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## Details

Genre/Form: | Electronic books |
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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:

## Reviews

*Editorial reviews*

Publisher Synopsis

"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 who has made significant contributions to the area of time series and stochastic processes, in addition to methodological developments ... The book is impressive in terms of the breadth of its coverage of the models and the in-depth discussion on the theoretical properties of both discrete-time and continuous-time that are specific to neuroscience data ... the numerous examples on constructing the state-space representation of the time series models were useful, as properly constructing state-space models can be challenging. Moreover, the numerous discussions on the computational challenges for estimating the parameters of state-space models were illuminating."-Journal of the American Statistical Association, December 2014"This is a very unusual book on time series, with much that is new, innovative , and usually not found in other books on time series, for example multivariate AR models, multivariate dynamic models, causal analysis and the Doob decomposition, and so on. Among the major pleasures of browsing through the book are the acquaintance with `Laplace's Demon', seeing Pearsonian and multimodal distributions as stationary distributions for dynamic models, Einstein's inductive use of Boltzmann entropy-to mention just a few of the novelties. But the hard core of the book is about state space modeling and its application to neuroscience data. The pages 331 through 351 are a richly textured but precise and detailed introduction to state space modeling. Here is a lovely summary by Ozaki that I have not seen elsewhere-it deals with time series dynamics ..."-Jayanta K. Ghosh, International Statistical Review (2013), 81"This book is essential for every quantitative scientist who is interested in developing rigorous statistical models for analyzing brain signals. It is written by an expert statistician who has made significant contributions to the area of time series and stochastic processes. ... His expertise on this subject and interest on the deep issues of statistical modeling of brain signals are clearly reflected in the character of this book. This book builds an important foundation for neurostatistics ... it is truly unique in its treatment of the topic because it has an eye towards modeling brain signals, such as electroencephalograms and functional magnetic resonance images, and thus builds on the specifics that are directly relevant to these particular data. ... At the University of California, Irvine, researchers have used this book recently and found it to be very helpful. Moreover, I intend to use this book as the primary text for a special topic course on neurostatistics in the Department of Statistics."-Hernando Ombao, Journal of Time Series Analysis, 2013 Read more...

*User-contributed reviews*

## Tags

## Similar Items

### Related Subjects:(11)

- 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.

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- CHSL New Books(190 items)
by mwwood updated 2014-01-06