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297
Filtering Via Simulation: Auxiliary Particle Filters
, 1997
"... This paper analyses the recently suggested particle approach to filtering time series. We suggest that the algorithm is not robust to outliers for two reasons: the design of the simulators and the use of the discrete support to represent the sequentially updating prior distribution. Both problems ar ..."
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Cited by 519 (15 self)
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This paper analyses the recently suggested particle approach to filtering time series. We suggest that the algorithm is not robust to outliers for two reasons: the design of the simulators and the use of the discrete support to represent the sequentially updating prior distribution. Both problems are tackled in this paper. We believe we have largely solved the first problem and have reduced the order of magnitude of the second. In addition we introduce the idea of stratification into the particle filter which allows us to perform online Bayesian calculations about the parameters which index the models and maximum likelihood estimation. The new methods are illustrated by using a stochastic volatility model and a time series model of angles. Some key words: Filtering, Markov chain Monte Carlo, Particle filter, Simulation, SIR, State space. 1 1
Stochastic Volatility: Likelihood Inference And Comparison With Arch Models
, 1994
"... this paper we exploit Gibbs sampling to provide a likelihood framework for the analysis of stochastic volatility models, demonstrating how to perform either maximum likelihood or Bayesian estimation. The paper includes an extensive Monte Carlo experiment which compares the efficiency of the maximum ..."
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Cited by 354 (37 self)
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this paper we exploit Gibbs sampling to provide a likelihood framework for the analysis of stochastic volatility models, demonstrating how to perform either maximum likelihood or Bayesian estimation. The paper includes an extensive Monte Carlo experiment which compares the efficiency of the maximum likelihood estimator with that of quasilikelihood and Bayesian estimators proposed in the literature. We also compare the fit of the stochastic volatility model to that of ARCH models using the likelihood criterion to illustrate the flexibility of the framework presented. Some key words: ARCH, Bayes estimation, Gibbs sampler, Heteroscedasticity, Maximum likelihood, Quasimaximum likelihood, Simulation, Stochastic EM algorithm, Stochastic volatility, Stock returns. 1 INTRODUCTION
An Introduction to MCMC for Machine Learning
, 2003
"... This purpose of this introductory paper is threefold. First, it introduces the Monte Carlo method with emphasis on probabilistic machine learning. Second, it reviews the main building blocks of modern Markov chain Monte Carlo simulation, thereby providing and introduction to the remaining papers of ..."
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Cited by 222 (2 self)
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This purpose of this introductory paper is threefold. First, it introduces the Monte Carlo method with emphasis on probabilistic machine learning. Second, it reviews the main building blocks of modern Markov chain Monte Carlo simulation, thereby providing and introduction to the remaining papers of this special issue. Lastly, it discusses new interesting research horizons.
Likelihood Inference for Discretely Observed NonLinear Diffusions
 Econometrica
, 1998
"... This paper is concerned with the Bayesian estimation of nonlinear stochastic differential equations when only discrete observations are available. The estimation is carried out using a tuned MCMC method, in particular a blocked MetropolisHastings algorithm, by introducing auxiliary points and usin ..."
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Cited by 155 (18 self)
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This paper is concerned with the Bayesian estimation of nonlinear stochastic differential equations when only discrete observations are available. The estimation is carried out using a tuned MCMC method, in particular a blocked MetropolisHastings algorithm, by introducing auxiliary points and using the EulerMaruyama discretisation scheme. Techniques for computing the likelihood function, the marginal likelihood and diagnostic measures (all based on the MCMC output) are presented. Examples using simulated and real data are presented and discussed in detail.
Mixture Kalman Filters
 J. R. Statist. Soc. B
, 2000
"... In treating dynamic systems, sequential Monte Carlo methods use discrete samples to represent a complicated probability distribution and use rejection sampling, importance sampling, and weighted resampling to complete the online "filtering" task. In this article we propose a special sequential Mont ..."
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Cited by 151 (5 self)
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In treating dynamic systems, sequential Monte Carlo methods use discrete samples to represent a complicated probability distribution and use rejection sampling, importance sampling, and weighted resampling to complete the online "filtering" task. In this article we propose a special sequential Monte Carlo method, the mixture Kalman filter, which uses random mixture of normal distributions to represent a target distribution. It is designed for online estimation and prediction of conditional and partial conditional dynamic linear models, which are themselves a class of widely used nonlinear system and also serve to approximate many other nonlinear systems. Compared with a few available filtering methods including Monte Carlo ones, the efficiency gain provided by the mixture Kalman filter can be very substantial. Another contribution of this article is the formulation of many nonlinear systems into conditional or partial conditional linear form, to which the mixture Kalman filter can be...
Variational learning for switching statespace models
 Neural Computation
, 1998
"... We introduce a new statistical model for time series which iteratively segments data into regimes with approximately linear dynamics and learns the parameters of each of these linear regimes. This model combines and generalizes two of the most widely used stochastic time series models  hidden Ma ..."
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Cited by 142 (6 self)
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We introduce a new statistical model for time series which iteratively segments data into regimes with approximately linear dynamics and learns the parameters of each of these linear regimes. This model combines and generalizes two of the most widely used stochastic time series models  hidden Markov models and linear dynamical systems  and is closely related to models that are widely used in the control and econometrics literatures. It can also be derived by extending the mixture of experts neural network (Jacobs et al., 1991) to its fully dynamical version, in which both expert and gating networks are recurrent. Inferring the posterior probabilities of the hidden states of this model is computationally intractable, and therefore the exact Expectation Maximization (EM) algorithm cannot be applied. However, we present a variational approximation that maximizes a lower bound on the log likelihood and makes use of both the forwardbackward recursions for hidden Markov models and the Kalman lter recursions for linear dynamical systems. We tested the algorithm both on artificial data sets and on a natural data set of respiration force from a patient with sleep apnea. The results suggest that variational approximations are a viable method for inference and learning in switching statespace models.
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.
Markovian Models for Sequential Data
, 1996
"... Hidden Markov Models (HMMs) are statistical models of sequential data that have been used successfully in many machine learning applications, especially for speech recognition. Furthermore, in the last few years, many new and promising probabilistic models related to HMMs have been proposed. We firs ..."
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Cited by 84 (2 self)
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Hidden Markov Models (HMMs) are statistical models of sequential data that have been used successfully in many machine learning applications, especially for speech recognition. Furthermore, in the last few years, many new and promising probabilistic models related to HMMs have been proposed. We first summarize the basics of HMMs, and then review several recent related learning algorithms and extensions of HMMs, including in particular hybrids of HMMs with artificial neural networks, InputOutput HMMs (which are conditional HMMs using neural networks to compute probabilities), weighted transducers, variablelength Markov models and Markov switching statespace models. Finally, we discuss some of the challenges of future research in this very active area. 1 Introduction Hidden Markov Models (HMMs) are statistical models of sequential data that have been used successfully in many applications in artificial intelligence, pattern recognition, speech recognition, and modeling of biological ...
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
Bayesian PSplines
 Journal of Computational and Graphical Statistics
, 2004
"... Psplines are an attractive approach for modelling nonlinear smooth effects of covariates within the generalized additive and varying coefficient models framework. In this paper we propose a Bayesian version for Psplines and generalize the approach for one dimensional curves to two dimensional surf ..."
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Cited by 67 (21 self)
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Psplines are an attractive approach for modelling nonlinear smooth effects of covariates within the generalized additive and varying coefficient models framework. In this paper we propose a Bayesian version for Psplines and generalize the approach for one dimensional curves to two dimensional surface fitting for modelling interactions between metrical covariates. A Bayesian approach to Psplines has the advantage of allowing for simultaneous estimation of smooth functions and smoothing parameters. Moreover, it can easily be extended to more complex formulations, for example to mixed models with random effects for serially or spatially correlated response. Additionally, the assumption of constant smoothing parameters can be replaced by allowing the smoothing parameters to be locally adaptive. This is particularly useful in situations with changing curvature of the underlying smooth function or where the function is highly oscillating. Inference is fully Bayesian and uses recent MCMC techniques for drawing random samples from the posterior. In a couple of simulation studies the performance of Bayesian Psplines is studied and compared to other approaches in the literature. We illustrate the approach by a complex application on rents for flats in Munich.