Access the full text.
Sign up today, get DeepDyve free for 14 days.
Loading next page...
/lp/springer-journals/advances-in-probability-and-mathematical-statistics-bayesian-non-b1fa0ZwJ5h
References (12)
-
P. Blasi, Asael Martínez, R. Mena, Igor Prünster (2020)
On the inferential implications of decreasing weight structures in mixture modelsComput. Stat. Data Anal., 147
-
J. Pitman (1996)
Some developments of the Blackwell-MacQueen urn scheme -
O. Kallenberg (2017)
Random Measures, Theory and Applications -
H. Ishwaran, Lancelot James (2001)
Gibbs Sampling Methods for Stick-Breaking PriorsJournal of the American Statistical Association, 96
-
S. Walker (2006)
Sampling the Dirichlet Mixture Model with SlicesCommunications in Statistics - Simulation and Computation, 36
-
T. Ferguson (1973)
A Bayesian Analysis of Some Nonparametric ProblemsAnnals of Statistics, 1
-
S. Ghosal, A. Vaart (2017)
Fundamentals of Nonparametric Bayesian Inference -
J. Kingman (1975)
Random Discrete DistributionsJournal of the royal statistical society series b-methodological, 37
-
R. Fuentes-García, R. Mena, S. Walker (2010)
A New Bayesian Nonparametric Mixture ModelCommunications in Statistics - Simulation and Computation, 39
-
I. Gormley, Sylvia Fruhwirth-Schnatter (2018)
Mixtures of Experts Models -
Lancelot James, A. Lijoi, Igor Prünster (2009)
Posterior Analysis for Normalized Random Measures with Independent IncrementsScandinavian Journal of Statistics, 36
-
E. Regazzini, A. Lijoi, Igor Prünster (2003)
Distributional results for means of normalized random measures with independent incrementsAnnals of Statistics, 31
- Publisher
- Springer International Publishing
- Copyright
- © The Editor(s) (if applicable) and The Author(s), under exclusive license to Springer Nature Switzerland AG 2021
- ISBN
- 978-3-030-85324-2
- Pages
- 71 –91
- DOI
- 10.1007/978-3-030-85325-9_5
- Publisher site
- See Chapter on Publisher Site
Abstract
[We study the construction of random discrete distributions, taking values in the infinite dimensional simplex, by means of a latent random subset of the natural numbers. The derived sequences of random weights are then used to establish a Bayesian non-parametric prior. A sufficient condition on the distribution of the random set is given, that assures the corresponding prior has full support, and taking advantage of the construction, we propose a general MCMC algorithm for density estimation purposes. This method is illustrated by building a new distribution over the space of all finite and non-empty subsets of ℕ\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document} $$\mathbb {N}$$ \end{document}, that subsequently leads to a general class of random probability measures termed Geometric product stick-breaking process. It is shown that Geometric product stick-breaking process approximate, in distribution, Dirichlet and Geometric processes, and that the respective weights sequences have heavy tails, thus leading to very flexible mixture models.]
Published: Aug 5, 2021
Keywords: Bayesian non-parametric prior; Density estimation; Dirichlet process; Geometric process; Random sets