Open Access
December 2010 Sequentially interacting Markov chain Monte Carlo methods
Anthony Brockwell, Pierre Del Moral, Arnaud Doucet
Ann. Statist. 38(6): 3387-3411 (December 2010). DOI: 10.1214/09-AOS747


Sequential Monte Carlo (SMC) is a methodology for sampling approximately from a sequence of probability distributions of increasing dimension and estimating their normalizing constants. We propose here an alternative methodology named Sequentially Interacting Markov Chain Monte Carlo (SIMCMC). SIMCMC methods work by generating interacting non-Markovian sequences which behave asymptotically like independent Metropolis–Hastings (MH) Markov chains with the desired limiting distributions. Contrary to SMC, SIMCMC allows us to iteratively improve our estimates in an MCMC-like fashion. We establish convergence results under realistic verifiable assumptions and demonstrate its performance on several examples arising in Bayesian time series analysis.


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Anthony Brockwell. Pierre Del Moral. Arnaud Doucet. "Sequentially interacting Markov chain Monte Carlo methods." Ann. Statist. 38 (6) 3387 - 3411, December 2010.


Published: December 2010
First available in Project Euclid: 30 November 2010

zbMATH: 1251.65002
MathSciNet: MR2766856
Digital Object Identifier: 10.1214/09-AOS747

Primary: 60J05 , 65C05
Secondary: 62F15

Keywords: Markov chain Monte Carlo , Normalizing constants , sequential Monte Carlo , state-space models

Rights: Copyright © 2010 Institute of Mathematical Statistics

Vol.38 • No. 6 • December 2010
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