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427
Markov Chain Monte Carlo in Conditionally Gaussian State Space Models
 Biometrika
, 1996
"... Introduction Linear Gaussian state space models are used extensively, with unknown parameters usually estimated by maximum likelihood: Wecker & Ansley (1983), Harvey (1989). However, many time series and nonparametric regression applications, such as change point problems, outlier detection and swit ..."
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Cited by 54 (3 self)
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Introduction Linear Gaussian state space models are used extensively, with unknown parameters usually estimated by maximum likelihood: Wecker & Ansley (1983), Harvey (1989). However, many time series and nonparametric regression applications, such as change point problems, outlier detection and switching regression, require the full generality of the conditionally Gaussian model: Harrison & Stevens (1976), Shumway & Stoffer (1991), West & Harrison (1989), Gordon & Smith (1990). The presence of a large number of indicator variables makes it difficult to estimate conditionally Gaussian models using maximum likelihood, and a Bayesian approach using Markov chain Monte Carlo appears more tractable. We propose a new sampler, which is used to estimate an unknown function nonparametrically when there are jumps in the function and outliers in the observations; it is also applied to a time series change point problem previously discussed by Gordon & Smith (1990). For the first example th
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.
A Generative Model for Music Transcription
, 2005
"... In this paper we present a graphical model for polyphonic music transcription. Our model, formulated as a Dynamical Bayesian Network, embodies a transparent and computationally tractable approach to this acoustic analysis problem. An advantage of our approach is that it places emphasis on explicitl ..."
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Cited by 42 (14 self)
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In this paper we present a graphical model for polyphonic music transcription. Our model, formulated as a Dynamical Bayesian Network, embodies a transparent and computationally tractable approach to this acoustic analysis problem. An advantage of our approach is that it places emphasis on explicitly modelling the sound generation procedure. It provides a clear framework in which both high level (cognitive) prior information on music structure can be coupled with low level (acoustic physical) information in a principled manner to perform the analysis. The model is a special case of the, generally intractable, switching Kalman filter model. Where possible, we derive, exact polynomial time inference procedures, and otherwise efficient approximations. We argue that our generative model based approach is computationally feasible for many music applications and is readily extensible to more general auditory scene analysis scenarios.
Recursive Monte Carlo filters: Algorithms and theoretical analysis
, 2003
"... powerful tool to perform computations in general state space models. We discuss and compare the accept–reject version with the more common sampling importance resampling version of the algorithm. In particular, we show how auxiliary variable methods and stratification can be used in the accept–rejec ..."
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Cited by 40 (0 self)
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powerful tool to perform computations in general state space models. We discuss and compare the accept–reject version with the more common sampling importance resampling version of the algorithm. In particular, we show how auxiliary variable methods and stratification can be used in the accept–reject version, and we compare different resampling techniques. In a second part, we show laws of large numbers and a central limit theorem for these Monte Carlo filters by simple induction arguments that need only weak conditions. We also show that, under stronger conditions, the required sample size is independent of the length of the observed series. 1. State space and hidden Markov models. A general state space or hidden Markov model consists of an unobserved state sequence (Xt) and an observation sequence (Yt) with the following properties: State evolution: X0,X1,X2,... is a Markov chain with X0 ∼ a0(x)dµ(x) and XtXt−1 = xt−1 ∼ at(xt−1,x)dµ(x). Generation of observations: Conditionally on (Xt), the Yt’s are independent and Yt depends on Xt only with YtXt = xt ∼ bt(xt,y)dν(y). These models occur in a variety of applications. Linear state space models are equivalent to ARMA models (see, e.g., [16]) and have become popular Received January 2003; revised August 2004. AMS 2000 subject classifications. Primary 62M09; secondary 60G35, 60J22, 65C05. Key words and phrases. State space models, hidden Markov models, filtering and smoothing, particle filters, auxiliary variables, sampling importance resampling, central limit theorem. This is an electronic reprint of the original article published by the
Particle Methods for Bayesian Modelling and Enhancement of Speech Signals
, 2000
"... This paper applies timevarying autoregressive (TVAR) models with stochastically evolving parameters to the problem of speech modelling and enhancement. The stochastic evolution models for the TVAR parameters are Markovian diusion processes. The main aim of the paper is to perform online estimation ..."
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Cited by 36 (5 self)
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This paper applies timevarying autoregressive (TVAR) models with stochastically evolving parameters to the problem of speech modelling and enhancement. The stochastic evolution models for the TVAR parameters are Markovian diusion processes. The main aim of the paper is to perform online estimation of the clean speech and model parameters, and to determine the adequacy of the chosen statistical models. Ecient particle methods are developed to solve the optimal ltering and xedlag smoothing problems. The algorithms combine sequential importance sampling (SIS), a selection step and Markov chain Monte Carlo (MCMC) methods. They employ several variance reduction strategies to make the best use of the statistical structure of the model. It is also shown how model adequacy may be determined by combining the particle lter with frequentist methods. The modelling and enhancement performance of the models and estimation algorithms are evaluated in simulation studies on both synthetic and re...
FX Trading and Exchange Rate Dynamics
, 2001
"... This paper provides new perspective on the poor performance of exchange rate models by focusing on the information structure of FX trading. I present a new theoretical model of FX trading that emphasizes the role of incomplete and heterogeneous information. The model shows how an equilibrium distr ..."
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Cited by 35 (7 self)
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This paper provides new perspective on the poor performance of exchange rate models by focusing on the information structure of FX trading. I present a new theoretical model of FX trading that emphasizes the role of incomplete and heterogeneous information. The model shows how an equilibrium distribution of FX transaction prices and orders can arise at each point in time from the optimal trading decisions of dealers. This result motivates an empirical investigation of how the equilibrium distribution of FX prices behaves using a new data set that details trading activity in the FX market. This analysis produces two striking results: (i) Much of the observed shortterm volatility in exchange rates comes from sampling the heterogeneous trading decisions of dealers in an equilibrium distribution that, under normal market conditions, changes comparatively slowly. (ii) In contrast to the assumptions of traditional macro models, public news is rarely the predominant source of exchange rate movements over any horizon.
2002): “Market Timing and Return Prediction Under Model Instability
 Journal of Empirical Finance
"... Despite mounting empirical evidence to the contrary, the literature on predictability of stock returns almost uniformly assumes a timeinvariant relationship between state variables and returns. In this paper we propose a twostage approach for forecasting of financial return series that are subject ..."
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Cited by 35 (9 self)
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Despite mounting empirical evidence to the contrary, the literature on predictability of stock returns almost uniformly assumes a timeinvariant relationship between state variables and returns. In this paper we propose a twostage approach for forecasting of financial return series that are subject to breaks. The first stage adopts a reversed ordered Cusum (ROC) procedure to determine in real time when the most recent break has occurred. In the second stage, postbreak data is used to estimate the parameters of the forecasting model. We compare this approach to existing alternatives for dealing with parameter instability such as the BaiPerron method and the timevarying parameter model. An outofsample forecasting experiment demonstrates considerable gains in market timing precision from adopting the proposed twostage forecasting method.
Signal Extraction and the Formulation of Unobserved Components Models
 ECONOMETRICS JOURNAL
, 2000
"... This paper looks at unobserved components models and examines the implied weighting patterns for signal extraction. There are three main themes. The first is the implications of correlated disturbances driving the components, especially those cases in which the correlation is perfect. The second is ..."
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Cited by 30 (7 self)
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This paper looks at unobserved components models and examines the implied weighting patterns for signal extraction. There are three main themes. The first is the implications of correlated disturbances driving the components, especially those cases in which the correlation is perfect. The second is how setting up models with t \Gamma distributed disturbances leads to weighting patterns which are robust to outliers and breaks. The third is a comparison of implied weighting patterns with kernels used in nonparametric trend estimation and equivalent kernels used in spline smoothing. We also examine how weighting patterns are affected by heteroscedasticity and irregular spacing and provide an illustrative example.
Commoninput models for multiple neural spiketrain data
 Data, Network: Comput. Neural Syst
, 2006
"... Recent developments in multielectrode recordings enable the simultaneous measurement of the spiking activity of many neurons. Analysis of such multineuronal data is one of the key challenges in computational neuroscience today. In this work, we develop a multivariate pointprocess model in which th ..."
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Cited by 30 (17 self)
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Recent developments in multielectrode recordings enable the simultaneous measurement of the spiking activity of many neurons. Analysis of such multineuronal data is one of the key challenges in computational neuroscience today. In this work, we develop a multivariate pointprocess model in which the observed activity of a network of neurons depends on three terms: 1) the experimentallycontrolled stimulus; 2) the spiking history of the observed neurons; and 3) a latent noise source that corresponds, for example, to “common input ” from an unobserved population of neurons that is presynaptic to two or more cells in the observed population. We develop an expectationmaximization algorithm for fitting the model parameters; here the expectation step is based on a continuoustime implementation of the extended Kalman smoother, and the maximization step involves two concave maximization problems which may be solved in parallel. The techniques developed allow us to solve a variety of inference problems in a straightforward, computationally efficient fashion; for example, we may use the model to predict network activity given an arbitrary stimulus, infer a neuron’s firing rate given the stimulus and the activity of the other observed neurons, and perform optimal stimulus decoding and prediction. We present several detailed simulation studies which explore the strengths and limitations of our approach. 1