# A marginal sampler for σ-Stable Poisson-Kingman mixture models

arXiv: https://arxiv.org/abs/1407.4211 · HTML: https://mlsanity.com/paper/1407.4211/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 16 Jul 2014.

## Built on by (most cited first, 1 of 1)

- [Why the Rich Get Richer? On the Balancedness of Random Partition Models](https://mlsanity.com/paper/2201.12697/) (2022)

## Abstract (arXiv)

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 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 making inference in Bayesian nonparametric mixture modeling. Specifically, we introduce a novel and efficient MCMC sampling scheme in an augmented space that has a fixed number of auxiliary variables per iteration. We apply our sampling scheme for a density estimation and clustering tasks with unidimensional and multidimensional datasets, and we compare it against competing sampling schemes.