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Author: Genshiro Kitagawa
Publisher: Springer Science & Business Media
ISBN: 1461207614
Category : Mathematics
Languages : en
Pages : 265
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Book Description
Smoothness Priors Analysis of Time Series addresses some of the problems of modeling stationary and nonstationary time series primarily from a Bayesian stochastic regression "smoothness priors" state space point of view. Prior distributions on model coefficients are parametrized by hyperparameters. Maximizing the likelihood of a small number of hyperparameters permits the robust modeling of a time series with relatively complex structure and a very large number of implicitly inferred parameters. The critical statistical ideas in smoothness priors are the likelihood of the Bayesian model and the use of likelihood as a measure of the goodness of fit of the model. The emphasis is on a general state space approach in which the recursive conditional distributions for prediction, filtering, and smoothing are realized using a variety of nonstandard methods including numerical integration, a Gaussian mixture distribution-two filter smoothing formula, and a Monte Carlo "particle-path tracing" method in which the distributions are approximated by many realizations. The methods are applicable for modeling time series with complex structures.
Author: Genshiro Kitagawa
Publisher: Springer Science & Business Media
ISBN: 1461207614
Category : Mathematics
Languages : en
Pages : 265
Get Book
Book Description
Smoothness Priors Analysis of Time Series addresses some of the problems of modeling stationary and nonstationary time series primarily from a Bayesian stochastic regression "smoothness priors" state space point of view. Prior distributions on model coefficients are parametrized by hyperparameters. Maximizing the likelihood of a small number of hyperparameters permits the robust modeling of a time series with relatively complex structure and a very large number of implicitly inferred parameters. The critical statistical ideas in smoothness priors are the likelihood of the Bayesian model and the use of likelihood as a measure of the goodness of fit of the model. The emphasis is on a general state space approach in which the recursive conditional distributions for prediction, filtering, and smoothing are realized using a variety of nonstandard methods including numerical integration, a Gaussian mixture distribution-two filter smoothing formula, and a Monte Carlo "particle-path tracing" method in which the distributions are approximated by many realizations. The methods are applicable for modeling time series with complex structures.
Author: Genshiro Kitagawa
Publisher:
ISBN: 9781461207627
Category :
Languages : en
Pages : 276
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Book Description
Author: David Brillinger
Publisher: Springer Science & Business Media
ISBN: 1461392969
Category : Mathematics
Languages : en
Pages : 391
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Book Description
This IMA Volume in Mathematics and its Applications NEW DIRECTIONS IN TIME SERIES ANALYSIS, PART II is based on the proceedings of the IMA summer program "New Directions in Time Series Analysis. " We are grateful to David Brillinger, Peter Caines, John Geweke, Emanuel Parzen, Murray Rosenblatt, and Murad Taqqu for organizing the program and we hope that the remarkable excitement and enthusiasm of the participants in this interdisciplinary effort are communicated to the reader. A vner Friedman Willard Miller, Jr. PREFACE Time Series Analysis is truly an interdisciplinary field because development of its theory and methods requires interaction between the diverse disciplines in which it is applied. To harness its great potential, strong interaction must be encouraged among the diverse community of statisticians and other scientists whose research involves the analysis of time series data. This was the goal of the IMA Workshop on "New Directions in Time Series Analysis. " The workshop was held July 2-July 27, 1990 and was organized by a committee consisting of Emanuel Parzen (chair), David Brillinger, Murray Rosenblatt, Murad S. Taqqu, John Geweke, and Peter Caines. Constant guidance and encouragement was provided by Avner Friedman, Director of the IMA, and his very helpful and efficient staff. The workshops were organized by weeks. It may be of interest to record the themes that were announced in the IMA newsletter describing the workshop: l.
Author: Genshiro Kitagawa
Publisher:
ISBN:
Category : Time-series analysis
Languages : en
Pages :
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Book Description
A smoothness priors approach to the modeling of time series with trends and seasonalities is shown. An observed time series is decomposed into local polynomial trend, seasonal, globally stationary autoregressive and observation error components. Each component is characterized by an unknown variance-white noise perturbed difference equation constraint. The constraints or Bayesian smoothness priors are expressed in state-space model form. A Kalman predictor yields the likelihood for the unknown variances (hyperparameters) with a computa- tional complexity, O(N). Likelihoods are computed for different constraint order models in different subsets of constraint equation model classes. Akaike's mini- mum AIC procedure is used to select the best model fitted to the data within and between the alternative model classes. Smoothing is achieved by a smoother algorithm. Examples are shown.
Author: Viktor K. Jirsa
Publisher: Springer
ISBN: 3540715126
Category : Technology & Engineering
Languages : en
Pages : 528
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Book Description
Our contemporary understanding of brain function is deeply rooted in the ideas of the nonlinear dynamics of distributed networks. Cognition and motor coordination seem to arise from the interactions of local neuronal networks, which themselves are connected in large scales across the entire brain. The spatial architectures between various scales inevitably influence the dynamics of the brain and thereby its function. But how can we integrate brain connectivity amongst these structural and functional domains? Our Handbook provides an account of the current knowledge on the measurement, analysis and theory of the anatomical and functional connectivity of the brain. All contributors are leading experts in various fields concerning structural and functional brain connectivity. In the first part of the Handbook, the chapters focus on an introduction and discussion of the principles underlying connected neural systems. The second part introduces the currently available non-invasive technologies for measuring structural and functional connectivity in the brain. Part three provides an overview of the analysis techniques currently available and highlights new developments. Part four introduces the application and translation of the concepts of brain connectivity to behavior, cognition and the clinical domain.
Author: David Brillinger
Publisher: Springer Science & Business Media
ISBN: 1468493868
Category : Mathematics
Languages : en
Pages : 262
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Book Description
This IMA Volume in Mathematics and its Applications TIME SERIES ANALYSIS AND APPLICATIONS TO GEOPHYSICAL SYSTEMS contains papers presented at a very successful workshop on the same title. The event which was held on November 12-15, 2001 was an integral part of the IMA 2001-2002 annual program on " Mathematics in the Geosciences. " We would like to thank David R. Brillinger (Department of Statistics, Uni versity of California, Berkeley), Enders Anthony Robinson (Department of Earth and Environmental Engineering, Columbia University), and Fred eric Paik Schoenberg (Department of Statistics, University of California, Los Angeles) for their superb role as workshop organizers and editors of the proceedings. We are also grateful to Robert H. Shumway (Department of Statistics, University of California, Davis) for his help in organizing the four-day event. We take this opportunity to thank the National Science Foundation for its support of the IMA. Series Editors Douglas N. Arnold, Director of the IMA Fadil Santosa, Deputy Director of the IMA v PREFACE This volume contains a collection of papers that were presented dur ing the Workshop on Time Series Analysis and Applications to Geophysical Systems at the Institute for Mathematics and its Applications (IMA) at the University of Minnesota from November 12-15, 2001. This was part of the IMA Thematic Year on Mathematics in the Geosciences, and was the last in a series of four Workshops during the Fall Quarter dedicated to Dynamical Systems and Ergodic Theory.
Author: Hirotugu Akaike
Publisher: Springer Science & Business Media
ISBN: 1461221625
Category : Mathematics
Languages : en
Pages : 388
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Book Description
A collection of applied papers on time series, appearing here for the first time in English. The applications are primarily found in engineering and the physical sciences.
Author: Raquel Prado
Publisher: CRC Press
ISBN: 1498747043
Category : Mathematics
Languages : en
Pages : 473
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Book Description
• Expanded on aspects of core model theory and methodology. • Multiple new examples and exercises. • Detailed development of dynamic factor models. • Updated discussion and connections with recent and current research frontiers.
Author: I. Gath
Publisher: Springer Science & Business Media
ISBN: 1475790988
Category : Technology & Engineering
Languages : en
Pages : 429
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Book Description
In recent years there has been rapid progress in the development of signal processing in general, and more specifically in the application of signal processing and pattern analysis to biological signals. Techniques, such as parametric and nonparametric spectral estimation, higher order spectral estimation, time-frequency methods, wavelet transform, and identifi cation of nonlinear systems using chaos theory, have been successfully used to elucidate basic mechanisms of physiological and mental processes. Similarly, biological signals recorded during daily medical practice for clinical diagnostic procedures, such as electroen cephalograms (EEG), evoked potentials (EP), electromyograms (EMG) and electrocardio grams (ECG), have greatly benefitted from advances in signal processing. In order to update researchers, graduate students, and clinicians, on the latest developments in the field, an International Symposium on Processing and Pattern Analysis of Biological Signals was held at the Technion-Israel Institute of Technology, during March 1995. This book contains 27 papers delivered during the symposium. The book follows the five sessions of the symposium. The first section, Processing and Pattern Analysis of Normal and Pathological EEG, accounts for some of the latest developments in the area of EEG processing, namely: time varying parametric modeling; non-linear dynamic modeling of the EEG using chaos theory; Markov analysis; delay estimation using adaptive least-squares filtering; and applications to the analysis of epileptic EEG, EEG recorded from psychiatric patients, and sleep EEG.
Author: Genshiro Kitagawa
Publisher: CRC Press
ISBN: 1584889225
Category : Mathematics
Languages : en
Pages : 315
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Book Description
In time series modeling, the behavior of a certain phenomenon is expressed in relation to the past values of itself and other covariates. Since many important phenomena in statistical analysis are actually time series and the identification of conditional distribution of the phenomenon is an essential part of the statistical modeling, it is very im
