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Probability Theory and Related Fields

, Volume 102, Issue 2, pp 145–158 | Cite as

Exchangeable and partially exchangeable random partitions

  • Jim Pitman
Article

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.

Mathematics Subject Classification

60G09 60C05 60J50 

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Copyright information

© Springer-Verlag 1995

Authors and Affiliations

  • Jim Pitman
    • 1
  1. 1.Department of StatisticsU.C. BerkeleyUSA

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