The Annals of Statistics
- Ann. Statist.
- Volume 33, Number 5 (2005), 1983-2021.
Recursive Monte Carlo filters: Algorithms and theoretical analysis
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.
Ann. Statist. Volume 33, Number 5 (2005), 1983-2021.
First available in Project Euclid: 25 November 2005
Permanent link to this document
Digital Object Identifier
Mathematical Reviews number (MathSciNet)
Zentralblatt MATH identifier
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
Künsch, Hans R. Recursive Monte Carlo filters: Algorithms and theoretical analysis. Ann. Statist. 33 (2005), no. 5, 1983--2021. doi:10.1214/009053605000000426. https://projecteuclid.org/euclid.aos/1132936554