Open Access
2014 Asymptotics for the number of blocks in a conditional Ewens-Pitman sampling model
Stefano Favaro, Shui Feng
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Electron. J. Probab. 19: 1-15 (2014). DOI: 10.1214/EJP.v19-2881


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.


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Stefano Favaro. Shui Feng. "Asymptotics for the number of blocks in a conditional Ewens-Pitman sampling model." Electron. J. Probab. 19 1 - 15, 2014.


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

zbMATH: 06291192
MathSciNet: MR3167885
Digital Object Identifier: 10.1214/EJP.v19-2881

Primary: 60F10
Secondary: 92D10

Keywords: Bayesian nonparametrics , Dirichlet process , Ewens-Pitman sampling model , Exchangeable random partition , fluctuation limit , large deviations , two parameter Poisson-Dirichlet process

Vol.19 • 2014
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