@article{EJP2881,
author = {Stefano Favaro and Shui Feng},
title = {Asymptotics for the number of blocks in a conditional Ewens-Pitman sampling model},
journal = {Electron. J. Probab.},
fjournal = {Electronic Journal of Probability},
volume = {19},
year = {2014},
keywords = {Bayesian nonparametrics; Dirichlet process; Ewens-Pitman sampling model; exchangeable random partition; fluctuation limit; large deviations; two parameter Poisson-Dirichlet process},
abstract = {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.},
pages = {no. 21, 1-15},
issn = {1083-6489},
doi = {10.1214/EJP.v19-2881},
url = {http://ejp.ejpecp.org/article/view/2881}}