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Stochastic approximations to the Pitman-Yor process

Julyan Arbel 1 Pierpaolo de Blasi 2 Igor Prünster 3
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 : In this paper we consider approximations to the popular Pitman-Yor process obtained by truncating the stick-breaking representation. The truncation is determined by a random stopping rule that achieves an almost sure control on the approximation error in total variation distance. We derive the asymptotic distribution of the random truncation point as the approximation error goes to zero in terms of a polynomially tilted positive stable random variable. The practical usefulness and effectiveness of this theoretical result is demonstrated by devising a sampling algorithm to approximate functionals of the-version of the Pitman-Yor process.
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Julyan Arbel, Pierpaolo de Blasi, Igor Prünster. Stochastic approximations to the Pitman-Yor process. Bayesian Analysis, International Society for Bayesian Analysis, 2019, 14 (3), pp.753-771. ⟨10.1214/18-BA1127⟩. ⟨hal-01950654⟩

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