Electronic Journal of Statistics

On the stick-breaking representation of $\sigma$-stable Poisson-Kingman models

Stefano Favaro, Maria Lomeli, Bernardo Nipoti, and Yee Whye Teh

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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.

Article information

Electron. J. Statist., Volume 8, Number 1 (2014), 1063-1085.

First available in Project Euclid: 5 August 2014

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Primary: 62F15: Bayesian inference 60G57: Random measures

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


Favaro, Stefano; Lomeli, Maria; Nipoti, Bernardo; Teh, Yee Whye. On the stick-breaking representation of $\sigma$-stable Poisson-Kingman models. Electron. J. Statist. 8 (2014), no. 1, 1063--1085. doi:10.1214/14-EJS921. https://projecteuclid.org/euclid.ejs/1407243242

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