Time series modeling of neuroscience data. (2012)

• Record Type: Book
• Further Information: Note: Tohru Ozaki.
• Other Names: Ozaki, Tohru, 1944-
• Contents: 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
• Publisher Details: Boca Raton : Taylor & Francis
• Publication Date: 2012
• Extent: 1 online resource (xxv, 532 pages), illustrations
• Subjects: 616.8/0475; Neurosciences -- Statistical methods; Neurosciences -- Mathematical models; Neurosciences -- Research -- Methodology; HEALTH & FITNESS -- Diseases -- Nervous System (incl. Brain); MEDICAL -- Neurology; Neurosciences -- methods; Diagnostic Techniques, Neurological -- statistics & numerical data; Brain Mapping -- statistics & numerical data; Data Interpretation, Statistical; Models, Neurological; Time Factors; Electronic books
• Languages: English
• ISBNs: 9781420094619; 1420094610
• Related ISBNs: 9781420094602; 1420094602
• Notes: Note: Includes bibliographical references (pages 519-532) and index.; Note: Print version record.
• Access Rights: Legal Deposit; Only available on premises controlled by the deposit library and to one user at any one time; The Legal Deposit Libraries (Non-Print Works) Regulations (UK).
• Access Usage: Restricted: Printing from this resource is governed by The Legal Deposit Libraries (Non-Print Works) Regulations (UK) and UK copyright law currently in force.