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February 2015 Looking-backward probabilities for Gibbs-type exchangeable random partitions
Sergio Bacallado, Stefano Favaro, Lorenzo Trippa
Bernoulli 21(1): 1-37 (February 2015). DOI: 10.3150/13-BEJ559

Abstract

Gibbs-type random probability measures and the exchangeable random partitions they induce represent the subject of a rich and active literature. They provide a probabilistic framework for a wide range of theoretical and applied problems that are typically referred to as species sampling problems. In this paper, we consider the class of looking-backward species sampling problems introduced in Lijoi et al. (Ann. Appl. Probab. 18 (2008) 1519–1547) in Bayesian nonparametrics. Specifically, given some information on the random partition induced by an initial sample from a Gibbs-type random probability measure, we study the conditional distributions of statistics related to the old species, namely those species detected in the initial sample and possibly re-observed in an additional sample. The proposed results contribute to the analysis of conditional properties of Gibbs-type exchangeable random partitions, so far focused mainly on statistics related to those species generated by the additional sample and not already detected in the initial sample.

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Sergio Bacallado. Stefano Favaro. Lorenzo Trippa. "Looking-backward probabilities for Gibbs-type exchangeable random partitions." Bernoulli 21 (1) 1 - 37, February 2015. https://doi.org/10.3150/13-BEJ559

Information

Published: February 2015
First available in Project Euclid: 17 March 2015

zbMATH: 1329.60091
MathSciNet: MR3322311
Digital Object Identifier: 10.3150/13-BEJ559

Keywords: Bayesian nonparametrics , conditional random partitions , Ewens–Pitman sampling model , Gibbs-type exchangeable random partitions , looking-backward probabilities , species diversity , species sampling problems

Rights: Copyright © 2015 Bernoulli Society for Mathematical Statistics and Probability

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Vol.21 • No. 1 • February 2015
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