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Author: Genshiro Kitagawa Publisher: Springer Science & Business Media ISBN: 1461207614 Category : Mathematics Languages : en Pages : 265
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
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: 9780387948195 Category : Gardening Languages : en Pages : 284
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: David Brillinger Publisher: Springer Science & Business Media ISBN: 1461392969 Category : Mathematics Languages : en Pages : 391
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: Viktor K. Jirsa Publisher: Springer ISBN: 3540715126 Category : Technology & Engineering Languages : en Pages : 525
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: I. Gath Publisher: Springer Science & Business Media ISBN: 1475790988 Category : Technology & Engineering Languages : en Pages : 429
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: Tohru Katayama Publisher: CRC Press ISBN: 1482273748 Category : Mathematics Languages : en Pages : 574
Book Description
Presenting statistical and stochastic methods for the analysis and design of technological systems in engineering and applied areas, this work documents developments in statistical modelling, identification, estimation and signal processing. The book covers such topics as subspace methods, stochastic realization, state space modelling, and identification and parameter estimation.
Author: Peter D. Congdon Publisher: CRC Press ISBN: 1584887214 Category : Mathematics Languages : en Pages : 606
Book Description
The use of Markov chain Monte Carlo (MCMC) methods for estimating hierarchical models involves complex data structures and is often described as a revolutionary development. An intermediate-level treatment of Bayesian hierarchical models and their applications, Applied Bayesian Hierarchical Methods demonstrates the advantages of a Bayesian approach
Author: Peter D. Congdon Publisher: CRC Press ISBN: 0429532903 Category : Mathematics Languages : en Pages : 487
Book Description
An intermediate-level treatment of Bayesian hierarchical models and their applications, this book demonstrates the advantages of a Bayesian approach to data sets involving inferences for collections of related units or variables, and in methods where parameters can be treated as random collections. Through illustrative data analysis and attention to statistical computing, this book facilitates practical implementation of Bayesian hierarchical methods. The new edition is a revision of the book Applied Bayesian Hierarchical Methods. It maintains a focus on applied modelling and data analysis, but now using entirely R-based Bayesian computing options. It has been updated with a new chapter on regression for causal effects, and one on computing options and strategies. This latter chapter is particularly important, due to recent advances in Bayesian computing and estimation, including the development of rjags and rstan. It also features updates throughout with new examples. The examples exploit and illustrate the broader advantages of the R computing environment, while allowing readers to explore alternative likelihood assumptions, regression structures, and assumptions on prior densities. Features: Provides a comprehensive and accessible overview of applied Bayesian hierarchical modelling Includes many real data examples to illustrate different modelling topics R code (based on rjags, jagsUI, R2OpenBUGS, and rstan) is integrated into the book, emphasizing implementation Software options and coding principles are introduced in new chapter on computing Programs and data sets available on the book’s website
Author: Peter Congdon Publisher: John Wiley & Sons ISBN: 0470092386 Category : Mathematics Languages : en Pages : 446
Book Description
The use of Bayesian methods for the analysis of data has grown substantially in areas as diverse as applied statistics, psychology, economics and medical science. Bayesian Methods for Categorical Data sets out to demystify modern Bayesian methods, making them accessible to students and researchers alike. Emphasizing the use of statistical computing and applied data analysis, this book provides a comprehensive introduction to Bayesian methods of categorical outcomes. * Reviews recent Bayesian methodology for categorical outcomes (binary, count and multinomial data). * Considers missing data models techniques and non-standard models (ZIP and negative binomial). * Evaluates time series and spatio-temporal models for discrete data. * Features discussion of univariate and multivariate techniques. * Provides a set of downloadable worked examples with documented WinBUGS code, available from an ftp site. The author's previous 2 bestselling titles provided a comprehensive introduction to the theory and application of Bayesian models. Bayesian Models for Categorical Data continues to build upon this foundation by developing their application to categorical, or discrete data - one of the most common types of data available. The author's clear and logical approach makes the book accessible to a wide range of students and practitioners, including those dealing with categorical data in medicine, sociology, psychology and epidemiology.
Author: Sueo Sugimoto Publisher: Ohmsha, Ltd. ISBN: 4274805026 Category : Mathematics Languages : en Pages : 457
Book Description
This book covers a broad range of filter theories, algorithms, and numerical examples. The representative linear and nonlinear filters such as the Kalman filter, the steady-state Kalman filter, the H infinity filter, the extended Kalman filter, the Gaussian sum filter, the statistically linearized Kalman filter, the unscented Kalman filter, the Gaussian filter, the cubature Kalman filter are first visited. Then, the non-Gaussian filters such as the ensemble Kalman filter and the particle filters based on the sequential Bayesian filter and the sequential importance resampling are described, together with their recent advances. Moreover, the information matrix in the nonlinear filtering, the nonlinear smoother based on the Markov Chain Monte Carlo, the continuous-discrete filters, factorized filters, and nonlinear filters based on stochastic approximation method are detailed. 1 Review of the Kalman Filter and Related Filters 2 Information Matrix in Nonlinear Filtering 3 Extended Kalman Filter and Gaussian Sum Filter 4 Statistically Linearized Kalman Filter 5 The Unscented Kalman Filter 6 General Gaussian Filters and Applications 7 The Ensemble Kalman Filter 8 Particle Filter 9 Nonlinear Smoother with Markov Chain Monte Carlo 10 Continuous-Discrete Filters 11 Factorized Filters 12 Nonlinear Filters Based on Stochastic Approximation Method
Author: Genshiro Kitagawa
Author: Genshiro Kitagawa
Author: Genshiro Kitagawa
Author: David Brillinger
Author: Viktor K. Jirsa
Author: I. Gath
Author: Tohru Katayama
Author: Peter D. Congdon
Author: Peter D. Congdon
Author: Peter Congdon
Author: Sueo Sugimoto