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35
Particle learning and smoothing
 Statistical Science
, 2010
"... In this paper we develop particle learning (PL) methods for state filtering, sequential parameter learning and smoothing in a general class of nonlinear state space models. The approach extends existing particle methods by incorporating static parameters and utilizing sufficient statistics for the p ..."
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Cited by 47 (15 self)
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In this paper we develop particle learning (PL) methods for state filtering, sequential parameter learning and smoothing in a general class of nonlinear state space models. The approach extends existing particle methods by incorporating static parameters and utilizing sufficient statistics for the parameters and/or the states as particles. State smoothing with parameter uncertainty is also solved as a by product of particle learning. In a number of applications, we show that our algorithms outperform existing particle filtering algorithms as well as MCMC.
Particle filtering in geophysical systems
, 2009
"... The application of particle filters in geophysical systems is reviewed. Some background on Bayesian filtering is provided, and the existing methods are discussed. The emphasis is on the methodology, and not so much on the applications themselves. It is shown that direct application of the basic part ..."
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Cited by 47 (1 self)
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The application of particle filters in geophysical systems is reviewed. Some background on Bayesian filtering is provided, and the existing methods are discussed. The emphasis is on the methodology, and not so much on the applications themselves. It is shown that direct application of the basic particle filter (i.e., importance sampling using the prior as the importance density) does not work in highdimensional systems, but several variants are shown to have potential. Approximations to the full problem that try to keep some aspects
Comparison of sequential data assimilation methods for the Kuramoto–Sivashinsky equation
, 2009
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Sequential Bayesian Filtering in Ocean Acoustics
, 2010
"... Sequential filtering provides an optimal framework for estimating and updating the unknown parameters of a system as data become available. Despite significant progress in the general theory and implementation, sequential Bayesian filters have been sparsely applied to ocean acoustics. The foundatio ..."
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Cited by 9 (7 self)
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Sequential filtering provides an optimal framework for estimating and updating the unknown parameters of a system as data become available. Despite significant progress in the general theory and implementation, sequential Bayesian filters have been sparsely applied to ocean acoustics. The foundations of sequential Bayesian filtering with emphasis on practical issues are first presented covering both Kalman and particle filter approaches. Filtering becomes a powerful estimation tool, employing prediction from previous estimates and updates stemming from physical and statistical models that relate acoustic measurements to the unknown parameters. Ocean acoustic applications are then discussed focusing on the estimation of environmental parameters evolving in time or space. The potential of particle filtering in ocean acoustics is further demonstrated through application to experimental data from the Shallow Water 2006 experiment.
Error bounds and normalizing constants for sequential Monte Carlo in high dimensions
, 2012
"... In a recent paper [3], the Sequential Monte Carlo (SMC) sampler introduced in [12, 19, 24] has been shown to be asymptotically stable in the dimension of the state space d at a cost that is only polynomial in d, when N the number of Monte Carlo samples, is fixed. More precisely, it has been establis ..."
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Cited by 8 (3 self)
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In a recent paper [3], the Sequential Monte Carlo (SMC) sampler introduced in [12, 19, 24] has been shown to be asymptotically stable in the dimension of the state space d at a cost that is only polynomial in d, when N the number of Monte Carlo samples, is fixed. More precisely, it has been established that the effective sample size (ESS) of the ensuing (approximate) sample and the Monte Carlo error of fixed dimensional marginals will converge as d grows, with a computational cost of O(Nd2). In the present work, further results on SMC methods in high dimensions are provided as d → ∞ and with N fixed. We deduce an explicit bound on the MonteCarlo error for estimates derived using the SMC sampler and the exact asymptotic relative L2error of the estimate of the normalizing constant. We also establish marginal propagation of chaos properties of the algorithm. The accuracy in highdimensions of some approximate SMCbased filtering schemes is also discussed.
Quantitative approximations of evolving probability measures and sequential Markov Chain Monte Carlo methods, Probability Theory and Related Fields, forthcoming
, 2012
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2012, Sequential Bayesian techniques applied to nonvolcanic tremor
 Journal of Geophysical Research
"... [1] This paper uses sequential Bayesian techniques such as particle filters and smoothers to track in time both the nonvolcanic tremor (NVT) source location on the plate interface and the angle of arrival via horizontal phase slowness. Sequential Bayesian techniques enable tracking of evolving geop ..."
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Cited by 4 (1 self)
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[1] This paper uses sequential Bayesian techniques such as particle filters and smoothers to track in time both the nonvolcanic tremor (NVT) source location on the plate interface and the angle of arrival via horizontal phase slowness. Sequential Bayesian techniques enable tracking of evolving geophysical parameters via sequential tremor observations. These techniques provide a formulation where the geophysical parameters that characterize dynamic, nonstationary processes are continuously estimated as new data become available. In addition to the optimal solution, particle filters and smoothers can calculate the underlying probability densities for the desired parameters, providing the uncertainties in the estimates. The tremor tracking has been performed using array beamforming. Here it is demonstrated that the uncertainties both in the NVT source location estimates and phase slowness estimates are reduced using a particle filter compared to just using a beamformer based inversion. Particle smoothers further reduces the uncertainty, giving the best performance out of the three methods used here.