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18
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 895 (69 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.
Monte Carlo Methods for Tempo Tracking and Rhythm Quantization
 JOURNAL OF ARTIFICIAL INTELLIGENCE RESEARCH
, 2003
"... We present a probabilistic generarive model for timing deviations in expressive music performance. The structure of the proposed model is equivalent to a switching state space model. The switch variables correspond to discrete note locations as in a musical score. The continuous hidden variables ..."
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Cited by 63 (10 self)
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We present a probabilistic generarive model for timing deviations in expressive music performance. The structure of the proposed model is equivalent to a switching state space model. The switch variables correspond to discrete note locations as in a musical score. The continuous hidden variables denote the tempo. We formulate two well known music recognition problems, namely tempo tracking and automatic transcription (rhythm quantization) as filtering and maximum a posteriori (MAP) state estimation tasks. Ex act computation of posterior features such as the MAP state is intractable in this model class, so we introduce Monte Carlo methods for integration and optimization. We compare Markov Chain Monte Carlo (MCMC) methods (such as Gibbs sampling, simulated annealing and iterative improvement) and sequential Monte Carlo methods (particle filters). Our simulation results suggest better results with sequential methods. The methods can be applied in both online and batch scenarios such as tempo tracking and transcription and are thus potentially useful in a number of music applications such as adaptive automatic accompaniment, score typesetting and music information retrieval.
Timeline: A Dynamic Hierarchical Dirichlet Process Model for Recovering Birth/Death and Evolution of Topics in Text Stream
"... Topic models have proven to be a useful tool for discovering latent structures in document collections. However, most document collections often come as temporal streams and thus several aspects of the latent structure such as the number of topics, the topics ’ distribution and popularity are timee ..."
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Cited by 26 (4 self)
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Topic models have proven to be a useful tool for discovering latent structures in document collections. However, most document collections often come as temporal streams and thus several aspects of the latent structure such as the number of topics, the topics ’ distribution and popularity are timeevolving. Several models exist that model the evolution of some but not all of the above aspects. In this paper we introduce infinite dynamic topic models, iDTM, that can accommodate the evolution of all the aforementioned aspects. Our model assumes that documents are organized into epochs, where the documents within each epoch are exchangeable but the order between the documents is maintained across epochs. iDTM allows for unbounded number of topics: topics can die or be born at any epoch, and the representation of each topic can evolve according to a Markovian dynamics. We use iDTM to analyze the birth and evolution of topics in the NIPS community and evaluated the efficacy of our model on both simulated and real datasets with favorable outcome. 1
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 24 (7 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 And NonGaussian State Space Modeling Using Sampling Techniques
 Annals of the Institute of Statistical Mathematics
, 2001
"... . In this paper, the nonlinear nonGaussian filters and smoothers are ..."
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Cited by 10 (1 self)
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. In this paper, the nonlinear nonGaussian filters and smoothers are
Nonlinearity, Nonstationarity, and Thick Tails: How They Interact to Generate Persistency in Memory 1
"... We consider nonlinear transformations of random walks driven by thicktailed innovations that may have infinite means or variances. These three nonstandard characteristics: nonlinearity, nonstationarity, and thick tails interact to generate a spectrum of asymptotic autocorrelation patterns consisten ..."
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Cited by 8 (4 self)
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We consider nonlinear transformations of random walks driven by thicktailed innovations that may have infinite means or variances. These three nonstandard characteristics: nonlinearity, nonstationarity, and thick tails interact to generate a spectrum of asymptotic autocorrelation patterns consistent with longmemory processes. Such autocorrelations may decay very slowly as the number of lags increases or may not decay at all and remain constant at all lags. Depending upon the type of transformation considered and how the model error is specified, the autocorrelation functions are given by random constants, deterministic functions that decay slowly at hyperbolic rates, or mixtures of the two. Such patterns, along with other sample characteristics of the transformed time series, such as jumps in the sample path, excessive volatility, and leptokurtosis, suggest the possibility that these three ingredients are involved in the data generating processes of many actual economic and financial time series data. In addition to time series characteristics, we explore nonlinear regression asymptotics when the regressor is observable and an alternative regression technique when it is unobservable. To illustrate, we examine two empirical applications: wholesale electricity price spikes driven by capacity shortfalls and exchange rates governed by a target zone.
Extending expectation propagation for graphical models
, 2005
"... Graphical models have been widely used in many applications, ranging from human behavior recognition to wireless signal detection. However, efficient inference and learning techniques for graphical models are needed to handle complex models, such as hybrid Bayesian networks. This thesis proposes ext ..."
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Cited by 8 (5 self)
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Graphical models have been widely used in many applications, ranging from human behavior recognition to wireless signal detection. However, efficient inference and learning techniques for graphical models are needed to handle complex models, such as hybrid Bayesian networks. This thesis proposes extensions of expectation propagation, a powerful generalization of loopy belief propagation, to develop efficient inference and learning algorithms for graphical models. The first two chapters of the thesis present inference algorithms for generative graphical models, and the next two propose learning algorithms for conditional graphical models. First, the thesis proposes a windowbased EP smoothing algorithm, as an alternative to batch EP, for hybrid dynamic Bayesian networks. For an application to digital wireless communications, windowbased EP smoothing achieves estimation accuracy comparable to sequential Monte Carlo methods, but with more than 10 times less computational cost. Second, it combines treestructured EP approximation with the junction tree algorithm
On Markov Chain Monte Carlo Methods For Nonlinear And NonGaussian StateSpace Models
 Communications in Statistics, Simulation and Computation, Vol.28, No.4, pp.867
, 1999
"... In this paper, a nonlinear and/or nonGaussian smoother utilizing Markov chain Monte Carlo Methods is proposed, where the measurement and transition equations are specified in any general formulation and the error terms in the statespace model are not necessarily normal. The random draws are direct ..."
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Cited by 8 (2 self)
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In this paper, a nonlinear and/or nonGaussian smoother utilizing Markov chain Monte Carlo Methods is proposed, where the measurement and transition equations are specified in any general formulation and the error terms in the statespace model are not necessarily normal. The random draws are directly generated from the smoothing densities. For random number generation, the MetropolisHastings algorithm and the Gibbs sampling technique are utilized. The proposed procedure is very simple and easy for programming, compared with the existing nonlinear and nonGaussian smoothing techniques. Moreover, taking several candidates of the proposal density function, we examine precision of the proposed estimator.
Estimation Of Unknown Parameters In Nonlinear And NonGaussian State Space Models
"... For the last decade, various simulationbased nonlinear ..."
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Cited by 2 (1 self)
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For the last decade, various simulationbased nonlinear