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April 2013 Bayesian nonparametric analysis of reversible Markov chains
Sergio Bacallado, Stefano Favaro, Lorenzo Trippa
Ann. Statist. 41(2): 870-896 (April 2013). DOI: 10.1214/13-AOS1102


We introduce a three-parameter random walk with reinforcement, called the $(\theta,\alpha,\beta)$ scheme, which generalizes the linearly edge reinforced random walk to uncountable spaces. The parameter $\beta$ smoothly tunes the $(\theta,\alpha,\beta)$ scheme between this edge reinforced random walk and the classical exchangeable two-parameter Hoppe urn scheme, while the parameters $\alpha$ and $\theta$ modulate how many states are typically visited. Resorting to de Finetti’s theorem for Markov chains, we use the $(\theta,\alpha,\beta)$ scheme to define a nonparametric prior for Bayesian analysis of reversible Markov chains. The prior is applied in Bayesian nonparametric inference for species sampling problems with data generated from a reversible Markov chain with an unknown transition kernel. As a real example, we analyze data from molecular dynamics simulations of protein folding.


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Sergio Bacallado. Stefano Favaro. Lorenzo Trippa. "Bayesian nonparametric analysis of reversible Markov chains." Ann. Statist. 41 (2) 870 - 896, April 2013.


Published: April 2013
First available in Project Euclid: 29 May 2013

zbMATH: 1360.62481
MathSciNet: MR3099124
Digital Object Identifier: 10.1214/13-AOS1102

Primary: 62M02
Secondary: 62C10

Keywords: Bayesian nonparametrics , mixtures of Markov chains , molecular dynamics , reinforced random walks , reversibility , Species sampling , two-parameter Hoppe urn

Rights: Copyright © 2013 Institute of Mathematical Statistics


Vol.41 • No. 2 • April 2013
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