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A simple proof of Pitman–Yor’s Chinese restaurant process from its stick-breaking representation

A simple proof of Pitman–Yor’s Chinese restaurant process from its stick-breaking representation AbstractFor a long time, the Dirichlet process has been the gold standard discrete random measure in Bayesian nonparametrics. The Pitman-Yor process provides a simple and mathematically tractable generalization, allowing for a very flexible control of the clustering behaviour. Two commonly used representations of the Pitman-Yor process are the stick-breaking process and the Chinese restaurant process. The former is a constructive representation of the process which turns out very handy for practical implementation, while the latter describes the partition distribution induced. Obtaining one from the other is usually done indirectly with use of measure theory. In contrast, we propose here an elementary proof of Pitman-Yor’s Chinese Restaurant process from its stick-breaking representation. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Dependence Modeling de Gruyter

A simple proof of Pitman–Yor’s Chinese restaurant process from its stick-breaking representation

Lawless, Caroline; Arbel, Julyan
Dependence Modeling , Volume 7 (1): 8 – Mar 1, 2019
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Publisher
de Gruyter
Copyright
© by Caroline Lawless, Julyan Arbel, published by De Gruyter
ISSN
2300-2298
eISSN
2300-2298
DOI
10.1515/demo-2019-0003
Publisher site
See Article on Publisher Site

Abstract

AbstractFor a long time, the Dirichlet process has been the gold standard discrete random measure in Bayesian nonparametrics. The Pitman-Yor process provides a simple and mathematically tractable generalization, allowing for a very flexible control of the clustering behaviour. Two commonly used representations of the Pitman-Yor process are the stick-breaking process and the Chinese restaurant process. The former is a constructive representation of the process which turns out very handy for practical implementation, while the latter describes the partition distribution induced. Obtaining one from the other is usually done indirectly with use of measure theory. In contrast, we propose here an elementary proof of Pitman-Yor’s Chinese Restaurant process from its stick-breaking representation.

Journal

Dependence Modeling – de Gruyter

Published: Mar 1, 2019

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