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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Abstract

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

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

Dates
First available in Project Euclid: 5 August 2014

Permanent link to this document
https://projecteuclid.org/euclid.ejs/1407243242

Digital Object Identifier
doi:10.1214/14-EJS921

Mathematical Reviews number (MathSciNet)
MR3263112

Zentralblatt MATH identifier
1298.62049

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

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

Citation

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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