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Bayesian nonparametric estimators derived from conditional Gibbs structures
 J. PHYS. A: MATH. GEN
, 2008
"... We consider discrete nonparametric priors which induce Gibbstype exchangeable random partitions and investigate their posterior behavior in detail. In particular, we deduce conditional distributions and the corresponding Bayesian nonparametric estimators, which can be readily exploited for predictin ..."
Abstract

Cited by 32 (8 self)
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We consider discrete nonparametric priors which induce Gibbstype exchangeable random partitions and investigate their posterior behavior in detail. In particular, we deduce conditional distributions and the corresponding Bayesian nonparametric estimators, which can be readily exploited for predicting various features of additional samples. The results provide useful tools for genomic applications where prediction of future outcomes is required.
Conditional formulae for Gibbstype exchangeable random partitions
 Ann. Appl. Probab
, 2013
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Lookingbackward probabilities for Gibbstype exchangeable random partitions
, 2014
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Asymptotics for the conditional number of blocks in the EwensPitman sampling model
, 2014
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Large deviation principles for the EwensPitman sampling model
, 2014
"... Let Ml,n be the number of blocks with frequency l in the exchangeable random partition induced by a sample of size n from the EwensPitman sampling model. We show that as n tends to infinity n−1Ml,n satisfies a large deviation principle and we characterize the corresponding rate function. A conditio ..."
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Let Ml,n be the number of blocks with frequency l in the exchangeable random partition induced by a sample of size n from the EwensPitman sampling model. We show that as n tends to infinity n−1Ml,n satisfies a large deviation principle and we characterize the corresponding rate function. A conditional counterpart of this large deviation principle is also presented. Specifically, given an initial observed sample of size n from the EwensPitman sampling model, we consider an additional unobserved sample of size m thus giving rise to an enlarged sample of size n+m. As m tends to infinity, and for any fixed n, we establish a large deviation principle for the conditional number of blocks with frequency l in the enlarged sample, given the initial sample. Interestingly this conditional large deviation principle coincides with the unconditional large deviation principle for Ml,n, namely there is no long lasting impact of the given initial sample. Applications of the conditional large deviation principle are discussed in the context of Bayesian nonparametric inference for species sampling problems.
Asymptotics for the number of blocks in a conditional EwensPitman sampling model
"... 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 ..."
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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 the 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 PoissonDirichlet process. In this paper we generalize some existing asymptotic results from this prior setting to the socalled posterior, or conditional, setting. Specifically, given an initial sample from a two parameter PoissonDirichlet process, we establish conditional fluctuation limits and conditional large deviation principles for the number of blocks generated by a large additional sample.