Recursive Monte Carlo Filters:
Algorithms and Theoretical Analysis
Hans R. Künsch
January 2003
Abstract
Recursive Monte Carlo filters, also called particle filters, are a powerful
tool to perform the 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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