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

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  • Zhang, Junyi
  • Dassios, Angelos

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.

Suggested Citation

  • Zhang, Junyi & Dassios, Angelos, 2023. "Truncated two-parameter Poisson-Dirichlet approximation for Pitman-Yor process hierarchical models," LSE Research Online Documents on Economics 120294, London School of Economics and Political Science, LSE Library.
    • Handle: RePEc:ehl:lserod:120294
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    File URL: http://eprints.lse.ac.uk/120294/
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    References listed on IDEAS

    as
    1. Omiros Papaspiliopoulos & Gareth O. Roberts, 2008. "Retrospective Markov chain Monte Carlo methods for Dirichlet process hierarchical models," Biometrika, Biometrika Trust, vol. 95(1), pages 169-186.
    2. Bassetti, Federico & Casarin, Roberto & Leisen, Fabrizio, 2014. "Beta-product dependent Pitman–Yor processes for Bayesian inference," Journal of Econometrics, Elsevier, vol. 180(1), pages 49-72.
    3. Ishwaran H. & James L. F, 2001. "Gibbs Sampling Methods for Stick Breaking Priors," Journal of the American Statistical Association, American Statistical Association, vol. 96, pages 161-173, March.
    4. François Caron & Emily B. Fox, 2017. "Sparse graphs using exchangeable random measures," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 79(5), pages 1295-1366, November.
    5. Dassios, Angelos & Zhang, Junyi, 2021. "Exact simulation of two-parameter Poisson-Dirichlet random variables," LSE Research Online Documents on Economics 107937, London School of Economics and Political Science, LSE Library.
    6. Stefano Favaro & Antonio Lijoi & Ramsés H. Mena & Igor Prünster, 2009. "Bayesian nonparametric inference for species variety with a two parameter Poisson-Dirichlet process prior," Carlo Alberto Notebooks 123, Collegio Carlo Alberto.
    7. Giulia Cereda & Fabio Corradi & Cecilia Viscardi, 2023. "Learning the two parameters of the Poisson–Dirichlet distribution with a forensic application," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 50(1), pages 120-141, March.
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    More about this item

    Keywords

    Bayesian non-parametric statistics; Markov chain Monte Carlo; mixture model; Pitman-Yor process; two-parameter Poisson-Dirichlet distribution;
    All these keywords.

    JEL classification:

    • C1 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General

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