Ozaki Time Series Modeling of Neuroscience Data

Erscheinungsjahr 2012
ISBN: 978-1-4200-9461-9
Verlag: Taylor & Francis
Format: PDF
Kopierschutz: Adobe DRM (»Systemvoraussetzungen)

E-Book, Englisch, 574 Seiten

Reihe: Chapman & Hall/CRC Interdisciplinary Statistics

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:

- A 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

- A state space modeling method for dynamicization of solutions for the Inverse Problems

- A 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 inference from the observed time series data plays an important role.

Zielgruppe

Researchers and graduate students in statistics and neuroscience; researchers in biomedical engineering, industrial engineering, financial engineering, and systems biology.

Autoren/Hrsg.

Ozaki, Tohru

Fachgebiete

• Medizin | Veterinärmedizin Medizin | Public Health | Pharmazie | Zahnmedizin Klinische und Innere Medizin Neurologie, Klinische Neurowissenschaft
• Medizin | Veterinärmedizin Medizin | Public Health | Pharmazie | Zahnmedizin Medizin, Gesundheitswesen Medizinische Mathematik & Informatik
• Medizin | Veterinärmedizin Medizin | Public Health | Pharmazie | Zahnmedizin Medizinische Fachgebiete Bildgebende Verfahren, Nuklearmedizin, Strahlentherapie Magnetresonanztomographie, Computertomographie (MRT, CT)

Inhaltsverzeichnis

Introduction
Time-Series Modeling
Continuous-Time Models and Discrete-Time Models
Unobserved Variables and State Space Modeling

Dynamic Models for Time Series Prediction
Time Series Prediction and the Power Spectrum
Fantasy and Reality of Prediction Errors
Power Spectrum of Time Series

Discrete-Time Dynamic Models
Linear Time Series Models
Parametric Characterization of Power Spectra
Tank Model and Introduction of Structural State Space Representation
Akaike’s Theory of Predictor Space
Dynamic Models with Exogenous Input Variables

Multivariate Dynamic Models
Multivariate AR Models
Multivariate AR Models and Feedback Systems
Multivariate ARMA Models
Multivariate State Space Models and Akaike’s Canonical Realization
Multivariate and Spatial Dynamic Models with Inputs

Continuous-Time Dynamic Models
Linear Oscillation Models
Power Spectrum
Continuous-Time Structural Modeling
Nonlinear Differential Equation Models

Some More Models
Nonlinear AR Models
Neural Network Models
RBF-AR Models
Characterization of Nonlinearities
Hammerstein Model and RBF-ARX Model
Discussion on Nonlinear Predictors
Heteroscedastic Time Series Models

Related Theories and Tools
Prediction and Doob Decomposition
Looking at the Time Series from Prediction Errors
Innovations and Doob Decompositions
Innovations and Doob Decomposition in Continuous Time

Dynamics and Stationary Distributions
Time Series and Stationary Distributions
Pearson System of Distributions and Stochastic Processes
Examples
Different Dynamics Can Arise from the Same Distribution.

Bridge between Continuous-Time Models and Discrete-Time Models
Four Types of Dynamic Models
Local Linearization Bridge
LL Bridges for the Higher Order Linear/Nonlinear Processes
LL Bridges for the Processes from the Pearson System
LL Bridge as a Numerical Integration Scheme

Likelihood of Dynamic Models
Innovation Approach
Likelihood for Continuous-Time Models
Likelihood of Discrete-Time Models
Computationally Efficient Methods and Algorithms
Log-Likelihood and the Boltzmann Entropy

State Space Modeling
Inference Problem (a) for State Space Models
State Space Models and Innovations
Solutions by the Kalman Filter
Nonlinear Kalman Filters
Other Solutions
Discussions

Inference Problem (b) for State Space Models
Introduction
Log-Likelihood of State Space Models in Continuous Time
Log-Likelihood of State Space Models in Discrete Time
Regularization Approach and Type II Likelihood
Identifiability Problems

Art of Likelihood Maximization
Introduction
Initial Value Effects and the Innovation Likelihood
Slow Convergence Problem
Innovation-Based Approach versus Innovation-Free.Approach
Innovation-Based Approach and the Local Levy State Space Models
Heteroscedastic State Space Modeling

Causality Analysis
Introduction
Granger Causality and Limitations
Akaike Causality
How to Define Pair-Wise Causality with Akaike Method
Identifying Power Spectrum for Causality Analysis
Instantaneous Causality
Application to fMRI Data
Discussions

Conclusion: The New and Old Problems
References
Index

Über Autor(innen)

Tohru Ozaki is a mathematician and statistician. He received his BSc in mathematics from the University of Tokyo in 1969. He then joined the Institute of Statistical Mathematics (ISM), Tokyo, in 1970 and study and worked with Hirotugu Akaike. He received his DSc from Tokyo Institute of Technology in 1981 under the supervision of Akaike. From 1987 to 2008, he was a professor at ISM and, after Akaike’s retirement, served as the director of the prediction and control group. His major research areas include time series analysis, nonlinear stochastic dynamic modeling, predictive control, signal processing and their applications in neurosciences, control engineering, and financial engineering.
While he was at ISM, Ozaki was engaged in various projects in applied time series analysis in science and engineering: EEG dynamic inverse problems, spatial time series modeling of fMRI data, causality analysis in behavioral science, modeling nonlinear dynamics in ship engineering, predictive control design in fossil power plant control, seasonal adjustment in official statistics, heteroscedastic modeling and risk-sensitive control in financial engineering, nonlinear dynamic modeling in macroeconomics, spectral analysis of seismology data, point process modeling of earthquake occurrence data, river-flow prediction in stochastic hydrology, etc.
Ozaki retired from ISM in 2008. Since then he has been a visiting professor at Tohoku University, Sendai, Japan, and at Queensland University of Technology, Brisbane, Australia. He has been involved in supporting several research projects (in dynamic modeling of neuroscience data, fossil power plant control design, and risk-sensitive control in financial engineering) in universities and industry. He has also led, through his international research network, a time series research group called Akaike Innovation School from his office in Mount Fuji and organizes seminars every summer.