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

Stefano Favaro (University of Torino and Collegio Carlo Alberto)
Shui Feng (McMaster University)


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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Pages: 1-15

Publication Date: February 18, 2014

DOI: 10.1214/EJP.v19-2881


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