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October 2013 Conditional formulae for Gibbs-type exchangeable random partitions
Stefano Favaro, Antonio Lijoi, Igor Prünster
Ann. Appl. Probab. 23(5): 1721-1754 (October 2013). DOI: 10.1214/12-AAP843


Gibbs-type random probability measures and the exchangeable random partitions they induce represent an important framework both from a theoretical and applied point of view. In the present paper, motivated by species sampling problems, we investigate some properties concerning the conditional distribution of the number of blocks with a certain frequency generated by Gibbs-type random partitions. The general results are then specialized to three noteworthy examples yielding completely explicit expressions of their distributions, moments and asymptotic behaviors. Such expressions can be interpreted as Bayesian nonparametric estimators of the rare species variety and their performance is tested on some real genomic data.


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Stefano Favaro. Antonio Lijoi. Igor Prünster. "Conditional formulae for Gibbs-type exchangeable random partitions." Ann. Appl. Probab. 23 (5) 1721 - 1754, October 2013.


Published: October 2013
First available in Project Euclid: 28 August 2013

zbMATH: 1287.60046
MathSciNet: MR3114915
Digital Object Identifier: 10.1214/12-AAP843

Primary: 60G57 , 62F15 , 62G05

Keywords: $\sigma$-diversity , Bayesian nonparametrics , exchangeable random partitions , Gibbs-type random partitions , Sampling formulae , small blocks , species sampling problems

Rights: Copyright © 2013 Institute of Mathematical Statistics


Vol.23 • No. 5 • October 2013
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