Statistical method for testing the neutral mutation hypothesis by DNA polymorphism.

Monte Carlo methods are revolutionizing the on-line analysis of data in fields as diverse as financial modeling, target tracking and computer vision. These methods, appearing under the names of bootstrap filters, condensation, optimal Monte Carlo filters, particle filters and survival of the fittest, have made it possible to solve numerically many complex, non-standard problems that were previously intractable. This book presents the first comprehensive treatment of these techniques, including convergence results and applications to tracking, guidance, automated target recognition, aircraft navigation, robot navigation, econometrics, financial modeling, neural networks, optimal control, optimal filtering, communications, reinforcement learning, signal enhancement, model averaging and selection, computer vision, semiconductor design, population biology, dynamic Bayesian networks, and time series analysis. This will be of great value to students, researchers and practitioners, who have some basic knowledge of probability. Arnaud Doucet received the Ph. D. degree from the University of Paris-XI Orsay in 1997. From 1998 to 2000, he conducted research at the Signal Processing Group of Cambridge University, UK. He is currently an assistant professor at the Department of Electrical Engineering of Melbourne University, Australia. His research interests include Bayesian statistics, dynamic models and Monte Carlo methods. Nando de Freitas obtained a Ph.D. degree in information engineering from Cambridge University in 1999. He is presently a research associate with the artificial intelligence group of the University of California at Berkeley. His main research interests are in Bayesian statistics and the application of on-line and batch Monte Carlo methods to machine learning. Neil Gordon obtained a Ph.D. in Statistics from Imperial College, University of London in 1993. He is with the Pattern and Information Processing group at the Defence Evaluation and Research Agency in the United Kingdom. His research interests are in time series, statistical data analysis, and pattern recognition with a particular emphasis on target tracking and missile guidance.

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Sequential Monte Carlo methods in practice

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Statistical Parametric Mapping The Analysis Of Functional Brain Images

We develop methods for performing smoothing computations in general state-space 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 forward-filtering backward-smoothing procedure that can be viewed as the nonlinear, non-Gaussian counterpart of standard Kalman filter-based simulation smoothers in the linear Gaussian case. Convergence in the mean squared 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 time-varying autoregression and parameterized in terms of time-varying partial correlation coefficients, comparing the results of our algorithm with those from a simple smoother based on the filte...

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Monte Carlo Smoothing for Nonlinear Time Series

In this paper, we introduce a new concept for constructing prior distributions. We exploit the natural nested structure inherent to many model components, which defines the model component to be a flexible extension of a base model. Proper priors are defined to penalise the complexity induced by deviating from the simpler base model and are formulated after the input of a user-defined scaling parameter for that model component, both in the univariate and the multivariate case. These priors are invariant to reparameterisations, have a natural connection to Jeffreys' priors, are designed to support Occam's razor and seem to have excellent robustness properties, all which are highly desirable and allow us to use this approach to define default prior distributions. Through examples and theoretical results, we demonstrate the appropriateness of this approach and how it can be applied in various situations.

Penalising model component complexity: A principled, practical approach to constructing priors

Focusing on Bayesian approaches and computations using up-to-date simulation-based methods for inference, Time Series: Modeling, Computation, and Inference integrates mainstream approaches for time series modeling with significant recent developments in methodology and applications of time series analysis. It encompasses a graduate-level account of Bayesian time series modeling and analysis, a broad range of references to state-of-the-art approaches to univariate and multivariate time series analysis, and emerging topics at research frontiers. The book presents overviews of several classes of models and related methodology for inference, statistical computation for model fitting and assessment, and forecasting. The authors also explore the connections between time- and frequency-domain approaches and develop various models and analyses using Bayesian tools, such as Markov chain Monte Carlo (MCMC) and sequential Monte Carlo (SMC) methods. They illustrate the models and methods with examples and case studies from a variety of fields, including signal processing, biomedicine, and finance. Data sets, R and MATLAB code, and other material are available on the authors websites. Along with core models and methods, this text offers sophisticated tools for analyzing challenging time series problems. It also demonstrates the growth of time series analysis into new application areas.

Time Series: Modeling, Computation, and Inference

We explore and illustrate the use of time series decomposition methods for evaluating and comparing latent structure in nonstationary electroencephalographic (EEG) traces obtained from depressed patients during brain seizures induced as part of electroconvulsive therapy (ECT). Analysis of the patterns of change over time in the frequency structure of such EEG data provides insight into the neurophysiological mechanisms of action of this effective but poorly understood antidepressant treatment, and allows clinicians to modify ECT treatments to optimize therapeutic benefits while minimizing associated side effects. Our work has introduced new methods of time-frequency analysis of EEG series that identify the complete pattern of time evolution of frequency structure over the course of a seizure, and usefully assist in these scientific and clinical studies. New methods of decomposition of flexible dynamic models provide time domain decompositions of individual EEG series into collections of latent co...

Evaluation and Comparison of EEG Traces: Latent Structure in Nonstationary Time Series

Two new computational models show that the EEG distinguishes three distinct mental states ranging from alert to fatigue. State 1 indicates heightened alertness and is frequently present during the first few minutes of time on task. State 2 indicates normal alertness, often following and lasting longer than State 1. State 3 indicates fatigue, usually following State 2, but sometimes alternating with State 1 and State 2. Thirty-channel EEGs were recorded from 16 subjects who performed up to 180 min of nonstop computer-based mental arithmetic. Alert or fatigued states were independently confirmed with measures of subjects performance and pre- or post-task mood. We found convergent evidence for a three-state model of fatigue using Bayesian analysis of two different types of EEG features, both computed for single 13-s EEG epochs: 1) kernel partial least squares scores representing composite multichannel power spectra; 2) amplitude and frequency parameters of multiple single-channel autoregressive models.

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EEG-based estimation of mental fatigue: convergent evidence for a three-state model

New methods of time series analysis of non-stationary EEG data: eigenstructure decompositions of time varying autoregressions.

A range of developments in Bayesian time series modelling in recent years has focussed on issues of identifying latent structure in time series This has led to new uses and interpretations of existing theory for latent process decompositions of dynamic models, and to new models for univariate and multivariate time series This article draws together concepts and modelling approaches that are central to applications of time series decomposition methods, and reviews recent modelling and applied developments Several applications in time series analyses in geology, climatology, psychiatry and finance are discussed, as are related modelling directions and current research frontiers

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Raquel Prado

Papers

Time Series: Modeling, Computation, and Inference

Evaluation and Comparison of EEG Traces: Latent Structure in Nonstationary Time Series

EEG-based estimation of mental fatigue: convergent evidence for a three-state model

New methods of time series analysis of non-stationary EEG data: eigenstructure decompositions of time varying autoregressions.

Bayesian Inference on Latent Structure in Time Series