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69
A tutorial on particle filters for online nonlinear/nonGaussian Bayesian tracking
 IEEE TRANSACTIONS ON SIGNAL PROCESSING
, 2002
"... Increasingly, for many application areas, it is becoming important to include elements of nonlinearity and nonGaussianity in order to model accurately the underlying dynamics of a physical system. Moreover, it is typically crucial to process data online as it arrives, both from the point of view o ..."
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Cited by 1137 (2 self)
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Increasingly, for many application areas, it is becoming important to include elements of nonlinearity and nonGaussianity in order to model accurately the underlying dynamics of a physical system. Moreover, it is typically crucial to process data online as it arrives, both from the point of view of storage costs as well as for rapid adaptation to changing signal characteristics. In this paper, we review both optimal and suboptimal Bayesian algorithms for nonlinear/nonGaussian tracking problems, with a focus on particle filters. Particle filters are sequential Monte Carlo methods based on point mass (or “particle”) representations of probability densities, which can be applied to any statespace model and which generalize the traditional Kalman filtering methods. Several variants of the particle filter such as SIR, ASIR, and RPF are introduced within a generic framework of the sequential importance sampling (SIS) algorithm. These are discussed and compared with the standard EKF through an illustrative example.
On Sequential Monte Carlo Sampling Methods for Bayesian Filtering
 STATISTICS AND COMPUTING
, 2000
"... In this article, we present an overview of methods for sequential simulation from posterior distributions. These methods are of particular interest in Bayesian filtering for discrete time dynamic models that are typically nonlinear and nonGaussian. A general importance sampling framework is develop ..."
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Cited by 660 (63 self)
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In this article, we present an overview of methods for sequential simulation from posterior distributions. These methods are of particular interest in Bayesian filtering for discrete time dynamic models that are typically nonlinear and nonGaussian. A general importance sampling framework is developed that unifies many of the methods which have been proposed over the last few decades in several different scientific disciplines. Novel extensions to the existing methods are also proposed. We show in particular how to incorporate local linearisation methods similar to those which have previously been employed in the deterministic filtering literature; these lead to very effective importance distributions. Furthermore we describe a method which uses RaoBlackwellisation in order to take advantage of the analytic structure present in some important classes of statespace models. In a final section we develop algorithms for prediction, smoothing and evaluation of the likelihood in dynamic models.
Particle Filters for State Estimation of Jump Markov Linear Systems
, 2001
"... Jump Markov linear systems (JMLS) are linear systems whose parameters evolve with time according to a finite state Markov chain. In this paper, our aim is to recursively compute optimal state estimates for this class of systems. We present efficient simulationbased algorithms called particle filter ..."
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Cited by 122 (11 self)
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Jump Markov linear systems (JMLS) are linear systems whose parameters evolve with time according to a finite state Markov chain. In this paper, our aim is to recursively compute optimal state estimates for this class of systems. We present efficient simulationbased algorithms called particle filters to solve the optimal filtering problem as well as the optimal fixedlag smoothing problem. Our algorithms combine sequential importance sampling, a selection scheme, and Markov chain Monte Carlo methods. They use several variance reduction methods to make the most of the statistical structure of JMLS. Computer
Statistical algorithms for models in state space using SsfPack 2.2
, 1999
"... This paper discusses and documents the algorithms of SsfPack 2.2. SsfPack is a suite of C routines for carrying out computations involving the statistical analysis of univariate and multivariate models in state space form. The emphasis is on documenting the link we have made to the Ox computing envi ..."
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Cited by 101 (27 self)
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This paper discusses and documents the algorithms of SsfPack 2.2. SsfPack is a suite of C routines for carrying out computations involving the statistical analysis of univariate and multivariate models in state space form. The emphasis is on documenting the link we have made to the Ox computing environment. SsfPack allows for a full range of different state space forms: from a simple timeinvariant model to a complicated timevarying model. Functions can be used which put standard models such as ARMA and cubic spline models in state space form. Basic functions are available for ltering, moment smoothing and simulation smoothing. Readytouse functions are provided for standard tasks such as likelihood evaluation, forecasting and signal extraction. We show that SsfPack can be easily used for implementing, tting and analysing Gaussian models relevant to many areas of econometrics and statistics. Some Gaussian illustrations are given.
A point process framework for relating neural spiking activity to spiking history, neural ensemble, and extrinsic covariate effects
 Journal of Neurophysiology
, 2005
"... Multiple factors simultaneously affect the spiking activity of individual neurons. Determining the effects and relative importance of these factors is a challenging problem in neurophysiology. We propose a statistical framework based on the point process likelihood function to relate a neuron’s spik ..."
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Cited by 96 (7 self)
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Multiple factors simultaneously affect the spiking activity of individual neurons. Determining the effects and relative importance of these factors is a challenging problem in neurophysiology. We propose a statistical framework based on the point process likelihood function to relate a neuron’s spiking probability to three typical covariates: the neuron’s own spiking history, concurrent ensemble activity and extrinsic covariates such as stimuli or behavior. The framework uses parametric models of the conditional intensity function to define a neuron’s spiking probability in terms of the covariates. The discrete time likelihood function for point processes is used to carry out model fitting and model analysis. We show that, by modeling the logarithm of the conditional intensity function as a linear combination of functions of the covariates, the discrete time point process likelihood function is readily analyzed in the generalized linear model (GLM) framework. We illustrate our approach for both GLM and nonGLM likelihood functions using simulated data and multivariate single unit
Monte Carlo smoothing for nonlinear time series
 JOURNAL OF THE AMERICAN STATISTICAL ASSOCIATION
, 2004
"... We develop methods for performing smoothing computations in general statespace models. The methods rely on a particle representation of the filtering distributions, and their evolution through time using sequential importance sampling and resampling ideas. In particular, novel techniques are pr ..."
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Cited by 95 (14 self)
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We develop methods for performing smoothing computations in general statespace models. The methods rely on a particle representation of the filtering distributions, and their evolution through time using sequential importance sampling and resampling ideas. In particular, novel techniques are presented for generation of sample realizations of historical state sequences. This is carried out in a forwardfiltering backwardsmoothing procedure which can be viewed as the nonlinear, nonGaussian counterpart of standard Kalman filterbased simulation smoothers in the linear Gaussian case. Convergence in the meansquared error sense of the smoothed trajectories is proved, showing the validity of our proposed method. The methods are tested in a substantial application for the processing of speech signals represented by a timevarying autoregression and parameterised in terms of timevarying partial correlation coe#cients, comparing the results of our algorithm with those from a simple smoother based upon the filtered trajectories.
Implementing approximate Bayesian inference for latent Gaussian models using integrated nested Laplace approximations: A manual for the inlaprogram
, 2008
"... Structured additive regression models are perhaps the most commonly used class of models in statistical applications. It includes, among others, (generalised) linear models, (generalised) additive models, smoothingspline models, statespace models, semiparametric regression, spatial and spatiotemp ..."
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Cited by 79 (16 self)
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Structured additive regression models are perhaps the most commonly used class of models in statistical applications. It includes, among others, (generalised) linear models, (generalised) additive models, smoothingspline models, statespace models, semiparametric regression, spatial and spatiotemporal models, logGaussian Coxprocesses, geostatistical and geoadditive models. In this paper we consider approximate Bayesian inference in a popular subset of structured additive regression models, latent Gaussian models, where the latent field is Gaussian, controlled by a few hyperparameters and with nonGaussian response variables. The posterior marginals are not available in closed form due to the nonGaussian response variables. For such models, Markov chain Monte Carlo methods can be implemented, but they are not without problems, both in terms of convergence and computational time. In some practical applications, the extent of these problems is such that Markov chain Monte Carlo is simply not an appropriate tool for routine analysis. We show that, by using an integrated nested Laplace approximation and its simplified version, we can directly compute very accurate approximations to the posterior marginals. The main benefit of these approximations
Estimating a StateSpace Model from Point Process Observations
, 2003
"... A widely used signal processing paradigm is the statespace model. The statespace model is defined by two equations: an observation equation that describes how the hidden state or latent process is observed and a state equation that defines the evolution of the process through time. Inspired by neu ..."
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Cited by 39 (4 self)
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A widely used signal processing paradigm is the statespace model. The statespace model is defined by two equations: an observation equation that describes how the hidden state or latent process is observed and a state equation that defines the evolution of the process through time. Inspired by neurophysiology experiments in which neural spiking activity is induced by an implicit (latent) stimulus, we develop an algorithm to estimate a statespace model observed through point process measurements. We represent the latent process modulating the neural spiking activity as a gaussian autoregressive model driven by an external stimulus. Given the latent process, neural spiking activity is characterized as a general point process defined by its conditional intensity function. We develop an approximate expectationmaximization (EM) algorithm to estimate the unobservable statespace process, its parameters, and the parameters of the point process. The EM algorithm combines a point process recursive nonlinear filter algorithm, the fixed interval smoothing algorithm, and the statespace covariance algorithm to compute the complete data log likelihood efficiently. We use a KolmogorovSmirnov test based on the timerescaling theorem to evaluate agreement between the model and point process data. We illustrate the model with two simulated data examples: an ensemble of Poisson neurons driven by a common stimulus and a single neuron whose conditional intensity function is approximated as a local Bernoulli process.
Dynamic Analyses of Information Encoding in Neural Ensembles
 Neural Computation
, 2004
"... Neural spike train decoding algorithms and techniques to compute Shannon
mutual information are important methods for analyzing how neural
systems represent biological signals.Decoding algorithms are also one of
several strategies being used to design controls for brainmachine interfaces.
Developin ..."
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Cited by 22 (1 self)
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Neural spike train decoding algorithms and techniques to compute Shannon
mutual information are important methods for analyzing how neural
systems represent biological signals.Decoding algorithms are also one of
several strategies being used to design controls for brainmachine interfaces.
Developing optimal strategies to desig n decoding algorithms and
compute mutual information are therefore important problems in computational
neuroscience. We present a general recursive lter decoding
algorithm based on a point process model of individual neuron spiking
activity and a linear stochastic statespace model of the biological signal.
We derive from the algorithm new instantaneous estimates of the entropy,
entropy rate, and the mutual information between the signal and
the ensemble spiking activity. We assess the accuracy of the algorithm
by computing, along with the decoding error, the true coverage probability
of the approximate 0.95 condence regions for the individual signal
estimates. We illustrate the new algorithm by reanalyzing the position
and ensemble neural spiking activity of CA1 hippocampal neurons from
two rats foraging in an open circular environment. We compare the performance
of this algorithm with a linear lter constructed by the widely
used reverse correlation method. The median decoding error for Animal
1 (2) during 10 minutes of open foraging was 5.9 (5.5) cm, the median
entropy was 6.9 (7.0) bits, the median information was 9.4 (9.4) bits, and
the true coverage probability for 0.95 condence regions was 0.67 (0.75)
using 34 (32) neurons. These ndings improve signicantly on our previous
results and suggest an integrated approach to dynamically reading
neural codes, measuring their properties, and quantifying the accuracy
with which encoded information is extracted.
Asymptotic Normality Of The Maximum Likelihood Estimator In State Space Models
 Ann. Statist
, 1998
"... State space models is a very general class of time series models capable of modeling dependent observations in a natural and interpretable way. Inference in such models have been studied by Bickel et al., who consider hidden Markov models, which are a special kind of state space models, and prove th ..."
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Cited by 20 (0 self)
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State space models is a very general class of time series models capable of modeling dependent observations in a natural and interpretable way. Inference in such models have been studied by Bickel et al., who consider hidden Markov models, which are a special kind of state space models, and prove that the maximum likelihood estimator is asymptotically normal under mild regularity conditions. In this paper we generalize the results of Bickel et al. to state space models, where the latent process is a continuous state Markov chain satisfying regularity conditions, which are fulfilled if the latent process takes values in a compact space. AMS 1991 subject classification. Primary 62F12; secondary 62M09. Keywords and phrases. State space models, asymptotic normality, maximum likelihood estimation. 1. Introduction. A state space model is a discrete time model for dependent observations fY k g, where the dependence is modelled via an unobserved Markov process fX k g such that, conditionall...