The Annals of Statistics

Recursive Monte Carlo filters: Algorithms and theoretical analysis

Hans R. Künsch

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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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Ann. Statist. Volume 33, Number 5 (2005), 1983-2021.

First available in Project Euclid: 25 November 2005

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Mathematical Reviews number (MathSciNet)

Primary: 62M09: Non-Markovian processes: estimation
Secondary: 60G35: Signal detection and filtering [See also 62M20, 93E10, 93E11, 94Axx] 60J22: Computational methods in Markov chains [See also 65C40] 65C05: Monte Carlo methods

State space models hidden Markov models filtering and smoothing particle filters auxiliary variables sampling importance resampling central limit theorem


Künsch, Hans R. Recursive Monte Carlo filters: Algorithms and theoretical analysis. The Annals of Statistics 33 (2005), no. 5, 1983--2021. doi:10.1214/009053605000000426.

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