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

作者：Lau John W^*

来源：Bernoulli, 2013, 19(5B): 2590-2626.

DOI：10.3150/12-BEJ467

• Bayesian non-parametric
• completely random measures
• Dirichlet process
• generalized gamma process
• Poisson Dirichlet process
• random probability measures
• tilting

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 Prunster (Ann. Statist. 31 (2003) 560-585), Lijoi, Mena and Prunster (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 Polya 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.

• 出版日期2013-11