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.

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

FAVARO, STEFANO;
2014-01-01

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.
2014
19
1
15
https://projecteuclid.org/euclid.ejp/1465065663
Bayesian nonparametrics, Dirichlet process, Ewens-Pitman sampling model, exchangeable random partition, fluctuation limit, large deviations, two parameter Poisson-Dirichlet process
S. Favaro; S. Feng
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/2318/155542
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