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32
Particle Filters for State Space Models With the Presence of Static Parameters
, 2002
"... In this paper particle filters for dynamic state space models handling unknown static parameters are discussed. The approach is based on marginalizing the static parameters out of the posterior distribution such that only the state vector needs to be considered. Such a marginalization can always be ..."
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Cited by 42 (0 self)
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In this paper particle filters for dynamic state space models handling unknown static parameters are discussed. The approach is based on marginalizing the static parameters out of the posterior distribution such that only the state vector needs to be considered. Such a marginalization can always be applied. However, realtime applications are only possible when the distribution of the unknown parameters given both observations and the hidden state vector depends on some lowdimensional sufficient statistics. Such sufficient statistics are present in many of the commonly used state space models. Marginalizing the static parameters avoids the problem of impoverishment which typically occur when static parameters are included as part of the state vector. The filters are tested on several different models, with promising results.
Parameter Estimation in General StateSpace Models using Particle Methods
 Annals of the Institute of Statistical Mathematics
, 2003
"... Particle filtering techniques are a set of powerful and versatile simulationbased methods to perform optimal state estimation in nonlinear nonGaussian statespace models. If the model includes fixed parameters, a standard technique to perform parameter estimation consists of extending the state wi ..."
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Cited by 40 (6 self)
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Particle filtering techniques are a set of powerful and versatile simulationbased methods to perform optimal state estimation in nonlinear nonGaussian statespace models. If the model includes fixed parameters, a standard technique to perform parameter estimation consists of extending the state with the parameter to transform the problem into an optimal filtering problem. However, this approach requires the use of special particle filtering techniques which su#er from several drawbacks. We consider here an alternative approach combining particle filtering and gradient algorithms to perform batch and recursive maximum likelihood parameter estimation. An original particle method is presented to implement these approaches and their # corresponding author.
Online ExpectationMaximization Type Algorithms For Parameter Estimation In General State Space Models
 Proc. IEEE Conf. ICASSP
, 2003
"... In this paper we present new online algorithms to estimate static parameters in nonlinear non Gaussian state space models. These algorithms rely on online ExpectationMaximization (EM) type algorithms. Contrary to standard Sequential Monte Carlo (SMC) methods recently proposed in the literature, the ..."
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Cited by 18 (2 self)
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In this paper we present new online algorithms to estimate static parameters in nonlinear non Gaussian state space models. These algorithms rely on online ExpectationMaximization (EM) type algorithms. Contrary to standard Sequential Monte Carlo (SMC) methods recently proposed in the literature, these algorithms do not degenerate over time.
Nonlinear and NonGaussian StateSpace Modeling with Monte Carlo Techniques: A Survey and Comparative Study
 In Rao, C., & Shanbhag, D. (Eds.), Handbook of Statistics
, 2000
"... Since Kitagawa (1987) and Kramer and Sorenson (1988) proposed the filter and smoother using numerical integration, nonlinear and/or nonGaussian state estimation problems have been developed. Numerical integration becomes extremely computerintensive in the higher dimensional cases of the state vect ..."
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Cited by 16 (4 self)
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Since Kitagawa (1987) and Kramer and Sorenson (1988) proposed the filter and smoother using numerical integration, nonlinear and/or nonGaussian state estimation problems have been developed. Numerical integration becomes extremely computerintensive in the higher dimensional cases of the state vector. Therefore, to improve the above problem, the sampling techniques such as Monte Carlo integration with importance sampling, resampling, rejection sampling, Markov chain Monte Carlo and so on are utilized, which can be easily applied to multidimensional cases. Thus, in the last decade, several kinds of nonlinear and nonGaussian filters and smoothers have been proposed using various computational techniques. The objective of this paper is to introduce the nonlinear and nonGaussian filters and smoothers which can be applied to any nonlinear and/or nonGaussian cases. Moreover, by Monte Carlo studies, each procedure is compared by the root mean square error criterion.
Time series analysis via mechanistic models. In review; prepublished at arxiv.org/abs/0802.0021
, 2008
"... The purpose of time series analysis via mechanistic models is to reconcile the known or hypothesized structure of a dynamical system with observations collected over time. We develop a framework for constructing nonlinear mechanistic models and carrying out inference. Our framework permits the consi ..."
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Cited by 13 (5 self)
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The purpose of time series analysis via mechanistic models is to reconcile the known or hypothesized structure of a dynamical system with observations collected over time. We develop a framework for constructing nonlinear mechanistic models and carrying out inference. Our framework permits the consideration of implicit dynamic models, meaning statistical models for stochastic dynamical systems which are specified by a simulation algorithm to generate sample paths. Inference procedures that operate on implicit models are said to have the plugandplay property. Our work builds on recently developed plugandplay inference methodology for partially observed Markov models. We introduce a class of implicitly specified Markov chains with stochastic transition rates, and we demonstrate its applicability to open problems in statistical inference for biological systems. As one example, these models are shown to give a fresh perspective on measles transmission dynamics. As a second example, we present a mechanistic analysis of cholera incidence data, involving interaction between two competing strains of the pathogen Vibrio cholerae. 1. Introduction. A
System Identification of Nonlinear StateSpace Models
, 2009
"... This paper is concerned with the parameter estimation of a relatively general class of nonlinear dynamic systems. A Maximum Likelihood (ML) framework is employed, and it is illustrated how an Expectation Maximisation (EM) algorithm may be used to compute these ML estimates. An essential ingredient i ..."
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Cited by 13 (6 self)
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This paper is concerned with the parameter estimation of a relatively general class of nonlinear dynamic systems. A Maximum Likelihood (ML) framework is employed, and it is illustrated how an Expectation Maximisation (EM) algorithm may be used to compute these ML estimates. An essential ingredient is the employment of socalled “particle smoothing” methods to compute required conditional expectations via a sequential Monte Carlo approach. Simulation examples demonstrate the efficacy of these techniques.
Population Monte Carlo algorithms
 In Transactions of the Japanese Society for Artificial Intelligence
, 2001
"... We give a crossdisciplinary survey on “population ” Monte Carlo algorithms. In these algorithms, a set of “walkers ” or “particles ” is used as a representation of a highdimensional vector. The computation is carried out by a random walk and split/deletion of these objects. The algorithms are deve ..."
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Cited by 11 (1 self)
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We give a crossdisciplinary survey on “population ” Monte Carlo algorithms. In these algorithms, a set of “walkers ” or “particles ” is used as a representation of a highdimensional vector. The computation is carried out by a random walk and split/deletion of these objects. The algorithms are developed in various fields in physics and statistical sciences and called by lots of different terms – “quantum Monte Carlo”, “transfermatrix Monte Carlo”, “Monte Carlo filter (particle filter)”,“sequential Monte Carlo ” and “PERM ” etc. Here we discuss them in a coherent framework. We also touch on related algorithms – genetic algorithms and annealed importance sampling.
Bayesian Hybrid ModelState Estimation Applied To Simultaneous Contact Formation Detection and Geometrical parameter Estimation
 INT. J. ROBOTICS RESEARCH
, 2005
"... This paper describes a Bayesian approach to model selection and state estimation for sensorbased robot tasks. The approach is illustrated with an example from autonomous compliant motion: simultaneous contact formation recognition and estimation of geometrical parameters. Previous research in t ..."
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Cited by 11 (5 self)
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This paper describes a Bayesian approach to model selection and state estimation for sensorbased robot tasks. The approach is illustrated with an example from autonomous compliant motion: simultaneous contact formation recognition and estimation of geometrical parameters. Previous research in this area mostly tries to solve one of the two subproblems, or treats the Contact Formation recognition problem separately, avoiding interaction between the Contact Formation detection and the geometrical parameter estimation problems. This limits the application area to task execution under small uncertainties. The problem shows similarities with the well known problems of data association in SLAM and model selection in global localisation. The paper discusses an experiment in which the performances of two well known Bayesian algorithms are compared with respect to this problem: Kalman Filter variants and Particle Filter solutions. This research allows the robot to handle large uncertainties during the execution of its sensorbased task through the estimation of a hybrid joint density of both unknown model and state variables.
A survey of sequential Monte Carlo methods for economics and finance
, 2009
"... This paper serves as an introduction and survey for economists to the field of sequential Monte Carlo methods which are also known as particle filters. Sequential Monte Carlo methods are simulation based algorithms used to compute the highdimensional and/or complex integrals that arise regularly in ..."
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Cited by 10 (1 self)
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This paper serves as an introduction and survey for economists to the field of sequential Monte Carlo methods which are also known as particle filters. Sequential Monte Carlo methods are simulation based algorithms used to compute the highdimensional and/or complex integrals that arise regularly in applied work. These methods are becoming increasingly popular in economics and finance; from dynamic stochastic general equilibrium models in macroeconomics to option pricing. The objective of this paper is to explain the basics of the methodology, provide references to the literature, and cover some of the theoretical results that justify the methods in practice.
Nonlinear filtering in discrete time: A particle convolution approach
, 2006
"... In this paper a new generation of particle filters for nonlinear discrete time processes is proposed, based on convolution kernel probability density estimation. The main advantage of this approach is to be free of the limitations encountered by the current particle filters when the likelihood of th ..."
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Cited by 10 (5 self)
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In this paper a new generation of particle filters for nonlinear discrete time processes is proposed, based on convolution kernel probability density estimation. The main advantage of this approach is to be free of the limitations encountered by the current particle filters when the likelihood of the observation variable is analytically unknown or when the observation noise is null or too small. To illustrate this convolution kernel approach the counterparts of the wellknown sequential importance sampling (SIS) and sequential importance samplingresampling (SISR) filters are considered and their stochastic convergence to the optimal filter under different modes are proved. Their good behaviour with respect to that of these filters is shown on several simulated case studies.