Truncated two-parameter Poisson-Dirichlet approximation for Pitman-Yor process hierarchical models

Zhang, Junyi ORCID: 0000-0001-8986-6588 and Dassios, Angelos ORCID: 0000-0002-3968-2366 (2023) Truncated two-parameter Poisson-Dirichlet approximation for Pitman-Yor process hierarchical models. Scandinavian Journal of Statistics. ISSN 0303-6898

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Abstract

In this paper, we construct an approximation to the Pitman–Yor process by truncating its two-parameter Poisson–Dirichlet representation. The truncation is based on a decreasing sequence of random weights, thus having a lower approximation error compared to the popular truncated stick-breaking process. We develop an exact simulation algorithm to sample from the approximation process and provide an alternative MCMC algorithm for the parameter regime where the exact simulation algorithm becomes slow. The effectiveness of the simulation algorithms is demonstrated by the estimation of the functionals of a Pitman–Yor process. Then we adapt the approximation process into a Pitman–Yor process mixture model and devise a blocked Gibbs sampler for posterior inference.

Item Type:	Article
Official URL:	https://onlinelibrary.wiley.com/journal/14679469
Additional Information:	© 2023 The Authors
Divisions:	Statistics
Subjects:	H Social Sciences > HA Statistics
Date Deposited:	28 Sep 2023 08:45
Last Modified:	25 Apr 2024 07:43
URI:	http://eprints.lse.ac.uk/id/eprint/120294

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