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Truncated Poisson-Dirichlet approximation for Dirichlet process hierarchical models

Zhang, Junyi ORCID: 0000-0001-8986-6588 and Dassios, Angelos ORCID: 0000-0002-3968-2366 (2023) Truncated Poisson-Dirichlet approximation for Dirichlet process hierarchical models. Statistics and Computing. ISSN 0960-3174

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The Dirichlet process was introduced by Ferguson in 1973 to use with Bayesian nonparametric inference problems. A lot of work has been done based on the Dirichlet process, making it the most fundamental prior in Bayesian nonparametric statistics. Since the construction of Dirichlet process involves an infinite number of random variables, simulation-based methods are hard to implement, and various finite approximations for the Dirichlet process have been proposed to solve this problem. In this paper, we construct a new random probability measure called the truncated Poisson–Dirichlet process. It sorts the components of a Dirichlet process in descending order according to their random weights, then makes a truncation to obtain a finite approximation for the distribution of the Dirichlet process. Since the approximation is based on a decreasing sequence of random weights, it has a lower truncation error comparing to the existing methods using stick-breaking process. Then we develop a blocked Gibbs sampler based on Hamiltonian Monte Carlo method to explore the posterior of the truncated Poisson–Dirichlet process. This method is illustrated by the normal mean mixture model and Caron–Fox network model. Numerical implementations are provided to demonstrate the effectiveness and performance of our algorithm.

Item Type: Article
Additional Information: © 2022 Springer.
Divisions: Statistics
Subjects: H Social Sciences > HA Statistics
Date Deposited: 04 Jan 2023 09:21
Last Modified: 16 May 2024 03:58

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