Time series modeling of neuroscience data:
Gespeichert in:
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| Format: | Buch |
| Sprache: | English |
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Boca Raton [u.a.]
CRC Press
2012
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| Schriftenreihe: | Interdisciplinary statistics series
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| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | "Recent advances in brain science measurement technology have given researchers access to very large-scale time series data such as EEG/MEG data (20 to 100 dimensional) and fMRI (140,000 dimensional) data. To analyze such massive data, efficient computational and statistical methods are required. Time Series Modeling of Neuroscience Data shows how to efficiently analyze neuroscience data by the Wiener-Kalman-Akaike approach, in which dynamic models of all kinds, such as linear/nonlinear differential equation models and time series models, are used for whitening the temporally dependent time series in the framework of linear/nonlinear state space models. Using as little mathematics as possible, this book explores some of its basic concepts and their derivatives as useful tools for time series analysis. Unique features include: statistical identification method of highly nonlinear dynamical systems such as the Hodgkin-Huxley model, Lorenz chaos model, Zetterberg Model, and more Methods and applications for Dynamic Causality Analysis developed by Wiener, Granger, and Akaike state space modeling method for dynamicization of solutions for the Inverse Problems heteroscedastic state space modeling method for dynamic non-stationary signal decomposition for applications to signal detection problems in EEG data analysis An innovation-based method for the characterization of nonlinear and/or non-Gaussian time series An innovation-based method for spatial time series modeling for fMRI data analysis The main point of interest in this book is to show that the same data can be treated using both a dynamical system and time series approach so that the neural and physiological information can be extracted more efficiently. Of course, time series modeling is valid not only in neuroscience data analysis but also in many other sciences and engineering fields where the statistical inf Includes bibliographical references and index |
| Beschreibung: | XXV, 548 S. graph. Darst. |
| ISBN: | 9781420094602 |
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| 100 | 1 | |a Ozaki, Tohru |e Verfasser |0 (DE-588)171609190 |4 aut | |
| 245 | 1 | 0 | |a Time series modeling of neuroscience data |c Tohru Ozaki |
| 264 | 1 | |a Boca Raton [u.a.] |b CRC Press |c 2012 | |
| 300 | |a XXV, 548 S. |b graph. Darst. | ||
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| 490 | 0 | |a Interdisciplinary statistics series | |
| 500 | |a "Recent advances in brain science measurement technology have given researchers access to very large-scale time series data such as EEG/MEG data (20 to 100 dimensional) and fMRI (140,000 dimensional) data. To analyze such massive data, efficient computational and statistical methods are required. Time Series Modeling of Neuroscience Data shows how to efficiently analyze neuroscience data by the Wiener-Kalman-Akaike approach, in which dynamic models of all kinds, such as linear/nonlinear differential equation models and time series models, are used for whitening the temporally dependent time series in the framework of linear/nonlinear state space models. Using as little mathematics as possible, this book explores some of its basic concepts and their derivatives as useful tools for time series analysis. Unique features include: statistical identification method of highly nonlinear dynamical systems such as the Hodgkin-Huxley model, Lorenz chaos model, Zetterberg Model, and more Methods and applications for Dynamic Causality Analysis developed by Wiener, Granger, and Akaike state space modeling method for dynamicization of solutions for the Inverse Problems heteroscedastic state space modeling method for dynamic non-stationary signal decomposition for applications to signal detection problems in EEG data analysis An innovation-based method for the characterization of nonlinear and/or non-Gaussian time series An innovation-based method for spatial time series modeling for fMRI data analysis The main point of interest in this book is to show that the same data can be treated using both a dynamical system and time series approach so that the neural and physiological information can be extracted more efficiently. Of course, time series modeling is valid not only in neuroscience data analysis but also in many other sciences and engineering fields where the statistical inf | ||
| 500 | |a Includes bibliographical references and index | ||
| 650 | 4 | |a Diagnostic Techniques, Neurological |x statistics & numerical data | |
| 650 | 4 | |a Brain Mapping |x statistics & numerical data | |
| 650 | 4 | |a Data Interpretation, Statistical | |
| 650 | 4 | |a Models, Neurological | |
| 650 | 4 | |a Time Factors | |
| 650 | 0 | 7 | |a Neurowissenschaften |0 (DE-588)7555119-6 |2 gnd |9 rswk-swf |
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Datensatz im Suchindex
| _version_ | 1804149446208913408 |
|---|---|
| adam_text | Titel: Time series modeling of neuroscience data
Autor: Ozaki, Tohru
Jahr: 2012
Contents
Preface...................................................................................................................xix
Acknowledgments............................................................................................xxiii
Author..................................................................................................................xxv
1. Introduction.....................................................................................................1
1.1 Time Series Modeling...........................................................................1
1.2 Continuous-Time Models and Discrete-Time Models.....................3
1.3 Unobserved Variables and State Space Modeling............................7
Part I Dynamic Models for Time Series Prediction
2. Time Series Prediction and the Power Spectrum..................................15
2.1 Fantasy and Reality of Prediction Errors........................................15
2.1.1 Laplace s Demon....................................................................15
2.1.2 Reality of Prediction Errors..................................................16
2.1.3 Prediction Error Variance and the Power Spectrum........17
2.2 Power Spectrum of Time Series........................................................18
2.2.1 Power Spectrum of Nondeterministic Processes
in Continuous Time...............................................................18
2.2.2 Power Spectrum of Nondeterministic Processes
in Discrete Time.....................................................................23
2.2.3 Aliasing Effect........................................................................25
2.2.4 From Discrete Time to Continuous Time...........................26
3. Discrete-Time Dynamic Models...............................................................29
3.1 Linear Time Series Models................................................................29
3.1.1 AR, MA, and ARMA Models...............................................29
3.1.2 Stationarity and Invertibility...............................................30
3.2 Parametric Characterization of Power Spectra...............................31
3.2.1 General Linear Process Representation..............................31
3.2.2 Parametric Auto Covariance Function...............................34
3.2.3 Parametric Power Spectrum Representation.....................35
3.2.3.1 Stationarity Conditions for the Parameters........36
3.2.3.2 Peak and Trough Frequencies..............................37
3.2.3.3 Efficient Parametric Characterization
of Power Spectrum.................................................38
Contents
3.2.3.4 Whitening and Power Spectrum.........................38
3.2.3.5 Parsimonious Parameterization...........................39
3.2.3.6 Causal Meaning of Model Coefficients...............40
3.2.4 Five Different Ways of Characterizing an AR(p) Model.....40
3.3 Tank Model and Introduction of Structural State
Space Representation..........................................................................45
3.3.1 State Space Representation and AR-MA Models..............45
3.3.2 Characteristic Roots and State Space Models....................45
3.3.2.1 Sequential-Type Structural Model.......................47
3.3.2.2 Parallel-Type Structural Model............................47
3.3.2.3 Mixed-Type Structural Model................ .............48
3.3.3 Parametric Power Spectrum of the Structural Models........50
3.3.4 Applications of Structural Models......................................52
3.3.4.1 EEG Power Spectrum Estimation........................52
3.3.4.2 Trend-Cycle Decomposition.................................52
3.4 Akaike s Theory of Predictor Space.................................................55
3.4.1 Input-Output System and the Predictor Space.................55
3.4.2 Feedback System and the Predictor Space.........................56
3.4.3 How to Constructs, B, and C..............................................58
3.4.4 Canonical State Space Model and ARMA
Representation........................................................................59
3.5 Dynamic Models with Exogenous Input Variables.......................62
Multivariate Dynamic Models..................1...............................................65
4.1 Multivariate AR Models.....................................................................66
4.1.1 Power Spectrum.....................................................................66
4.1.2 Multivariate Yule-Walker Equations..................................68
4.1.3 Eigenvalues.............................................................................69
4.1.4 Forward and Backward Models..........................................70
4.1.5 Multivariate Levinson Procedure........................................70
4.1.6 Advantages and Disadvantages..........................................73
4.2 Multivariate AR Models and Feedback Systems............................74
4.2.1 Feedback System and the Difficulty
of Parameter Estimation.......................................................74
4.2.2 Bivariate Feedback Systems..................................................75
4.2.3 Multivariate Feedback Systems...........................................77
4.3 Multivariate ARMA Models..............................................................78
4.3.1 Multivariate ARMA Processes and the Power Spectrum.....78
4.3.2 Nonuniqueness of the Multivariate
ARMA Representation..........................................................80
4.3.3 State Space Model for Multivariate ARMA Processes.....82
4.3.3.1 Nonuniqueness of the State
Space Representation.............................................82
Contents xi
4.3.3.2 Stationary Multivariate ARMA Model
and the Impulse Response Function...................83
4.3.3.3 From ARMA Model to State Space Model..........83
4.3.3.4 Block-Wise State Space Model..............................84
4.3.3.5 From State Space Model to ARMA Model..........86
4.4 Multivariate State Space Models and Akaike s
Canonical Realization.........................................................................86
4.4.1 Input-Output System and the Predictor Space.................86
4.4.2 Feedback System and the Predictor Space.........................88
4.4.3 How Are A, B, and C Determined?.....................................89
4.4.4 Uniqueness..............................................................................91
4.4.5 How It Works..........................................................................93
4.4.5.1 Example 1................................................................93
4.4.5.2 Example 2................................................................96
4.4.5.3 Example 3................................................................98
4.4.6 Discussion.............................................................................101
4.5 Multivariate and Spatial Dynamic Models with Inputs.............102
4.5.1 Multivariate ARX Model....................................................102
4.5.2 Spatial Time Series Models for fMRI Data.......................102
4.5.2.1 fMRI Time Series..................................................102
4.5.2.2 NN-ARX Model...................................................103
5. Continuous-Time Dynamic Models.......................................................109
5.1 Linear Oscillation Models...............................................................109
5.1.1 Pendulum and Damping Oscillation Systems.................109
5.1.2 Damping Oscillations with Random Force......................Ill
5.2 Power Spectrum................................................................................112
5.2.1 Power Spectrum and Auto Covariance Function...........112
5.2.2 Characteristic Roots and the Power Spectrum................115
5.2.2.1 Example 1: Damping Oscillation Model...........115
5.2.2.2 Example 2: pth-Order Linear Differential
Equation System...................................................116
5.3 Continuous-Time Structural Modeling.........................................117
5.3.1 Parallel Structural Model in Continuous Time...............117
5.3.2 Advantage of Continuous-Time
Structural Modeling.................................................................120
5.3.3 Tank Model for fMRI Hemodynamic Response.............120
5.3.4 More General Tank Models................................................122
5.3.5 Structural Modeling for Spectral Decomposition...........123
5.4 Nonlinear Differential Equation Models.......................................126
5.4.1 Nonlinear Random Oscillations........................................126
5.4.2 Zetterberg Model.................................................................129
5.4.3 Hodgkin-Huxley Model.....................................................131
xii Contents
5.4.4 Balloon Model......................................................................136
5.4.5 Dynamic Causal Model......................................................138
Some More Models.....................................................................................141
6.1 Nonlinear AR Models......................................................................141
6.2 Neural Network Models..................................................................143
6.2.1 Multilayer Neural Network Models.................................143
6.2.2 Single-Layer Neural Network Models and RBFs............145
6.3 RBF-AR Models.................................................................................147
6.4 Characterization of Nonlinearities.................................................150
6.4.1 State-Dependent Eigenvalues.............................................150
6.4.2 Examples of State-Dependent Eigenvalues......................153
6.4.2.1 ExpAR(2) Model....................................................153
6.4.2.2 RBF-AR(p) Model..................................................156
6.4.3 Discrete-Time Nonlinear Model and Local
Linearization........................................................................157
6.4.4 History of ExpAR Model and RBF-AR Model.................161
6.5 Hammerstein Model and RBF-ARX Model..................................162
6.5.1 Hammerstein Model...........................................................162
6.5.2 RBF-ARX Model...................................................................163
6.5.3 Multivariate RBF-ARX Models..........................................164
6.6 Discussion on Nonlinear Predictors..............................................165
6.7 Heteroscedastic Time Series Models..............................................168
6.7.1 Temporally Inhomogeneous Prediction Errors
and the Innovation Approach............................................168
6.7.2 ARCH Model and GARCH Model....................................170
Part II Related Theories and Tools
7. Prediction and Doob Decomposition.....................................................175
7.1 Looking at the Time Series from Prediction Errors.....................175
7.2 Innovations and Doob Decompositions........................................176
7.2.1 Causal Relations and Causally Invertible Relations.......177
7.2.2 Input-Output System Representations.............................178
7.2.3 Markov Processes and Innovation Representations.......179
7.2.4 Initial-Value Effect and Wold Decomposition.................181
7.3 Innovations and Doob Decomposition in Continuous Time......182
7.3.1 Martingale in Continuous Time........................................183
7.3.2 Doob Decomposition and Stochastic Differential
Equation Model....................................................................184
7.3.3 Markov Process and Fokker-Planck Equation................186
7.3.4 Frost-Kailath Theorem for the Processes
with Observation Noise......................................................187
Contents xiii
8. Dynamics and Stationary Distributions...............................................191
8.1 Time Series and Stationary Distributions...........................;.........191
8.1.1 Exponential AR Models and Marginal
Density Distributions..........................................................191
8.1.2 Continuous-Time Cases......................................................193
8.2 Pearson System of Distributions and Stochastic Processes........195
8.2.1 Stationary Markov Diffusion Processes
and Marginal Distributions...............................................195
8.2.2 Pearson System and the Associated
Dynamical Systems.............................................................197
8.3 Examples............................................................................................200
8.3.1 Leptokurtic Distributions and Nonlinear Dynamics......200
8.3.2 Trimodal Density Distributions and Nonlinear
Dynamics..............................................................................201
8.3.3 Distributions of the Exponential Family
and Nonlinear Dynamics...................................................202
8.3.4 Fat-Tailed Distributions and Nonlinear Dynamics........203
8.3.5 Beta Distributions and Nonlinear Dynamics..................204
8.3.6 Gamma Distributions and Nonlinear Dynamics...........205
8.4 Different Dynamics Can Arise from the Same Distribution......206
8.4.1 Oscillatory Dynamics and Distributions.........................209
8.4.2 Gamma-Distributed Oscillation Model............................210
8.4.3 Type-IV Gamma-Distributed Process...............................211
8.4.4 Variable Transformation and the Innovation
Approach.............................................................................213
9. Bridge between Continuous-Time Models
and Discrete-Time Models.......................................................................215
9.1 Four Types of Dynamic Models......................................................215
9.1.1 Why We Need Them...........................................................215
9.1.2 Discretization Bridge and Stability...................................217
9.1.3 Bridge for the Stochastic Case............................................219
9.1.4 How to Choose Ai................................................................221
9.2 Local Linearization Bridge..............................................................221
9.2.1 Bridge for Nonlinear Dynamic Models............................221
9.2.2 Discretization and the Instability Problem:
Deterministic Cases.............................................................223
9.2.3 Discretization and Instability Problem:
Stochastic Cases...................................................................225
9.2.4 LL Scheme for Deterministic Systems..............................226
9.2.5 LL Scheme for Stochastic Systems.....................................228
9.2.6 LL Scheme for Stochastic Systems
with an Exogenous Input....................................................230
xiv Contents
9.3 LL Bridges for Higher Order Linear/Nonlinear Processes........232
9.3.1 Linear Processes...................................................................232
9.3.2 Instability Problem of Nonlinear
Oscillatory Processes.........................................................240
9.3.3 ExpAR(2) Model and Nonlinear
Oscillatory Processes......................................................242
9.3.4 LL Discretization of Nonlinear Oscillatory Models.......243
9.4 LL Bridges for Processes from the Pearson System.....................247
9.4.1 Discretized Cauchy-Distributed Process.........................248
9.4.2 Discretized Beta-Distributed Process...............................249
9.4.3 Discretized Type I Gamma-Distributed Process............251
9.4.4 Discretized Type II Gamma-Distributed Process...........253
9.4.5 /(y)and(p(y()..........................................................................254
9.4.6 Discussions...........................................................................255
9.4.7 Crossing the Bridge from Discrete to Continuous..........256
9.5 LL Bridge as a Numerical Integration Scheme.............................257
9.5.1 Numerical Integration Scheme and Required
Properties..............................................................................257
9.5.2 A-Stability.............................................................................259
9.5.3 Implicit Schemes..................................................................259
9.5.4 LL Scheme with Ito Calculus.............................................260
9.5.5 Order of Convergence.........................................................263
9.5.6 Discussions...........................................................................265
9.5.6.1 Integration Schemes and Innovation
Approach...............................................................265
9.5.6.2 Multidimensional LL Schemes...........................266
9.5.6.3 Related Topics.......................................................267
10. Likelihood of Dynamic Models..............................................................269
10.1 Innovation Approach.......................................................................269
10.2 Likelihood for Continuous-Time Models......................................271
10.2.1 Innovation-Based Likelihood.............................................271
10.2.2 Examples...............................................................................272
10.2.2.1 Linear Stochastic Dynamical System................272
10.2.2.2 Linear Oscillation Models...................................273
10.2.2.3 General pih Order Differential
Equation Models...................................................275
10.2.2.4 Tank Models..........................................................277
10.2.2.5 Spectral Decomposition Model..........................278
10.3 Likelihood of Discrete-Time Models..............................................279
10.3.1 Likelihood of Discrete-Time Nonlinear
Dynamic Models.................................................................280
10.3.1.1 Likelihood of Univariate Nonlinear
Time Series Models..............................................280
Contents xv
10.3.1.2 Nonlinear Parameters and Linear
Parameters...........................................................282
10.3.1.3 Nonlinear Multivariate RBF-AR Models
for Nonlinear Feedback Systems.......................285
10.3.1.4 Multivariate RBF-AR Model...............................287
10.3.2 Likelihood of Discrete-Time Linear
Dynamic Models......................................................................291
10.3.2.1 ARMA Models......................................................291
10.3.2.2 Univariate AR Models.........................................296
10.3.2.3 Linear Multivariate AR Models.........................298
10.3.2.4 Linear Multivariate ARMA Models..................298
10.3.2.5 Linear Spatial Time Series Models....................300
10.3.3 Likelihood of Linear/Nonlinear Time Series
Models with Exogenous Inputs.........................................303
10.4 Computationally Efficient Methods and Algorithms..................304
10.4.1 Least Squares Methods for Univariate AR Models........305
10.4.1.1 Yule-Walker Equation (Moment Method)........305
10.4.1.2 Least Squares Estimates......................................307
10.4.1.3 Levinson Estimate................................................310
10.4.1.4 Burg Algorithm and MEM Estimate.................311
10.4.2 Least Squares Method for Multivariate AR Models.......313
10.4.2.1 Yule-Walker Estimates........................................314
10.4.2.2 Levinson-Whittle Estimate.................................314
10.4.2.3 Least Squares Estimates......................................316
10.4.3 Least Squares Method for Multivariate
ARX Models..........................................................................319
10.5 Log-Likelihood and the Boltzmann Entropy................................321
10.5.1 Akaike s Entropy Maximization Principle.......................322
10.5.2 Prevailing Confusions about the Entropy and AIC........324
10.5.3 Einstein s Inductive Use of Boltzmann Entropy..............326
Part III State Space Modeling
11. Inference Problem (a) for State Space Models......................................331
11.1 State Space Models and Innovations..............................................331
11.1.1 Linear State Space Models..................................................331
11.1.2 Nonlinear State Space Models:
Hodgkin-Huxley Model.....................................................334
11.1.3 Whitening through ARMA(k,k).........................................334
11.1.4 Two Types of Inference Problems: (a) and (b)...................336
11.2 Solutions by the Kaiman Filter........................................................338
11.2.1 Predictors, Filters, and Smoothers...»................................338
11.2.2 Minimum Variance Principle.............................................339
xvi Contents
11.2.3 Innovations and Kaiman Filter..........................................342
11.2.4 Kaiman Filter as a Real-Time Whitening Operator........348
11.2.5 Observability and Controllability.....................................349
11.2.6 Ill-Posed Inverse Problem and Observability..................350
11.2.7 Kaiman Filter and Input-Output System Models...........351
11.2.8 Probabilistic Meaning of Kaiman Filter...........................352
11.2.9 Kaiman Filters in Continuous Time..................................354
11.3 Nonlinear Kaiman Filters................................................................359
11.3.1 Kushner s General Solution................................................362
11.3.2 Extended Kaiman Filters....................................................364
11.3.3 Local Gauss State Space Models and Two Types
of Approximations...............................................................368
11.3.3.1 Scheme of F-D Route............................................368
11.3.3.2 Scheme of D-F Route............................................369
11.3.3.3 D-F Route versus F-D Route...............................369
11.3.3.4 D-F Route and Discretizations of the Local
Gauss State Space Model.....................................370
11.3.4 Local Linearization Filter....................................................372
11.3.5 Discussions...........................................................................373
11.3.6 Nonlinear Observation Equations.....................................376
11.3.6.1 Simple Approximations.......................................376
11.3.6.2 Nonuniqueness Problem.....................................377
11.4 Other Solutions..................................................................................381
11.4.1 Smoothers.............................................................................382
11.4.2 On-Line Smoothers..............................................................385
11.4.3 Regularization Approach...................................................386
11.4.3.1 Regularization and Constrained Least
Squares Method....................................................386
11.4.3.2 Examples................................................................389
11.5 Discussions........................................................................................393
11.5.1 Model Formulations............................................................393
11.5.2 Independence of Errors or Homogeneity
of Errors ............................................................................396
12. Inference Problem (b) for State Space Models......................................397
12.1 Introduction.......................................................................................397
12.2 Log-Likelihood of State Space Models in Continuous Time........398
12.2.1 Linear Models and Nonlinear Models: Examples..........400
12.2.1.1 Log-Likelihood of TankModels.........................400
12.2.1.2 Nonlinear Continuous-Time State
Space Model..........................................................401
12.2.1.3 Hodgkin-Huxley Model with Exogenous
Inputs.....................................................................403
Contents xvii
12.2.2 How It Works with Innovations: The Case
of Lorenz Chaos...................................................................405
12.2.2.1 State Space Model for Lorenz Chaos.................406
12.2.2.2 Prediction Errors of Lorenz Chaos....................409
12.2.3 What We Win by Maximizing the Log-Likelihood:
The Case of Rikitake Chaos................................................411
12.3 Log-Likelihood of State Space Models in Discrete Time.............415
12.3.1 General Linear State Space Models...................................415
12.3.2 Spectral Decomposition Model..........................................417
12.3.3 Nonlinear Discrete-Time State Space Model...................418
12.3.4 RBF-AR Type State Space Model.......................................419
12.4 Regularization Approach and Type II Likelihood.......................421
12.4.1 How to Choose d2?...............................................................421
12.4.2 Computational Cost and EM Algorithm..........................422
12.4.3 Jazwinski Scheme and General Nonlinear
Non-Gaussian Filter.............................................................423
12.5 Identifiability Problems....................................................................424
12.5.1 Gramians...............................................................................427
12.5.2 Instability Problem..............................................................428
12.5.3 Instability and Variable Transformations........................430
12.5.4 Overparameterization Problem.........................................432
13. Art of Likelihood Maximization.............................................................435
13.1 Introduction.......................................................................................436
13.2 Initial Value Effects and the Innovation Likelihood....................437
13.2.1 Innovation Approach..........................................................438
13.2.2 Durbin-Koopman Approach.............................................440
13.2.3 Schumway-Stoffer Approach............................................441
13.3 Slow Convergence Problem.............................................................443
13.3.1 111 Conditions near Optimal Point.....................................443
13.3.2 Ill-Conditioned Optimizations..........................................451
13.4 Innovation-Based Approach versus Innovation-Free
Approach............................................................................................452
13.4.1 Temporal Homogeneity of Errors......................................453
13.4.2 Temporal Independence of Errors.....................................454
13.4.3 Innovation-Free Approach and Local Non-Gauss
State Space Models...............................................................455
13.5 Innovation-Based Approach and the Local Levy State
Space Models.....................................................................................458
13.5.1 Likelihood of Local-Levy State Space Models.................459
13.5.2 Recursive Computations.....................................................462
13.5.3 Algorithm..............................................................................466
13.5.4 Discussions...........................................................................468
xviii Contents
13.6 Heteroscedastic State Space Modeling...........................................470
13.6.1 A Heteroscedastic State Space Modeling
for EEG Power Spectrum Estimation................................471
13.6.2 Compartment-GARCH Model...........................................474
13.6.3 Application to Nonstationary EEG Power
Spectrum Estimation...........................................................477
14. Causality Analysis.....................................................................................479
14.1 Introduction.......................................................................................479
14.2 Granger Causality and Limitations................................................480
14.2.1 Mathematical Criteria for Pair-Wise Causality...............481
14.2.2 Limitations of Granger Causality......................................482
14.2.3 Log-Likelihood instead of Coefficients.............................484
14.2.3.1 Example A.............................................................484
14.2.3.2 Example B..............................................................485
14.3 Akaike Causality...............................................................................486
14.3.1 Innovation Contribution Ratio...........................................486
14.3.2 Causality and Feedback Systems.......................................488
14.3.3 Application to Gaze Data....................................................490
14.4 How to Define Pair-Wise Causality with Akaike Method..........494
14.4.1 Partial Pair-Wise Causality.................................................494
14.4.2 Partial Causality and Total Causality...............................497
14.5 Identifying Power Spectrum for Causality Analysis...................498
14.5.1 Mathematical Criteria for Total Causality........................500
14.5.2 Statistical Criteria for Total Causality................................501
14.6 Instantaneous Causality..................................................................502
14.6.1 Introduction of a Latent Noise Variable...........................503
14.6.2 Innovation Contribution through Latent Variable..........505
14.7 Application to fMRI Data.................................................................507
14.8 Discussions........................................................................................511
Acknowledgment.........................................................................................513
15. Conclusion: The New and Old Problems..............................................515
References...........................................................................................................519
Index.....................................................................................................................533
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| any_adam_object | 1 |
| author | Ozaki, Tohru |
| author_GND | (DE-588)171609190 |
| author_facet | Ozaki, Tohru |
| author_role | aut |
| author_sort | Ozaki, Tohru |
| author_variant | t o to |
| building | Verbundindex |
| bvnumber | BV040398050 |
| classification_tum | MAT 634f BIO 107f |
| ctrlnum | (OCoLC)783456275 (DE-599)BVBBV040398050 |
| dewey-full | 612.8 |
| dewey-hundreds | 600 - Technology (Applied sciences) |
| dewey-ones | 612 - Human physiology |
| dewey-raw | 612.8 |
| dewey-search | 612.8 |
| dewey-sort | 3612.8 |
| dewey-tens | 610 - Medicine and health |
| discipline | Biologie Mathematik Medizin |
| format | Book |
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Time Series Modeling of Neuroscience Data shows how to efficiently analyze neuroscience data by the Wiener-Kalman-Akaike approach, in which dynamic models of all kinds, such as linear/nonlinear differential equation models and time series models, are used for whitening the temporally dependent time series in the framework of linear/nonlinear state space models. Using as little mathematics as possible, this book explores some of its basic concepts and their derivatives as useful tools for time series analysis. 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| id | DE-604.BV040398050 |
| illustrated | Illustrated |
| indexdate | 2024-07-10T00:23:09Z |
| institution | BVB |
| isbn | 9781420094602 |
| language | English |
| lccn | 2011046671 |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-025251290 |
| oclc_num | 783456275 |
| open_access_boolean | |
| owner | DE-91G DE-BY-TUM DE-83 |
| owner_facet | DE-91G DE-BY-TUM DE-83 |
| physical | XXV, 548 S. graph. Darst. |
| publishDate | 2012 |
| publishDateSearch | 2012 |
| publishDateSort | 2012 |
| publisher | CRC Press |
| record_format | marc |
| series2 | Interdisciplinary statistics series |
| spelling | Ozaki, Tohru Verfasser (DE-588)171609190 aut Time series modeling of neuroscience data Tohru Ozaki Boca Raton [u.a.] CRC Press 2012 XXV, 548 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Interdisciplinary statistics series "Recent advances in brain science measurement technology have given researchers access to very large-scale time series data such as EEG/MEG data (20 to 100 dimensional) and fMRI (140,000 dimensional) data. To analyze such massive data, efficient computational and statistical methods are required. Time Series Modeling of Neuroscience Data shows how to efficiently analyze neuroscience data by the Wiener-Kalman-Akaike approach, in which dynamic models of all kinds, such as linear/nonlinear differential equation models and time series models, are used for whitening the temporally dependent time series in the framework of linear/nonlinear state space models. Using as little mathematics as possible, this book explores some of its basic concepts and their derivatives as useful tools for time series analysis. Unique features include: statistical identification method of highly nonlinear dynamical systems such as the Hodgkin-Huxley model, Lorenz chaos model, Zetterberg Model, and more Methods and applications for Dynamic Causality Analysis developed by Wiener, Granger, and Akaike state space modeling method for dynamicization of solutions for the Inverse Problems heteroscedastic state space modeling method for dynamic non-stationary signal decomposition for applications to signal detection problems in EEG data analysis An innovation-based method for the characterization of nonlinear and/or non-Gaussian time series An innovation-based method for spatial time series modeling for fMRI data analysis The main point of interest in this book is to show that the same data can be treated using both a dynamical system and time series approach so that the neural and physiological information can be extracted more efficiently. Of course, time series modeling is valid not only in neuroscience data analysis but also in many other sciences and engineering fields where the statistical inf Includes bibliographical references and index Diagnostic Techniques, Neurological statistics & numerical data Brain Mapping statistics & numerical data Data Interpretation, Statistical Models, Neurological Time Factors Neurowissenschaften (DE-588)7555119-6 gnd rswk-swf Zeitreihenanalyse (DE-588)4067486-1 gnd rswk-swf Zeitreihenanalyse (DE-588)4067486-1 s Neurowissenschaften (DE-588)7555119-6 s DE-604 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=025251290&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Ozaki, Tohru Time series modeling of neuroscience data Diagnostic Techniques, Neurological statistics & numerical data Brain Mapping statistics & numerical data Data Interpretation, Statistical Models, Neurological Time Factors Neurowissenschaften (DE-588)7555119-6 gnd Zeitreihenanalyse (DE-588)4067486-1 gnd |
| subject_GND | (DE-588)7555119-6 (DE-588)4067486-1 |
| title | Time series modeling of neuroscience data |
| title_auth | Time series modeling of neuroscience data |
| title_exact_search | Time series modeling of neuroscience data |
| title_full | Time series modeling of neuroscience data Tohru Ozaki |
| title_fullStr | Time series modeling of neuroscience data Tohru Ozaki |
| title_full_unstemmed | Time series modeling of neuroscience data Tohru Ozaki |
| title_short | Time series modeling of neuroscience data |
| title_sort | time series modeling of neuroscience data |
| topic | Diagnostic Techniques, Neurological statistics & numerical data Brain Mapping statistics & numerical data Data Interpretation, Statistical Models, Neurological Time Factors Neurowissenschaften (DE-588)7555119-6 gnd Zeitreihenanalyse (DE-588)4067486-1 gnd |
| topic_facet | Diagnostic Techniques, Neurological statistics & numerical data Brain Mapping statistics & numerical data Data Interpretation, Statistical Models, Neurological Time Factors Neurowissenschaften Zeitreihenanalyse |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=025251290&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| work_keys_str_mv | AT ozakitohru timeseriesmodelingofneurosciencedata |