Bernoulli

  • Bernoulli
  • Volume 11, Number 5 (2005), 847-861.

Binary sequential representations of random partitions

James E. Young

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Abstract

Random partitions can be thought of as a consistent family of exchangeable random partitions of the sets {1,2,...,n} for n≥1. Historically, random partitions were constructed by sampling an infinite population of types and partitioning individuals of the same type into a single class. A particularly tractable way to construct random partitions is via random sequences of 0s and 1s. The only random partition derived from an independent 0-1 sequence is Ewens' one-parameter family of partitions which plays a predominant role in population genetics. A two-parameter generalization of Ewens' partition is obtained by considering random partitions constructed from discrete renewal processes and introducing a convolution-type product on 0-1 sequences.

Article information

Source
Bernoulli, Volume 11, Number 5 (2005), 847-861.

Dates
First available in Project Euclid: 23 October 2005

Permanent link to this document
https://projecteuclid.org/euclid.bj/1130077597

Digital Object Identifier
doi:10.3150/bj/1130077597

Mathematical Reviews number (MathSciNet)
MR2172844

Zentralblatt MATH identifier
1093.60008

Keywords
combinatorial probability combinatorial stochastic process exchangeable random partition sequential construction

Citation

Young, James E. Binary sequential representations of random partitions. Bernoulli 11 (2005), no. 5, 847--861. doi:10.3150/bj/1130077597. https://projecteuclid.org/euclid.bj/1130077597


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