Statistics and Computing

, Volume 25, Issue 1, pp 67–78 | Cite as

On a class of \(\sigma \)-stable Poisson–Kingman models and an effective marginalized sampler

Article

Abstract

We investigate the use of a large class of discrete random probability measures, which is referred to as the class \(\mathcal {Q}\), in the context of Bayesian nonparametric mixture modeling. The class \(\mathcal {Q}\) encompasses both the the two-parameter Poisson–Dirichlet process and the normalized generalized Gamma process, thus allowing us to comparatively study the inferential advantages of these two well-known nonparametric priors. Apart from a highly flexible parameterization, the distinguishing feature of the class \(\mathcal {Q}\) is the availability of a tractable posterior distribution. This feature, in turn, leads to derive an efficient marginal MCMC algorithm for posterior sampling within the framework of mixture models. We demonstrate the efficacy of our modeling framework on both one-dimensional and multi-dimensional datasets.

Keywords

Bayesian nonparametrics Normalized generalized Gamma process Marginalized MCMC sampler Mixture model \(\sigma \)-Stable Poisson–Kingman model Two parameter Poisson–Dirichlet process 

Notes

Acknowledgments

The authors are grateful to an Associate Editor and two Referees for their valuable remarks and suggestions that have led to a substantial improvement of the paper. We would also like to thank Lancelot F. James for helpful suggestions. Stefano Favaro is supported by the European Research Council (ERC) through StG N-BNP 306406. Yee Whye Teh’s research leading to these results is supported by the European Research Council under the European Union’s Seventh Framework Programme (FP7/2007–2013) ERC Grant Agreement No. 617411. Maria Lomeli is supported by the Gatsby Charitable Foundation.

Supplementary material

11222_2014_9499_MOESM1_ESM.pdf (195 kb)
ESM (PDF 196 kb)

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Copyright information

© Springer Science+Business Media New York 2014

Authors and Affiliations

  1. 1.University of Torino and Collegio Carlo AlbertoTurinItaly
  2. 2.Gatsby Computational Neuroscience UnitUniversity College LondonLondonUK
  3. 3.Department of StatisticsUniversity of OxfordOxfordUK

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