On the posterior distribution of classes of random means
AbstractThe 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 known by now 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) and mixtures of NRMI: for 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 and also of the two parameter Poisson-Dirichlet process.
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Bibliographic InfoPaper provided by Collegio Carlo Alberto in its series Carlo Alberto Notebooks with number 134.
Length: 24 pages
Date of creation: 2009
Date of revision:
Bayesian Nonparametrics; Completely random measures; Means of random probability measures; Normalized random measures; Poisson-Dirichlet process; Posterior distribution; Species sampling models;
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- Antonio Lijoi & Igor Pruenster, 2009. "Distributional Properties of means of Random Probability Measures," ICER Working Papers - Applied Mathematics Series 22-2009, ICER - International Centre for Economic Research.
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