Recursive Monte Carlo filters: Algorithms and theoretical analysis

Details Recursive Monte Carlo filters: Algorithms and theoretical analysis Recursive Monte Carlo filters: Algorithms and theoretical analysis

2006-02-10

arxiv.org/abs/math/0602211v1

Annals of Statistics 2005, Vol. 33, No. 5, 1983-2021

Mathematics

Statistics Theory

Published at http://dx.doi.org/10.1214/009053605000000426 in the Annals of Statistics (http://www.imstat.org/aos/) by the Inst

Scientific paper

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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