Recursive Monte Carlo filters: Algorithms and theoretical analysis

• 成果类型: Article
• 署名作者: Künsch, HR
• 署名单位: Swiss Federal Institutes of Technology Domain; ETH Zurich
• 刊物名称: ANNALS OF STATISTICS
• ISSN/ISSBN: 0090-5364
• DOI: 10.1214/009053605000000426
• 发表日期: 2005
• 页码: 1983-2021
• 关键词: stability; likelihood

摘要

Recursive Monte Carlo filters, also called particle filters, are a powerful tool to perform computations in general state space models. We discuss and compare the accept-reject version with the more common sampling importance resampling version of the algorithm. In particular, we show how auxiliary variable methods and stratification can be used in the accept-reject version, and we compare different resampling techniques. In a second part, we show laws of large numbers and a central limit theorem for these Monte Carlo filters by simple induction arguments that need only weak conditions. We also show that, under stronger conditions, the required sample size is independent of the length of the observed series.