A conjugate class of random probability measures based on tilting and with its posterior analysis

    Research output: Contribution to journalArticle

    1 Citation (Scopus)

    Abstract

    This article constructs a class of random probability measures based on exponentially and polynomially tilting operated on the laws of completely random measures. The class is proved to be conjugate in that it covers both prior and posterior random probability measures in the Bayesian sense. Moreover, the class includes some common and widely used random probability measures, the normalized completely random measures (James (Poisson process partition calculus with applications to exchangeable models and Bayesian nonparametrics (2002) Preprint), Regazzini, Lijoi and Prünster (Ann. Statist. 31 (2003) 560-585), Lijoi, Mena and Prünster (J. Amer. Statist. Assoc. 100 (2005) 1278-1291)) and the Poisson-Dirichlet process (Pitman and Yor (Ann. Probab. 25 (1997) 855-900), Ishwaran and James (J. Amer. Statist. Assoc. 96 (2001) 161-173), Pitman (In Science and Statistics: A Festschrift for Terry Speed (2003) 1-34 IMS)), in a single construction. We describe an augmented version of the Blackwell-MacQueen Pólya urn sampling scheme (Blackwell and MacQueen (Ann. Statist. 1 (1973) 353-355)) that simplifies implementation and provide a simulation study for approximating the probabilities of partition sizes. © 2013 ISI/BS.
    Original languageEnglish
    Pages (from-to)2590-2626
    JournalBernoulli
    Volume19
    Issue number5 B
    DOIs
    Publication statusPublished - 2013

    Fingerprint Dive into the research topics of 'A conjugate class of random probability measures based on tilting and with its posterior analysis'. Together they form a unique fingerprint.

    Cite this