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Lookahead strategies for sequential Monte Carlo. (English) Zbl 1332.62144

Summary: Based on the principles of importance sampling and resampling, sequential Monte Carlo (SMC) encompasses a large set of powerful techniques dealing with complex stochastic dynamic systems. Many of these systems possess strong memory, with which future information can help sharpen the inference about the current state. By providing theoretical justification of several existing algorithms and introducing several new ones, we study systematically how to construct efficient SMC algorithms to take advantage of the “future” information without creating a substantially high computational burden. The main idea is to allow for lookahead in the Monte Carlo process so that future information can be utilized in weighting and generating Monte Carlo samples, or resampling from samples of the current state.

MSC:

62G09 Nonparametric statistical resampling methods
65C05 Monte Carlo methods
65C40 Numerical analysis or methods applied to Markov chains
62M10 Time series, auto-correlation, regression, etc. in statistics (GARCH)
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