Sequentially interacting Markov chain Monte Carlo methods
Anthony Brockwell, Pierre Del Moral, Arnaud Doucet
The Annals of Statistics · 2010 · Volume 38 · Issue 6
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.
Keywords
60J05, 62F15, 65C05, Markov chain Monte Carlo, Normalizing constants, sequential Monte Carlo, state-space models
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