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Time series modeling of neuroscience data

Author: Tohru Ozaki
Publisher: Boca Raton : Taylor & Francis, 2012.
Series: Interdisciplinary statistics.
Edition/Format:   eBook : Document : EnglishView all editions and formats
Summary:
"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  Read more...
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Genre/Form: Electronic books
Additional Physical Format: Print version:
Ozaki, Tohru, 1944-
Time series modeling of neuroscience data.
Boca Raton : Taylor & Francis, 2012
(DLC) 2011046671
(OCoLC)234431016
Material Type: Document, Internet resource
Document Type: Internet Resource, Computer File
All Authors / Contributors: Tohru Ozaki
ISBN: 9781420094619 1420094610
OCLC Number: 773297973
Description: 1 online resource (xxv, 532 pages) : illustrations.
Contents: IntroductionTime-Series ModelingContinuous-Time Models and Discrete-Time ModelsUnobserved Variables and State Space ModelingDynamic Models for Time Series PredictionTime Series Prediction and the Power SpectrumFantasy and Reality of Prediction ErrorsPower Spectrum of Time SeriesDiscrete-Time Dynamic ModelsLinear Time Series ModelsParametric Characterization of Power SpectraTank Model and Introduction of Structural State Space RepresentationAkaike's Theory of Predictor SpaceDynamic Models with Exogenous Input VariablesMultivariate Dynamic ModelsMultivariate AR ModelsMultivariate AR Models and Feedback Systems Multivariate ARMA ModelsMultivariate State Space Models and Akaike's Canonical Realization Multivariate and Spatial Dynamic Models with InputsContinuous-Time Dynamic ModelsLinear Oscillation ModelsPower SpectrumContinuous-Time Structural ModelingNonlinear Differential Equation ModelsSome More ModelsNonlinear AR ModelsNeural Network ModelsRBF-AR ModelsCharacterization of NonlinearitiesHammerstein Model and RBF-ARX ModelDiscussion on Nonlinear PredictorsHeteroscedastic Time Series ModelsRelated Theories and ToolsPrediction and Doob DecompositionLooking at the Time Series from Prediction ErrorsInnovations and Doob DecompositionsInnovations and Doob Decomposition in Continuous TimeDynamics and Stationary DistributionsTime Series and Stationary DistributionsPearson System of Distributions and Stochastic ProcessesExamplesDifferent Dynamics Can Arise from the Same Distribution.Bridge between Continuous-Time Models and Discrete-Time ModelsFour Types of Dynamic ModelsLocal Linearization BridgeLL Bridges for the Higher Order Linear/Nonlinear Processes LL Bridges for the Processes from the Pearson SystemLL Bridge as a Numerical Integration SchemeLikelihood of Dynamic ModelsInnovation ApproachLikelihood for Continuous-Time ModelsLikelihood of Discrete-Time ModelsComputationally Efficient Methods and AlgorithmsLog-Likelihood and the Boltzmann EntropyState Space ModelingInference Problem (a) for State Space ModelsState Space Models and InnovationsSolutions by the Kalman FilterNonlinear Kalman FiltersOther SolutionsDiscussionsInference Problem (b) for State Space ModelsIntroductionLog-Likelihood of State Space Models in Continuous TimeLog-Likelihood of State Space Models in Discrete TimeRegularization Approach and Type II LikelihoodIdentifiability ProblemsArt of Likelihood MaximizationIntroductionInitial Value Effects and the Innovation LikelihoodSlow Convergence ProblemInnovation-Based Approach versus Innovation-Free .Approach Innovation-Based Approach and the Local Levy State Space Models Heteroscedastic State Space ModelingCausality AnalysisIntroductionGranger Causality and LimitationsAkaike CausalityHow to Define Pair-Wise Causality with Akaike MethodIdentifying Power Spectrum for Causality AnalysisInstantaneous CausalityApplication to fMRI DataDiscussionsConclusion: The New and Old ProblemsReferencesIndex
Series Title: Interdisciplinary statistics.
Responsibility: Tohru Ozaki.

Abstract:

"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 inference from the observed time series data plays an important role"--Provided by publisher.

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"With more statisticians working in the direction of methodological and theoretical research with applications in the neurosciences, the present book is timely. The author is an expert statistician Read more...

 
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