The Annals of Applied Probability

Conditional formulae for Gibbs-type exchangeable random partitions

Stefano Favaro, Antonio Lijoi, and Igor Prünster

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Abstract

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.

Article information

Source
Ann. Appl. Probab., Volume 23, Number 5 (2013), 1721-1754.

Dates
First available in Project Euclid: 28 August 2013

Permanent link to this document
https://projecteuclid.org/euclid.aoap/1377696296

Digital Object Identifier
doi:10.1214/12-AAP843

Mathematical Reviews number (MathSciNet)
MR3114915

Zentralblatt MATH identifier
1287.60046

Subjects
Primary: 60G57: Random measures 62G05: Estimation 62F15: Bayesian inference

Keywords
Bayesian nonparametrics Exchangeable random partitions Gibbs-type random partitions sampling formulae small blocks species sampling problems $\sigma$-diversity

Citation

Favaro, Stefano; Lijoi, Antonio; Prünster, Igor. Conditional formulae for Gibbs-type exchangeable random partitions. Ann. Appl. Probab. 23 (2013), no. 5, 1721--1754. doi:10.1214/12-AAP843. https://projecteuclid.org/euclid.aoap/1377696296


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