Bernoulli

Looking-backward probabilities for Gibbs-type exchangeable random partitions

Sergio Bacallado, Stefano Favaro, and Lorenzo Trippa

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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.

Article information

Source
Bernoulli, Volume 21, Number 1 (2015), 1-37.

Dates
First available in Project Euclid: 17 March 2015

Permanent link to this document
https://projecteuclid.org/euclid.bj/1426597062

Digital Object Identifier
doi:10.3150/13-BEJ559

Mathematical Reviews number (MathSciNet)
MR3322311

Zentralblatt MATH identifier
1329.60091

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

Citation

Bacallado, Sergio; Favaro, Stefano; Trippa, Lorenzo. Looking-backward probabilities for Gibbs-type exchangeable random partitions. Bernoulli 21 (2015), no. 1, 1--37. doi:10.3150/13-BEJ559. https://projecteuclid.org/euclid.bj/1426597062


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