Dimensional Reduction for a Bayesian Filter

An adaptive strategy is proposed for reducing the number of unknowns in the calculation of a proposal distribution in a sequential Monte Carlo implementation of a Bayesian filter for nonlinear dynamics. The idea is to solve only in directions in which the dynamics is expanding, found adaptively; thi...

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Published inProceedings of the National Academy of Sciences - PNAS Vol. 101; no. 42; pp. 15013 - 15017
Main Authors Chorin, Alexandre J., Krause, Paul
Format Journal Article
LanguageEnglish
Published United States National Academy of Sciences 19.10.2004
National Acad Sciences
Subjects
Bayesian analysis
Burger equation
Eigenvalues
Eigenvectors
Filters
Mathematical vectors
Mathematics
Matrices
Monte Carlo simulation
Musical intervals
Nonlinear systems
Ordinary differential equations
Partial differential equations
Physical Sciences
Probability distributions
Statistical variance
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Summary:An adaptive strategy is proposed for reducing the number of unknowns in the calculation of a proposal distribution in a sequential Monte Carlo implementation of a Bayesian filter for nonlinear dynamics. The idea is to solve only in directions in which the dynamics is expanding, found adaptively; this strategy is suggested by earlier work on optimal prediction. The construction should be of value in data assimilation, for example, in geophysical fluid dynamics.
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Contributed by Alexandre J. Chorin, August 26, 2004
Abbreviation: KS, Kuramoto–Sivashinski.
To whom correspondence should be addressed. E-mail: chorin@math.berkeley.edu.
ISSN:0027-8424
1091-6490
DOI:10.1073/pnas.0406222101