Bayesian Analysis

On the Stick-Breaking Representation for Homogeneous NRMIs

S. Favaro, A. Lijoi, C. Nava, B. Nipoti, I. Prünster, and Y. W. Teh

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Abstract

In this paper, we consider homogeneous normalized random measures with independent increments (hNRMI), a class of nonparametric priors recently introduced in the literature. Many of their distributional properties are known by now but their stick-breaking representation is missing. Here we display such a representation, which will feature dependent stick-breaking weights, and then derive explicit versions for noteworthy special cases of hNRMI. Posterior characterizations are also discussed. Finally, we devise an algorithm for slice sampling mixture models based on hNRMIs, which relies on the representation we have obtained, and implement it to analyze real data.

Article information

Source
Bayesian Anal., Volume 11, Number 3 (2016), 697-724.

Dates
First available in Project Euclid: 26 August 2015

Permanent link to this document
https://projecteuclid.org/euclid.ba/1440594949

Digital Object Identifier
doi:10.1214/15-BA964

Mathematical Reviews number (MathSciNet)
MR3498043

Zentralblatt MATH identifier
1357.60050

Keywords
Bayesian Nonparametrics generalized Dirichlet process normalized generalized gamma process normalized random measures with independent increments normalized stable process normalized inverse-Gaussian process random probability measure stick-breaking representation

Citation

Favaro, S.; Lijoi, A.; Nava, C.; Nipoti, B.; Prünster, I.; Teh, Y. W. On the Stick-Breaking Representation for Homogeneous NRMIs. Bayesian Anal. 11 (2016), no. 3, 697--724. doi:10.1214/15-BA964. https://projecteuclid.org/euclid.ba/1440594949


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