On the posterior distribution of classes of random means

Abstract

The study of properties of mean functionals of random probability measures is an important area of research in the theory of Bayesian nonparametric statistics. Many results are now known for random Dirichlet means, but little is known, especially in terms of posterior distributions, for classes of priors beyond the Dirichlet process. In this paper, we consider normalized random measures with independent increments (NRMI's) and mixtures of NRMI. In both cases, we are able to provide exact expressions for the posterior distribution of their means. These general results are then specialized, leading to distributional results for means of two important particular cases of NRMI's and also of the two-parameter Poisson--Dirichlet process.

arXiv commentPublished in at http://dx.doi.org/10.3150/09-BEJ200 the Bernoulli (http://isi.cbs.nl/bernoulli/) by the International Statistical Institute/Bernoulli Society (http://isi.cbs.nl/BS/bshome.htm)

References in corpus (8)

• Means of a Dirichlet process and multiple hypergeometric functions
• Poisson calculus for spatial neutral to the right processes
• Normalized random measures driven by increasing additive processes
• Distributions of linear functionals of two parameter Poisson--Dirichlet random measures
• Large sample asymptotics for the two-parameter Poisson--Dirichlet process
• Functionals of Dirichlet processes, the Cifarelli-Regazzini identity and Beta-Gamma processes
• Boundary driven zero-range processes in random media
• Multiple integral representation for functionals of Dirichlet processes

Cited by in corpus (6)

• MCMC for Normalized Random Measure Mixture Models
• The two-parameter Poisson--Dirichlet point process
• Stochastic approximations to the Pitman-Yor process
• Nonparametric priors with full-range borrowing of information
• Perpetuity property of the Dirichlet distribution
• The Dirichlet curve of a probability in ${\mathbb{R}}^d$