Approximating Predictive Probabilities of Gibbs-Type Priors

Julyan Arbel () and Stefano Favaro ()
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Julyan Arbel: Université Grenoble Alpes, Inria, CNRS, LJK
Stefano Favaro: University of Torino and Collegio Carlo Alberto

Sankhya A: The Indian Journal of Statistics, 2021, vol. 83, issue 1, No 21, 496-519

Abstract: 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.

Keywords: Bayesian nonparametrics; First and second order asymptotic approximations; Gibbs-type prior; Predictive probabilities; Mixture modeling; Normalized generalized Gamma prior; Two parameter Poisson–Dirichlet prior; Primary 62F15; Secondary 62G99 (search for similar items in EconPapers)
Date: 2021
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DOI: 10.1007/s13171-019-00187-y

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