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Recursive Monte Carlo filters: algorithms and theoretical analysis. (English) Zbl 1086.62106
Summary: 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.
62M20Prediction; filtering (statistics)
65C60Computational problems in statistics
62M09Non-Markovian processes: estimation
60F05Central limit and other weak theorems
60G35Signal detection and filtering (stochastic processes)
60J22Computational methods in Markov chains
65C05Monte Carlo methods