Sequentially interacting Markov chain Monte Carlo methods

Abstract

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.

Published in at http://dx.doi.org/10.1214/09-AOS747 the Annals of Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical Statistics (http://www.imstat.org)

References in corpus (3)

• On the ergodicity properties of some adaptive MCMC algorithms
• Equi-energy sampler with applications in statistical inference and statistical mechanics
• Interacting Markov chain Monte Carlo methods for solving nonlinear measure-valued equations

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• Interacting Markov chain Monte Carlo methods for solving nonlinear measure-valued equations
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• Adaptive Equi-Energy Sampler : Convergence and Illustration
• Small World MCMC with Tempering: Ergodicity and Spectral Gap