Künsch, Hans R. Recursive Monte Carlo filters: algorithms and theoretical analysis. (English) Zbl 1086.62106 Ann. Stat. 33, No. 5, 1983-2021 (2005). Summary: 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. Cited in 1 ReviewCited in 59 Documents MSC: 62M20 Inference from stochastic processes and prediction 65C60 Computational problems in statistics (MSC2010) 62M09 Non-Markovian processes: estimation 60F05 Central limit and other weak theorems 60G35 Signal detection and filtering (aspects of stochastic processes) 60J22 Computational methods in Markov chains 65C05 Monte Carlo methods Keywords:state space models; hidden Markov models; filtering; smoothing; auxiliary variables; sampling importance resampling; central limit theorem × Cite Format Result Cite Review PDF Full Text: DOI arXiv References: [1] Atar, R. and Zeitouni, O. (1997). Exponential stability for nonlinear filtering. Ann. Inst. H. Poincaré Probab. Statist. 33 697-725. · Zbl 0888.93057 · doi:10.1016/S0246-0203(97)80110-0 [2] Carpenter, J., Clifford, P. and Fearnhead, P. (1999). Improved particle filter for nonlinear problems. IEE Proceedings F , Radar , Sonar and Navigation 146 2-7. [3] Chopin, N. (2004). 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