Bernoulli

  • Bernoulli
  • Volume 18, Number 3 (2012), 1002-1030.

A class of measure-valued Markov chains and Bayesian nonparametrics

Stefano Favaro, Alessandra Guglielmi, and Stephen G. Walker

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Abstract

Measure-valued Markov chains have raised interest in Bayesian nonparametrics since the seminal paper by (Math. Proc. Cambridge Philos. Soc. 105 (1989) 579–585) where a Markov chain having the law of the Dirichlet process as unique invariant measure has been introduced. In the present paper, we propose and investigate a new class of measure-valued Markov chains defined via exchangeable sequences of random variables. Asymptotic properties for this new class are derived and applications related to Bayesian nonparametric mixture modeling, and to a generalization of the Markov chain proposed by (Math. Proc. Cambridge Philos. Soc. 105 (1989) 579–585), are discussed. These results and their applications highlight once again the interplay between Bayesian nonparametrics and the theory of measure-valued Markov chains.

Article information

Source
Bernoulli, Volume 18, Number 3 (2012), 1002-1030.

Dates
First available in Project Euclid: 28 June 2012

Permanent link to this document
https://projecteuclid.org/euclid.bj/1340887011

Digital Object Identifier
doi:10.3150/11-BEJ356

Mathematical Reviews number (MathSciNet)
MR2948910

Zentralblatt MATH identifier
1243.62064

Keywords
Bayesian nonparametrics Dirichlet process exchangeable sequences linear functionals of Dirichlet processes measure-valued Markov chains mixture modeling Pólya urn scheme random probability measures

Citation

Favaro, Stefano; Guglielmi, Alessandra; Walker, Stephen G. A class of measure-valued Markov chains and Bayesian nonparametrics. Bernoulli 18 (2012), no. 3, 1002--1030. doi:10.3150/11-BEJ356. https://projecteuclid.org/euclid.bj/1340887011


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