SEQUENTIALLY INTERACTING MARKOV CHAIN MONTE CARLO METHODS

• 成果类型: Article
• 署名作者: Brockwell, Anthony; Del Moral, Pierre; Doucet, Arnaud
• 署名单位: Carnegie Mellon University; University of British Columbia; University of British Columbia
• 刊物名称: ANNALS OF STATISTICS
• ISSN/ISSBN: 0090-5364
• DOI: 10.1214/09-AOS747
• 发表日期: 2010
• 页码: 3387-3411
• 关键词: particle filter; simulation; CONVERGENCE; ergodicity; inference

摘要

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.