Particle Smoothing in Continuous Time: A Fast Approach via Density Estimation

We consider the particle smoothing problem for state-space models where the transition density is not available in closed form, in particular for continuous-time, nonlinear models expressed via stochastic differential equations (SDEs). Conventional forward-backward and two-filter smoothers for the p...

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Bibliographic Details
Published in:IEEE transactions on signal processing 2011-03, Vol.59 (3), p.1017-1026
Main Authors: Murray, Lawrence, Storkey, Amos
Format: Article
Language:English
Subjects:
Applied sciences
Approximation methods
Biological and medical sciences
Biological system modeling
Computerized, statistical medical data processing and models in biomedicine
Continuous time
Density
density estimation
Detection, estimation, filtering, equalization, prediction
Differential equations
Discretization
Exact sciences and technology
Exact solutions
Information, signal and communications theory
Mathematical analysis
Mathematical model
Medical management aid. Diagnosis aid
Medical sciences
Miscellaneous
Numerical models
particle filter
Proposals
Runge-Kutta method
sequential Monte Carlo
Signal and communications theory
Signal processing
Signal processing algorithms
Signal, noise
Smoothing
Smoothing methods
state-space models
Stochastic processes
Telecommunications and information theory
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Summary:We consider the particle smoothing problem for state-space models where the transition density is not available in closed form, in particular for continuous-time, nonlinear models expressed via stochastic differential equations (SDEs). Conventional forward-backward and two-filter smoothers for the particle filter require a closed-form transition density, with the linear-Gaussian Euler-Maruyama discretization usually applied to the SDEs to achieve this. We develop a pair of variants using kernel density approximations to relieve the dependence, and in doing so enable use of faster and more accurate discretization schemes such as Runge-Kutta. In addition, the new methods admit arbitrary proposal distributions, providing an avenue to deal with degeneracy issues. Experimental results on a functional magnetic resonance imaging (fMRI) deconvolution task demonstrate comparable accuracy and significantly improved runtime over conventional techniques.
ISSN:1053-587X
1941-0476
DOI:10.1109/TSP.2010.2096418