Results 1  10
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12
The Unscented Particle Filter
, 2000
"... In this paper, we propose a new particle filter based on sequential importance sampling. The algorithm uses a bank of unscented filters to obtain the importance proposal distribution. This proposal has two very "nice" properties. Firstly, it makes efficient use of the latest available info ..."
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Cited by 163 (9 self)
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In this paper, we propose a new particle filter based on sequential importance sampling. The algorithm uses a bank of unscented filters to obtain the importance proposal distribution. This proposal has two very "nice" properties. Firstly, it makes efficient use of the latest available information and, secondly, it can have heavy tails. As a result, we find that the algorithm outperforms standard particle filtering and other nonlinear filtering methods very substantially. This experimental finding is in agreement with the theoretical convergence proof for the algorithm. The algorithm also includes resampling and (possibly) Markov chain Monte Carlo (MCMC) steps.
Tracking Multiple Objects with Particle Filtering
, 2000
"... We address the problem of multitarget tracking encountered in many situations in signal or image processing. We consider stochastic dynamic systems detected by observation processes. The difficulty lies on the fact that the estimation of the states requires the assignment of the observations to the ..."
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Cited by 82 (4 self)
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We address the problem of multitarget tracking encountered in many situations in signal or image processing. We consider stochastic dynamic systems detected by observation processes. The difficulty lies on the fact that the estimation of the states requires the assignment of the observations to the multiple targets. We propose an extension of the classical particle filter where the stochastic vector of assignment is estimated by a Gibbs sampler. This algorithm is used to estimate the trajectories of multiple targets from their noisy bearings, thus showing its ability to solve the data association problem. Moreover this algorithm is easily extended to multireceiver observations where the receivers can produce measurements of various nature with different frequencies.
Robust Full Bayesian Learning for Radial Basis Networks
, 2001
"... We propose a hierachical full Bayesian model for radial basis networks. This model treats the model dimension (number of neurons), model parameters,... ..."
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Cited by 25 (4 self)
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We propose a hierachical full Bayesian model for radial basis networks. This model treats the model dimension (number of neurons), model parameters,...
Sequential Bayesian Estimation And Model Selection For Dynamic Kernel Machines
, 2000
"... In this paper, we address the complex problem of sequential Bayesian estimation and model selection/averaging. This problem does not usually admit any type of closedform analytical solutions and, as a result, one has to resort to numerical methods. We propose here an original and powerful sequentia ..."
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Cited by 11 (7 self)
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In this paper, we address the complex problem of sequential Bayesian estimation and model selection/averaging. This problem does not usually admit any type of closedform analytical solutions and, as a result, one has to resort to numerical methods. We propose here an original and powerful sequential simulationbased strategy to perform the necessary computations. This strategy is based on Monte Carlo particle methods and model selection/averaging using predictive distributions. It combines sequential importance sampling, RaoBlackwellisation, a selection procedure and reversible jump MCMC moves. We demonstrate the eectiveness of the method by performing inference and learning on a hybrid model consisting of a dynamic linear model and a dynamic mixture of kernel basis functions.
Bayesian Computational Approaches to Model Selection
, 2000
"... this paper was to provide a summary of the stateof theart theory on Bayesian model selection and the application of MCMC algorithms. It has been shown how applications of considerable complexity can be handled successfully within this framework. Several methods for dealing with the use of default, ..."
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Cited by 7 (1 self)
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this paper was to provide a summary of the stateof theart theory on Bayesian model selection and the application of MCMC algorithms. It has been shown how applications of considerable complexity can be handled successfully within this framework. Several methods for dealing with the use of default, improper priors in the Bayesian model selection 506 Andrieu, Doucet et al. framework has been shown. Special care has been taken to pinpoint the subtleties of jumping from one parameter space to another, and in general, to show the construction of MCMC samplers in such scenarios. The focus in the paper was on the reversible jump MCMC algorithm as this is the most widely used of all existing methods; it is easy to use, flexible and has nice properties. Many references have been cited, with the emphasis being given to articles with signal processing applications. A Notation
Second order filter distribution approximations for financial time series with extreme outlier. submitted Available from http://www4.fe.uc.pt/gemf/estudos/resumos/2003/resumo2003 03.htm
, 2003
"... Particle Filters are now regularly used to obtain the filter distributions associated with state space financial time series. Most commonly used nowadays is the auxiliary particle filter method in conjunction with a first order Taylor expansion of the loglikelihood. We argue in this paper that for ..."
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Cited by 1 (0 self)
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Particle Filters are now regularly used to obtain the filter distributions associated with state space financial time series. Most commonly used nowadays is the auxiliary particle filter method in conjunction with a first order Taylor expansion of the loglikelihood. We argue in this paper that for series such as stock returns, which exhibit fairly frequent and extreme outliers, filters based on this first order approximation can easily break down. However, an auxiliary particle filter based on the much more rarely used second order approximation appears to perform well in these circumstances. To detach the issue of algorithm design from problems related to model misspecification and parameter estimation, we demonstrate the lack of robustness of the first order approximation and the feasibility of a specific second order approximation using simulated data.
NONLINEAR BAYESIAN FILTERING WITH APPLICATIONS TO ESTIMATION AND NAVIGATION
, 2005
"... Chair of Advisory Committee: Dr. Kyle T. Alfriend In principle, general approaches to optimal nonlinear filtering can be described in a unified way from the recursive Bayesian approach. The central idea to this recursive Bayesian estimation is to determine the probability density function of the st ..."
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Chair of Advisory Committee: Dr. Kyle T. Alfriend In principle, general approaches to optimal nonlinear filtering can be described in a unified way from the recursive Bayesian approach. The central idea to this recursive Bayesian estimation is to determine the probability density function of the state vector of the nonlinear systems conditioned on the available measurements. However, the optimal exact solution to this Bayesian filtering problem is intractable since it requires an infinite dimensional process. For practical nonlinear filtering applications approximate solutions are required. Recently efficient and accurate approximate nonlinear filters as alternatives to the extended Kalman filter are proposed for recursive nonlinear estimation of the states and parameters of dynamical systems. First, as samplingbased nonlinear filters, the sigma point filters, the unscented Kalman filter and the divided difference filter are investigated. Secondly, a direct numerical nonlinear filter is introduced where the state conditional probability density is calculated by applying fast numerical solvers to the FokkerPlanck equation in continuousdiscrete system models. As simulationbased nonlinear filters, a universally effective
Expectation Propagation for Neural Networks with
"... We propose a novel approach for nonlinear regression using a twolayer neural network (NN) model structure with sparsityfavoring hierarchical priors on the network weights. We present an expectation propagation (EP) approach for approximate integration over the posterior distribution of the weights ..."
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We propose a novel approach for nonlinear regression using a twolayer neural network (NN) model structure with sparsityfavoring hierarchical priors on the network weights. We present an expectation propagation (EP) approach for approximate integration over the posterior distribution of the weights, the hierarchical scale parameters of the priors, and the residual scale. Using a factorized posterior approximation we derive a computationally efficient algorithm, whose complexity scales similarly to an ensemble of independent sparse linear models. The approach enables flexible definition of weight priors with different sparseness properties such as independent Laplace priors with a common scale parameter or Gaussian automatic relevance determination (ARD) priors with different relevance parameters for all inputs. The approach can be extended beyond standard activation functions and NN model structures to form flexible nonlinear predictors from multiple sparse linear models. The effects of the hierarchical priors and the predictive performance of the algorithm are assessed using both simulated and realworld data. Comparisons are made to two alternative models with ARD priors: a Gaussian process with a NN covariance function and marginal maximum a posteriori estimates of the relevance parameters, and a NN with Markov chain Monte Carlo integration over all the unknown model parameters.
Second Order Filter Distribution Approximations for Financial Time Series with Extreme Outliers Forthcoming in the Journal of Business and Economic Statistics American Statistical Association
, 2005
"... Particle Filters are now regularly used to obtain the filter distributions associated with state space financial time series. Most commonly used nowadays is the auxiliary particle filter method in conjunction with a first order Taylor expansion of the loglikelihood. We argue in this paper that for ..."
Abstract
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Particle Filters are now regularly used to obtain the filter distributions associated with state space financial time series. Most commonly used nowadays is the auxiliary particle filter method in conjunction with a first order Taylor expansion of the loglikelihood. We argue in this paper that for series such as stock returns, which exhibit fairly frequent and extreme outliers, filters based on this first order approximation can easily break down. However, an auxiliary particle filter based on the much more rarely used second order approximation appears to perform well in these circumstances. To detach the issue of algorithm design from problems related to model misspecification and parameter estimation, we demonstrate the lack of robustness of the first order approximation and the feasibility of a specific second order approximation using simulated data.