Distributions of linear functionals of two parameter Poisson-Dirichlet random measures

DOI10.1214/07-AAP462zbMath1138.60040arXivmath/0609488OpenAlexW2032738098MaRDI QIDQ2426604

Lancelot F. James, Igor Prünster, Antonio Lijoi

Publication date: 23 April 2008

Published in: The Annals of Applied Probability (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/math/0609488

zbMATH Keywords

occupation timesPoisson-Dirichlet processCauchy-Stieltjes transformBayesian nonparametric statisticsCifarelli-Regazzini identityfunctionals of random probability measures\(\alpha \)-stable subordinator

Mathematics Subject Classification ID

Infinitely divisible distributions; stable distributions (60E07) Processes with independent increments; Lévy processes (60G51) Bayesian inference (62F15) Random measures (60G57)

Related Items (18)

A two-parameter family of measure-valued diffusions with Poisson-Dirichlet stationary distributions ⋮ On the posterior distribution of classes of random means ⋮ The two-parameter Poisson-Dirichlet point process ⋮ On the stick-breaking representation of \(\sigma\)-stable Poisson-Kingman models ⋮ Specification of the Base Measure of Nonparametric Priors via Random Means ⋮ Optimal sample size for estimating the mean concentration of invasive organisms in ballast water via a semiparametric Bayesian analysis ⋮ Dirichlet mean identities and laws of a class of subordinators ⋮ Quantile clocks ⋮ Continuum tree asymptotics of discrete fragmentations and applications to phylogenetic mod\-els ⋮ A Monte Carlo Markov chain algorithm for a class of mixture time series models ⋮ Distributional properties of means of random probability measures ⋮ Some diffusion processes associated with two parameter Poisson-Dirichlet distribution and Dirichlet process ⋮ A reversible allelic partition process and Pitman sampling formula ⋮ Lamperti-type laws ⋮ On a class of \(\sigma \)-stable Poisson-Kingman models and an effective marginalized sampler ⋮ Ranked masses in two-parameter Fleming–Viot diffusions ⋮ Subordinated Brownian motion: last time the process reaches its supremum ⋮ On simulation and properties of the stable law

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