Bernoulli

  • Bernoulli
  • Volume 19, Number 5B (2013), 2590-2626.

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

John W. Lau

Full-text: Open access

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.

Article information

Source
Bernoulli, Volume 19, Number 5B (2013), 2590-2626.

Dates
First available in Project Euclid: 3 December 2013

Permanent link to this document
https://projecteuclid.org/euclid.bj/1386078614

Digital Object Identifier
doi:10.3150/12-BEJ467

Mathematical Reviews number (MathSciNet)
MR3160565

Zentralblatt MATH identifier
06254573

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

Citation

Lau, John W. A conjugate class of random probability measures based on tilting and with its posterior analysis. Bernoulli 19 (2013), no. 5B, 2590--2626. doi:10.3150/12-BEJ467. https://projecteuclid.org/euclid.bj/1386078614


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