- Bayesian Anal.
- Volume 14, Number 4 (2019), 1201-1219.
Stochastic Approximations to the Pitman–Yor Process
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.
Bayesian Anal., Volume 14, Number 4 (2019), 1201-1219.
First available in Project Euclid: 11 June 2019
Permanent link to this document
Digital Object Identifier
Mathematical Reviews number (MathSciNet)
Zentralblatt MATH identifier
Primary: 62E20: Asymptotic distribution theory
Secondary: 62C10: Bayesian problems; characterization of Bayes procedures
Arbel, Julyan; De Blasi, Pierpaolo; Prünster, Igor. Stochastic Approximations to the Pitman–Yor Process. Bayesian Anal. 14 (2019), no. 4, 1201--1219. doi:10.1214/18-BA1127. https://projecteuclid.org/euclid.ba/1560240026
- Supplementary Material of “Stochastic Approximations to the Pitman–Yor Process”. Algorithm 3 for generating from a polynomially tilted positive stable random variable (in a separate document).