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August 2012 A class of measure-valued Markov chains and Bayesian nonparametrics
Stefano Favaro, Alessandra Guglielmi, Stephen G. Walker
Bernoulli 18(3): 1002-1030 (August 2012). DOI: 10.3150/11-BEJ356


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.


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Stefano Favaro. Alessandra Guglielmi. Stephen G. Walker. "A class of measure-valued Markov chains and Bayesian nonparametrics." Bernoulli 18 (3) 1002 - 1030, August 2012.


Published: August 2012
First available in Project Euclid: 28 June 2012

zbMATH: 1243.62064
MathSciNet: MR2948910
Digital Object Identifier: 10.3150/11-BEJ356

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

Rights: Copyright © 2012 Bernoulli Society for Mathematical Statistics and Probability


Vol.18 • No. 3 • August 2012
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