Stochastic approximations to the Pitman-Yor process

DOI10.1214/18-BA1127zbMath1435.62076arXiv1806.10867MaRDI QIDQ2290710

Igor Prünster, Pierpaolo De Blasi, Julyan Arbel

Publication date: 29 January 2020

Published in: Bayesian Analysis (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1806.10867

zbMATH Keywords

asymptotic distributionstochastic approximationBayesian nonparametricsstopping rulePitman-Yor processrandom probability measurerandom functionals

Mathematics Subject Classification ID

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

Related Items (7)

Importance conditional sampling for Pitman-Yor mixtures ⋮ On quasi-infinitely divisible random measures ⋮ Bayesian Nonparametric Panel Markov-Switching GARCH Models ⋮ Sampling hierarchies of discrete random structures ⋮ A simple proof of Pitman-Yor's Chinese restaurant process from its stick-breaking representation ⋮ Stochastic approximations to the Pitman-Yor process ⋮ Bernstein-von Mises theorem for the Pitman-Yor process of nonnegative type

Uses Software

• DPpackage

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Beta-product dependent Pitman-Yor processes for Bayesian inference
• Bayesian semiparametric inference for multivariate doubly-interval-censored data
• On the posterior distribution of classes of random means
• The Bernoulli sieve revisited
• Notes on the occupancy problem with infinitely many boxes: general asymptotics and power laws
• Regeneration in random combinatorial structures
• Size-biased sampling of Poisson point processes and excursions
• The two-parameter Poisson-Dirichlet distribution derived from a stable subordinator
• The Bernoulli sieve
• Exchangeable and partially exchangeable random partitions
• On simulations from the two-parameter Poisson-Dirichlet process and the normalized inverse-Gaussian process
• Stochastic approximations to the Pitman-Yor process
• Combinatorial stochastic processes. Ecole d'Eté de Probabilités de Saint-Flour XXXII -- 2002.
• A Bayesian analysis of some nonparametric problems
• Extremes and gaps in sampling from a GEM random discrete distribution
• The asymptotic expansion of a ratio of gamma functions
• Heterogeneous reciprocal graphical models
• The Representation of Partition Structures
• Bayesian Nonparametric Estimation of the Probability of Discovering New Species
• Approximating distributions of random functionals of Ferguson-Dirichlet priors
• Random variate generation for exponentially and polynomially tilted stable distributions
• Bayesian Non-Parametric Inference for Species Variety with a Two-Parameter Poisson–Dirichlet Process Prior
• Exact and approximate sum representations for the Dirichlet process
• Gibbs Sampling Methods for Stick-Breaking Priors
• Some issues in nonparametric Bayesian modeling using species sampling models
• On the Pitman–Yor process with spike and slab base measure
• Fundamentals of Nonparametric Bayesian Inference
• Probability: A Graduate Course

This page was built for publication: Stochastic approximations to the Pitman-Yor process