Open Access
2014 On the stick-breaking representation of $\sigma$-stable Poisson-Kingman models
Stefano Favaro, Maria Lomeli, Bernardo Nipoti, Yee Whye Teh
Electron. J. Statist. 8(1): 1063-1085 (2014). DOI: 10.1214/14-EJS921


In this paper we investigate the stick-breaking representation for the class of $\sigma$-stable Poisson-Kingman models, also known as Gibbs-type random probability measures. This class includes as special cases most of the discrete priors commonly used in Bayesian nonparametrics, such as the two parameter Poisson-Dirichlet process and the normalized generalized Gamma process. Under the assumption $\sigma=u/v$, for any coprime integers $1\leq u<v$ such that $u/v\leq1/2$, we show that a $\sigma$-stable Poisson-Kingman model admits an explicit stick-breaking representation in terms of random variables which are obtained by suitably transforming Gamma random variables and products of independent Beta and Gamma random variables.


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Stefano Favaro. Maria Lomeli. Bernardo Nipoti. Yee Whye Teh. "On the stick-breaking representation of $\sigma$-stable Poisson-Kingman models." Electron. J. Statist. 8 (1) 1063 - 1085, 2014.


Published: 2014
First available in Project Euclid: 5 August 2014

zbMATH: 1298.62049
MathSciNet: MR3263112
Digital Object Identifier: 10.1214/14-EJS921

Primary: 60G57 , 62F15

Keywords: $\sigma$-stable Poisson-Kingman model , $G$-functions , Bayesian nonparametrics , Beta random variable , discrete random probability measure , exponential tilting , Gamma random variable , stick-breaking prior

Rights: Copyright © 2014 The Institute of Mathematical Statistics and the Bernoulli Society

Vol.8 • No. 1 • 2014
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