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October 2005 Recursive Monte Carlo filters: Algorithms and theoretical analysis
Hans R. Künsch
Ann. Statist. 33(5): 1983-2021 (October 2005). DOI: 10.1214/009053605000000426


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.


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Hans R. Künsch. "Recursive Monte Carlo filters: Algorithms and theoretical analysis." Ann. Statist. 33 (5) 1983 - 2021, October 2005.


Published: October 2005
First available in Project Euclid: 25 November 2005

zbMATH: 1086.62106
MathSciNet: MR2211077
Digital Object Identifier: 10.1214/009053605000000426

Primary: 62M09
Secondary: 60G35 , 60J22 , 65C05

Keywords: auxiliary variables , central limit theorem , filtering and smoothing , Hidden Markov models , Particle filters , sampling importance resampling , state space models

Rights: Copyright © 2005 Institute of Mathematical Statistics


Vol.33 • No. 5 • October 2005
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