On a class of $$\sigma $$ σ -stable Poisson–Kingman models and an effective marginalized sampler
| Autor: | Maria Lomeli, Yee Whye Teh, Stefano Favaro |
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| Rok vydání: | 2014 |
| Předmět: |
Statistics and Probability
Posterior probability Gamma process Context (language use) Poisson distribution Theoretical Computer Science Bayesian nonparametrics symbols.namesake Prior probability Bayesian nonparametrics Normalized generalized Gamma process Marginalized MCMC sampler Mixture model σ-Stable Poisson–Kingman model Two parameter Poisson–Dirichlet process Mathematics Probability measure Mixture model Discrete mathematics Marginalized MCMC sampler business.industry Nonparametric statistics Pattern recognition Two parameter Poisson–Dirichlet process Computational Theory and Mathematics σ-Stable Poisson–Kingman model Normalized generalized Gamma process symbols Artificial intelligence Statistics Probability and Uncertainty business |
| Zdroj: | Statistics and Computing. 25:67-78 |
| ISSN: | 1573-1375 0960-3174 |
| DOI: | 10.1007/s11222-014-9499-4 |
| Popis: | We investigate the use of a large class of discrete random probability measures, which is referred to as the class $$\mathcal {Q}$$Q, in the context of Bayesian nonparametric mixture modeling. The class $$\mathcal {Q}$$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 $$\mathcal {Q}$$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. |
| Databáze: | OpenAIRE |
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