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Permanent link (DOI): https://doi.org/10.7939/R39S1KN7W
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Resampled Branching Particle Filters Open Access
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Kouritzin, Michael A.
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Central Limit Theorem
Exchangeable Random Variables
Bayesian Model Selection
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A large class of discrete-time branching particle ﬁlters with Bayesian model selection ca-pabilities and eﬀective resampling is introduced in algorithmic form, shown empirically to outperform the popular bootstrap algorithm and analyzed mathematically. The particles interact weakly in the resampling procedure. The weighted particle ﬁlter, which has no resampling, and the fully-resampled branching particle ﬁlter are included in the class as extreme points. Each particle ﬁlter in the class is coupled to a McKean-Vlasov particle system, corresponding to a reduced, unimplementable particle ﬁlter, for which Marcinkiewicz strong laws of large numbers (Mllns) and the central limit theorem (clt) can be written down. Coupling arguments are used to show the reduced system can be used to predict performance of the particle ﬁlter and to transfer the Mllns to the original weakly-interacting particle ﬁlter. This clt is also shown transferable when extra particles are used.
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- © 2015 Michael A. Kouritzin. This version of this article is open access and can be downloaded and shared. The original author and source must be cited.
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