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Exchangeable and partially exchangeable random partitions
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  • Published: June 1995

Exchangeable and partially exchangeable random partitions

  • Jim Pitman1 

Probability Theory and Related Fields volume 102, pages 145–158 (1995)Cite this article

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Summary

Call a random partition of the positive integerspartially exchangeable if for each finite sequence of positive integersn 1,...,n k, the probability that the partition breaks the firstn 1+...+nk integers intok particular classes, of sizesn 1,...,nk in order of their first elements, has the same valuep(n 1,...,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(n 1,...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.

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Authors and Affiliations

  1. Department of Statistics, U.C. Berkeley, 94720, CA, USA

    Jim Pitman

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  1. Jim Pitman
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Additional information

Research supported by N.S.F. Grants MCS91-07531 and DMS-9404345

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Cite this article

Pitman, J. Exchangeable and partially exchangeable random partitions. Probab. Th. Rel. Fields 102, 145–158 (1995). https://doi.org/10.1007/BF01213386

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  • Received: 05 May 1992

  • Accepted: 25 November 1994

  • Issue Date: June 1995

  • DOI: https://doi.org/10.1007/BF01213386

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Mathematics Subject Classification

  • 60G09
  • 60C05
  • 60J50
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