Jim Pitman and Yuri Yakubovich",
year = "2018",
month = jun,
day = "1",
doi = "10.1214/17-AAP1343",
language = "English",
volume = "28",
pages = "1793--1820",
journal = "Annals of Applied Probability",
issn = "1050-5164",
publisher = "Institute of Mathematical Statistics",
number = "3",

}

RIS

TY - JOUR

T1 - Ordered and size-biased frequencies in GEM and Gibbs’ models for species sampling

AU - Pitman, Jim

AU - Yakubovich, Yuri

PY - 2018/6/1

Y1 - 2018/6/1

N2 - We describe the distribution of frequencies ordered by sample values in a random sample of size n from the two parameter GEM(a, ?) random discrete distribution on the positive integers. These frequencies are a (size-a)-biased random permutation of the sample frequencies in either ranked order, or in the order of appearance of values in the sampling process. This generalizes a well-known identity in distribution due to Donnelly and Tavaré [Adv. in Appl. Probab. 18 (1986) 1–19] for a = 0 to the case 0 = a < 1. This description extends to sampling from Gibbs(a) frequencies obtained by suitable conditioning of the GEM(a, ?) model, and yields a value-ordered version of the Chinese restaurant construction of GEM(a, ?) and Gibbs(a) frequencies in the more usual size-biased order of their appearance. The proofs are based on a general construction of a finite sample (X1, . . ., Xn) from any random frequencies in size-biased order from the associated exchangeable random partition 8 of N which they generate.

AB - We describe the distribution of frequencies ordered by sample values in a random sample of size n from the two parameter GEM(a, ?) random discrete distribution on the positive integers. These frequencies are a (size-a)-biased random permutation of the sample frequencies in either ranked order, or in the order of appearance of values in the sampling process. This generalizes a well-known identity in distribution due to Donnelly and Tavaré [Adv. in Appl. Probab. 18 (1986) 1–19] for a = 0 to the case 0 = a < 1. This description extends to sampling from Gibbs(a) frequencies obtained by suitable conditioning of the GEM(a, ?) model, and yields a value-ordered version of the Chinese restaurant construction of GEM(a, ?) and Gibbs(a) frequencies in the more usual size-biased order of their appearance. The proofs are based on a general construction of a finite sample (X1, . . ., Xn) from any random frequencies in size-biased order from the associated exchangeable random partition 8 of N which they generate.

KW - Chinese restaurant construction

KW - GEM distribution

KW - Gibbs’ partitions

KW - Random exchangeable partition

KW - Size-biased order

KW - Species sampling

KW - PRIORS

KW - ALLELES

KW - REPRESENTATION

KW - EXCHANGEABLE RANDOM PARTITIONS

KW - DISTRIBUTIONS

KW - Gibbs' partitions

KW - random exchangeable partition

KW - REVERSIBILITY

KW - DIFFUSION

KW - size-biased order

KW - AGE

UR - http://www.scopus.com/inward/record.url?scp=85048042330&partnerID=8YFLogxK

UR - http://www.mendeley.com/research/ordered-sizebiased-frequencies-gem-gibbs-models-species-sampling

U2 - 10.1214/17-AAP1343

DO - 10.1214/17-AAP1343

M3 - Article

AN - SCOPUS:85048042330

VL - 28

SP - 1793

EP - 1820

JO - Annals of Applied Probability

JF - Annals of Applied Probability

SN - 1050-5164

IS - 3

ER -

ID: 32734430