A class of measure-valued Markov chains and Bayesian nonparametrics
Stefano Favaro, Alessandra Guglielmi, and Stephen G. Walker
Source: Bernoulli Volume 18, Number 3
(2012), 1002-1030.
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.
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Keywords: Bayesian nonparametrics; Dirichlet process; exchangeable sequences; linear functionals of Dirichlet processes; measure-valued Markov chains; mixture modeling; Pólya urn scheme; random probability measures
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Digital Object Identifier: doi:10.3150/11-BEJ356
Zentralblatt MATH identifier: 06064471
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