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

Junyi Zhang and Angelos Dassios

LSE Research Online Documents on Economics from London School of Economics and Political Science, LSE Library

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.

Keywords: Bayesian non-parametric statistics; Markov chain Monte Carlo; mixture model; Pitman-Yor process; two-parameter Poisson-Dirichlet distribution (search for similar items in EconPapers)
JEL-codes: C1 (search for similar items in EconPapers)
Pages: 22 pages
Date: 2023-09-28
New Economics Papers: this item is included in nep-ecm
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Published in Scandinavian Journal of Statistics, 28, September, 2023. ISSN: 0303-6898

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Persistent link: https://EconPapers.repec.org/RePEc:ehl:lserod:120294

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