Distributional properties of means of random probability measures
AbstractThe present paper provides a review of the results concerning distributional properties of means of random probability measures. Our interest in this topic has originated from inferential problems in Bayesian Nonparametrics. Nonetheless, it is worth noting that these random quantities play an important role in seemingly unrelated areas of research. In fact, there is a wealth of contributions both in the statistics and in the probability literature that we try to summarize in a unified framework. Particular attention is devoted to means of the Dirichlet process given the relevance of the Dirichlet process in Bayesian Nonparametrics. We then present a number of recent contributions concerning means of more general random probability measures and highlight connections with the moment problem, combinatorics, special functions, excursions of stochastic processes and statistical physics.
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Bibliographic InfoPaper provided by Collegio Carlo Alberto in its series Carlo Alberto Notebooks with number 120.
Length: 51 pages
Date of creation: 2009
Date of revision:
Bayesian Nonparametrics; Completely random measures; Cifarelli-Regazzini identity; Dirichlet process; Functionals of random probability measures; Generalized Stieltjes transform; Neutral to the right processes; Normalized random measures; Posterior distribution; Random means; Random probability measure; Two-parameter Poisson-Dirichlet process;
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