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Arbel, Julyan; De Blasi, Pierpaolo; Prünster, Igor

Stochastic approximations to the Pitman-Yor process. (English) Zbl 1435.62076

Bayesian Anal. 14, No. 4, 1201-1219 (2019).
Summary: 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 \(\epsilon\) 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 \(\epsilon\)-version of the Pitman-Yor process.

Cited in 8 Documents

MSC:

62E20 Asymptotic distribution theory in statistics
62C10 Bayesian problems; characterization of Bayes procedures
60G57 Random measures
62L20 Stochastic approximation

Keywords:

stochastic approximation; asymptotic distribution; Bayesian nonparametrics; Pitman-Yor process; random functionals; random probability measure; stopping rule

Software:

DPpackage
Cite Review PDF
Full Text: DOI arXiv Euclid

References:

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