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Construction of Jointly Distributed Random Samples Drawn from the Beta Two-Parameter Process

Author

Listed:
  • Hassan Akell

    (Faculty of Mathematics & Statistics)

  • Farkhondeh-Alsadat Sajadi

    (Faculty of Mathematics & Statistics)

  • Iraj Kazemi

    (Faculty of Mathematics & Statistics)

Abstract

Several extensions of the familiar Dirichlet process have been widely investigated to nonparametric Bayesian model fittings parallel with appealing subsequent studies on their particular properties. This paper presents an explicit form for the joint distribution of drawn samples from the beta two-parameter process using an extension of stick-breaking construction. In particular, we evaluate the joint distribution of a random sequence for a specific process case and compare it with the Blackwell-MacQueen process. We obtain moments of the beta two-parameter process and present a formula for the number of distinct values in the sample. We establish the precision ratio and explore its effect on this number.

Suggested Citation

  • Hassan Akell & Farkhondeh-Alsadat Sajadi & Iraj Kazemi, 2023. "Construction of Jointly Distributed Random Samples Drawn from the Beta Two-Parameter Process," Methodology and Computing in Applied Probability, Springer, vol. 25(3), pages 1-12, September.
    • Handle: RePEc:spr:metcap:v:25:y:2023:i:3:d:10.1007_s11009-023-10046-x
    DOI: 10.1007/s11009-023-10046-x
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    References listed on IDEAS

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    1. Felix Heinzl & Ludwig Fahrmeir & Thomas Kneib, 2012. "Additive mixed models with Dirichlet process mixture and P-spline priors," AStA Advances in Statistical Analysis, Springer;German Statistical Society, vol. 96(1), pages 47-68, January.
    2. Antonio Lijoi & Ramsés Mena & Igor Prünster, 2005. "Bayesian Nonparametric Analysis for a Generalized Dirichlet Process Prior," Statistical Inference for Stochastic Processes, Springer, vol. 8(3), pages 283-309, December.
    3. Bhattacharya, Indrabati & Ghosal, Subhashis, 2021. "Bayesian multivariate quantile regression using Dependent Dirichlet Process prior," Journal of Multivariate Analysis, Elsevier, vol. 185(C).
    4. Teh, Yee Whye & Jordan, Michael I. & Beal, Matthew J. & Blei, David M., 2006. "Hierarchical Dirichlet Processes," Journal of the American Statistical Association, American Statistical Association, vol. 101, pages 1566-1581, December.
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