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2013 Marginals of multivariate Gibbs distributions with applications in Bayesian species sampling
Annalisa Cerquetti
Electron. J. Statist. 7: 697-716 (2013). DOI: 10.1214/13-EJS784


Gibbs partition models are the largest class of infinite exchangeable partitions of the positive integers generalizing the product form of the probability function of the two-parameter Poisson-Dirichlet family. Here we call into question the current approach to Bayesian nonparametric estimation in species sampling problems under Gibbs priors, which incorrectly relies on treating exchangeable partition probability functions (EPPFs) as multivariate distributions on compositions of the positive integers. We show that once those multivariate distributions are correctly derived, results for corresponding sampling formulas can be obtained, generalized and sometimes fixed, working with marginals and a known result on falling factorial moments of a sum of non independent indicators. We provide an application of our findings to a recently proposed Bayesian nonparametric estimation under Gibbs priors of the predictive probability to observe a species already observed a certain number of times.


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Annalisa Cerquetti. "Marginals of multivariate Gibbs distributions with applications in Bayesian species sampling." Electron. J. Statist. 7 697 - 716, 2013.


Published: 2013
First available in Project Euclid: 17 March 2013

zbMATH: 1327.62196
MathSciNet: MR3035269
Digital Object Identifier: 10.1214/13-EJS784

Primary: 60G57, 62G05
Secondary: 62F15

Rights: Copyright © 2013 The Institute of Mathematical Statistics and the Bernoulli Society


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