Approximating predictive probabilities of Gibbs-type priors

Julyan Arbel 1 Stefano Favaro 2
1 MISTIS - Modelling and Inference of Complex and Structured Stochastic Systems
Inria Grenoble - Rhône-Alpes, LJK - Laboratoire Jean Kuntzmann, INPG - Institut National Polytechnique de Grenoble
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 for the mathematical tractability and interpretability of its predictive probabilities, which made it the natural candidate in several applications. Given a sample of size n, in this paper we show that the predictive probabilities of any Gibbs-type prior 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.
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Julyan Arbel, Stefano Favaro. Approximating predictive probabilities of Gibbs-type priors. 2018. 〈hal-01693333〉

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