Exchangeable and partially exchangeable random partitions
J. Pitman. Probability Theory and Related Fields, 102 (2):
145--158(June 1995)
Abstract
Summary Call a random partition of the positive integerspartially exchangeable if for each finite sequence of positive integersn1,...,nk, the probability that the partition breaks the firstn1+...+nk integers intok particular classes, of sizesn1,...,nk in order of their first elements, has the same valuep(n1,...,nk) for every possible choice of classes subject to the sizes constraint. A random partition is exchangeable iff it is partially exchangeable for a symmetric functionp(n1,...nk). A representation is given for partially exchangeable random partitions which provides a useful variation of Kingman's representation in the exchangeable case. Results are illustrated by the two-parameter generalization of Ewens' partition structure.
ER -
Description
Exchangeable and partially exchangeable random partitions
%0 Journal Article
%1 pitman-ptrf-95
%A Pitman, Jim
%D 1995
%J Probability Theory and Related Fields
%K Poisson_Dirichlet_distribution Poisson_process exchangeability partitions subordinators
%N 2
%P 145--158
%T Exchangeable and partially exchangeable random partitions
%U http://dx.doi.org/10.1007/BF01213386
%V 102
%X Summary Call a random partition of the positive integerspartially exchangeable if for each finite sequence of positive integersn1,...,nk, the probability that the partition breaks the firstn1+...+nk integers intok particular classes, of sizesn1,...,nk in order of their first elements, has the same valuep(n1,...,nk) for every possible choice of classes subject to the sizes constraint. A random partition is exchangeable iff it is partially exchangeable for a symmetric functionp(n1,...nk). A representation is given for partially exchangeable random partitions which provides a useful variation of Kingman's representation in the exchangeable case. Results are illustrated by the two-parameter generalization of Ewens' partition structure.
ER -
@article{pitman-ptrf-95,
abstract = {Summary Call a random partition of the positive integerspartially exchangeable if for each finite sequence of positive integersn1,...,nk, the probability that the partition breaks the firstn1+...+nk integers intok particular classes, of sizesn1,...,nk in order of their first elements, has the same valuep(n1,...,nk) for every possible choice of classes subject to the sizes constraint. A random partition is exchangeable iff it is partially exchangeable for a symmetric functionp(n1,...nk). A representation is given for partially exchangeable random partitions which provides a useful variation of Kingman's representation in the exchangeable case. Results are illustrated by the two-parameter generalization of Ewens' partition structure.
ER -},
added-at = {2009-04-23T05:33:54.000+0200},
author = {Pitman, Jim},
biburl = {https://www.bibsonomy.org/bibtex/2ca72b744ca0deb3da977fb5df4a2dad0/peter.ralph},
description = {Exchangeable and partially exchangeable random partitions},
interhash = {5230941904836593bfc7893faecaf33a},
intrahash = {ca72b744ca0deb3da977fb5df4a2dad0},
journal = {Probability Theory and Related Fields},
keywords = {Poisson_Dirichlet_distribution Poisson_process exchangeability partitions subordinators},
month = {#jun#},
number = 2,
pages = {145--158},
timestamp = {2009-04-23T05:33:54.000+0200},
title = {Exchangeable and partially exchangeable random partitions},
url = {http://dx.doi.org/10.1007/BF01213386},
volume = 102,
year = 1995
}