Lomelí, M;
Favaro, S;
Teh, YW;
(2017)
A Marginal Sampler for σ-Stable Poisson–Kingman Mixture Models.
Journal of Computational and Graphical Statistics
, 26
(1)
pp. 44-53.
10.1080/10618600.2015.1110526.
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Abstract
We investigate the class of σ-stable Poisson–Kingman random probability measures (RPMs) in the context of Bayesian nonparametric mixture modeling. This is a large class of discrete RPMs, which encompasses most of the popular discrete RPMs used in Bayesian nonparametrics, such as the Dirichlet process, Pitman–Yor process, the normalized inverse Gaussian process, and the normalized generalized Gamma process. We show how certain sampling properties and marginal characterizations of σ-stable Poisson–Kingman RPMs can be usefully exploited for devising a Markov chain Monte Carlo (MCMC) algorithm for performing posterior inference with a Bayesian nonparametric mixture model. Specifically, we introduce a novel and efficient MCMC sampling scheme in an augmented space that has a small number of auxiliary variables per iteration. We apply our sampling scheme to a density estimation and clustering tasks with unidimensional and multidimensional datasets, and compare it against competing MCMC sampling schemes. Supplementary materials for this article are available online.
| Type: | Article |
|---|---|
| Title: | A Marginal Sampler for σ-Stable Poisson–Kingman Mixture Models |
| Open access status: | An open access version is available from UCL Discovery |
| DOI: | 10.1080/10618600.2015.1110526 |
| Publisher version: | http://dx.doi.org/10.1111/nan.1230710.1080/1061860... |
| Language: | English |
| Additional information: | This is an Accepted Manuscript of an article published by Taylor & Francis in Journal of Computational and Graphical Statistics on 21 January 2016, available online: http://www.tandfonline.com/10.1080/10618600.2015.1110526. |
| Keywords: | Bayesian nonparametrics, MCMC posterior sampling, Mixture models, Normalized generalized gamma process, Pitman–Yor process, σ-stable Poisson–Kingman random probability measures |
| UCL classification: | UCL UCL > Provost and Vice Provost Offices UCL > Provost and Vice Provost Offices > School of Life and Medical Sciences UCL > Provost and Vice Provost Offices > School of Life and Medical Sciences > Faculty of Life Sciences |
| URI: | https://discovery.ucl.ac.uk/id/eprint/1543093 |
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