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P. Blasi, Asael Martínez, R. Mena, Igor Prünster (2020)
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[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
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