Electronic Journal of Probability

Asymptotics for the number of blocks in a conditional Ewens-Pitman sampling model

Stefano Favaro and Shui Feng

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The study of random partitions has been an active research area in probability over the last twenty years. A quantity that has attracted a lot of attention is the number of blocks in the random partition. Depending on the area of applications this quantity could represent the number of species in a sample from a population of individuals or he number of cycles in a random permutation, etc. In the context of Bayesian nonparametric inference such a quantity is associated with the exchangeable random partition induced by sampling from certain prior models, for instance the Dirichlet process and the two parameter Poisson-Dirichlet process. In this paper we generalize some existing asymptotic results from this prior setting to the so-called posterior, or conditional, setting. Specifically, given an initial sample from a two parameter Poisson-Dirichlet process, we establish conditional fluctuation limits and conditional large deviation principles for the number of blocks generated by a large additional sample.

Article information

Electron. J. Probab., Volume 19 (2014), paper no. 21, 15 pp.

Accepted: 18 February 2014
First available in Project Euclid: 4 June 2016

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 60F10: Large deviations
Secondary: 92D10: Genetics {For genetic algebras, see 17D92}

Bayesian nonparametrics Dirichlet process Ewens-Pitman sampling model exchangeable random partition fluctuation limit large deviations two parameter Poisson-Dirichlet process

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Favaro, Stefano; Feng, Shui. Asymptotics for the number of blocks in a conditional Ewens-Pitman sampling model. Electron. J. Probab. 19 (2014), paper no. 21, 15 pp. doi:10.1214/EJP.v19-2881. https://projecteuclid.org/euclid.ejp/1465065663

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