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Approximating Predictive Probabilities of Gibbs-Type Priors

Author

Listed:
  • Julyan Arbel

    (Université Grenoble Alpes, Inria, CNRS, LJK)

  • Stefano Favaro

    (University of Torino and Collegio Carlo Alberto)

Abstract

Gibbs-type random probability measures, or Gibbs-type priors, are arguably the most “natural” generalization of the celebrated Dirichlet prior. Among them the two parameter Poisson–Dirichlet prior certainly stands out in terms of mathematical tractability and interpretability of its predictive probabilities, which made it the natural candidate in a plethora of applications. Given a random sample of size n from an arbitrary Gibbs-type prior, we show that the corresponding predictive probabilities admit a large n approximation, with an error term vanishing as o(1/n), which maintains the same desirable features as the predictive probabilities of the two parameter Poisson–Dirichlet prior. Our result is illustrated through an extensive simulation study, which includes an application in the context of Bayesian nonparametric mixture modeling.

Suggested Citation

  • Julyan Arbel & Stefano Favaro, 2021. "Approximating Predictive Probabilities of Gibbs-Type Priors," Sankhya A: The Indian Journal of Statistics, Springer;Indian Statistical Institute, vol. 83(1), pages 496-519, February.
    • Handle: RePEc:spr:sankha:v:83:y:2021:i:1:d:10.1007_s13171-019-00187-y
    DOI: 10.1007/s13171-019-00187-y
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    References listed on IDEAS

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