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A tutorial on particle filtering and smoothing: fifteen years later
 OXFORD HANDBOOK OF NONLINEAR FILTERING
, 2011
"... Optimal estimation problems for nonlinear nonGaussian statespace models do not typically admit analytic solutions. Since their introduction in 1993, particle filtering methods have become a very popular class of algorithms to solve these estimation problems numerically in an online manner, i.e. r ..."
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Cited by 141 (12 self)
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Optimal estimation problems for nonlinear nonGaussian statespace models do not typically admit analytic solutions. Since their introduction in 1993, particle filtering methods have become a very popular class of algorithms to solve these estimation problems numerically in an online manner, i.e. recursively as observations become available, and are now routinely used in fields as diverse as computer vision, econometrics, robotics and navigation. The objective of this tutorial is to provide a complete, uptodate survey of this field as of 2008. Basic and advanced particle methods for filtering as well as smoothing are presented.
A sequential smoothing algorithm with linear computational cost
, 2008
"... In this paper we propose a new particle smoother that has a computational complexity of O(N), where N is the number of particles. This compares favourably with the O(N 2) computational cost of most smoothers and will result in faster rates of convergence for fixed computational cost. The new method ..."
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Cited by 23 (1 self)
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In this paper we propose a new particle smoother that has a computational complexity of O(N), where N is the number of particles. This compares favourably with the O(N 2) computational cost of most smoothers and will result in faster rates of convergence for fixed computational cost. The new method also overcomes some of the degeneracy problems we identify in many existing algorithms. Through simulation studies we show that substantial gains in efficiency are obtained for practical amounts of computational cost. It is shown both through these simulation studies, and on the analysis of an athletics data set, that our new method also substantially outperforms the simple FilterSmoother (the only other smoother with computational cost that is linear in the number of particles). 1
Bayesian parameter inference for stochastic biochemical network models using particle mcmc
 Interface Focus
, 2011
"... Computational systems biology is concerned with the development of detailed mechanistic models of biological processes. Such models are often stochastic and analytically intractable, containing uncertain parameters which must be estimated from time course data. Inference for the parameters of comple ..."
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Cited by 21 (4 self)
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Computational systems biology is concerned with the development of detailed mechanistic models of biological processes. Such models are often stochastic and analytically intractable, containing uncertain parameters which must be estimated from time course data. Inference for the parameters of complex nonlinear multivariate stochastic process models is a challenging problem, but algorithms based on particle MCMC turn out to be a very effective computationally intensive approach to the problem. 1
2008: Adaptive methods for sequential importance sampling with application to state space models
 Statistics and Computing
"... Abstract. In this paper we discuss new adaptive proposal strategies for sequential Monte Carlo algorithms—also known as particle filters—relying on criteria evaluating the quality of the proposed particles. The choice of the proposal distribution is a major concern and can dramatically influence the ..."
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Cited by 17 (3 self)
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Abstract. In this paper we discuss new adaptive proposal strategies for sequential Monte Carlo algorithms—also known as particle filters—relying on criteria evaluating the quality of the proposed particles. The choice of the proposal distribution is a major concern and can dramatically influence the quality of the estimates. Thus, we show how the longused coefficient of variation (suggested by Kong et al. (1994)) of the weights can be used for estimating the chisquare distance between the target and instrumental distributions of the auxiliary particle filter. As a byproduct of this analysis we obtain an auxiliary adjustment multiplier weight type for which this chisquare distance is minimal. Moreover, we establish an empirical estimate of linear complexity of the KullbackLeibler divergence between the involved distributions. Guided by these results, we discuss adaptive designing of the particle filter proposal distribution and illustrate the methods on a numerical example. 1.
Efficient Bayesian analysis of multiple changepoint models with dependence across segments
, 2010
"... We consider Bayesian analysis of a class of multiple changepoint models. While there are a variety of efficient ways to analyse these models if the parameters associated with each segment are independent, there are few general approaches for models where the parameters are dependent. Under the assu ..."
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Cited by 4 (0 self)
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We consider Bayesian analysis of a class of multiple changepoint models. While there are a variety of efficient ways to analyse these models if the parameters associated with each segment are independent, there are few general approaches for models where the parameters are dependent. Under the assumption that the dependence is Markov, we propose an efficient online algorithm for sampling from an approximation to the posterior distribution of the number and position of the changepoints. In a simulation study, we show that the approximation introduced is negligible. We illustrate the power of our approach through fitting piecewise polynomial models to data, under a model which allows for either continuity or discontinuity of the underlying curve at each changepoint. This method is competitive with, or outperforms, other methods for inferring curves from noisy data; and uniquely it allows for inference of the locations of discontinuities in the underlying curve.
Markov and semiMarkov switching linear mixed models for identifying forest tree growth components
 n o 6618, INRIA, 2008, http://wwwsop.inria.fr/virtualplants/Publications/2008/CGLT08. Virtual Plants 29
"... 2 Markov and semiMarkov switching linear mixed models used to identify forest tree growth components ..."
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Cited by 4 (0 self)
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2 Markov and semiMarkov switching linear mixed models used to identify forest tree growth components
Particle Filtering and Smoothing: Fifteen years Later, Handbook of Nonlinear Filtering
"... Optimal estimation problems for nonlinear nonGaussian statespace models do not typically admit finitedimensional solutions. Since their introduction in 1993, particle filtering methods have become a very popular class of algorithms to solve these estimation problems numerically in an online mann ..."
Abstract

Cited by 3 (0 self)
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Optimal estimation problems for nonlinear nonGaussian statespace models do not typically admit finitedimensional solutions. Since their introduction in 1993, particle filtering methods have become a very popular class of algorithms to solve these estimation problems numerically in an online manner (that is, recursively, as observations become available), and are now routinely used in fields as diverse as computer vision, econometrics, robotics and navigation. The objective of this tutorial is to provide a complete, uptodate survey of this field as of 2008. Basic and advanced particle methods for filtering as well as smoothing are presented.
Optimal SIR algorithm vs. fully adapted auxiliary particle filter: a matter of conditional independence
 in: Proc. IEEE ICASSP
, 2011
"... Particle filters (PF) and auxiliary particle filters (APF) are widely used sequential Monte Carlo (SMC) techniques. In this paper we comparatively analyse the Sampling Importance Resampling (SIR) PF with optimal conditional importance distribution (CID) and the fully adapted APF (FAAPF). Both algor ..."
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Cited by 2 (1 self)
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Particle filters (PF) and auxiliary particle filters (APF) are widely used sequential Monte Carlo (SMC) techniques. In this paper we comparatively analyse the Sampling Importance Resampling (SIR) PF with optimal conditional importance distribution (CID) and the fully adapted APF (FAAPF). Both algorithms share the same Sampling (S), Weighting (W) and Resampling (R) steps, and only differ in the order in which these steps are performed. The order of the operations is not unsignificant: starting at time n − 1 from a common set of particles, we show that one single updated particle at time n will marginally be sampled in both algorithms from the same probability density function (pdf), but as a whole the full set of particles will be conditionally independent if created by the FAAPF algorithm, and dependent if created by the SIR algorithm, which results in support degeneracy.