Time Series Analysis informed by Dynamical Systems Theory

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dc.contributor.advisorProf. Dr. Gordon Pipa
dc.creatorSchumacher, Johannes
dc.description.abstractThis thesis investigates time series analysis tools for prediction, as well as detection and characterization of dependencies, informed by dynamical systems theory. Emphasis is placed on the role of delays with respect to information processing in dynamical systems, as well as with respect to their effect in causal interactions between systems. The three main features that characterize this work are, first, the assumption that time series are measurements of complex deterministic systems. As a result, functional mappings for statistical models in all methods are justified by concepts from dynamical systems theory. To bridge the gap between dynamical systems theory and data, differential topology is employed in the analysis. Second, the Bayesian paradigm of statistical inference is used to formalize uncertainty by means of a consistent theoretical apparatus with axiomatic foundation. Third, the statistical models are strongly informed by modern nonlinear concepts from machine learning and nonparametric modeling approaches, such as Gaussian process theory. Consequently, unbiased approximations of the functional mappings implied by the prior system level analysis can be achieved. Applications are considered foremost with respect to computational neuroscience but extend to generic time series measurements.eng
dc.rightsNamensnennung - Nicht-kommerziell - Weitergabe unter gleichen Bedingungen 3.0 Unported-
dc.subjectTime Series Analysiseng
dc.subjectDynamical Systemseng
dc.subjectMachine Learningeng
dc.subject.ddc510 - Mathematik
dc.subject.ddc500 - Naturwissenschaften
dc.titleTime Series Analysis informed by Dynamical Systems Theoryeng
dc.typeDissertation oder Habilitation [doctoralThesis]-
thesis.typeDissertation [thesis.doctoral]-
dc.contributor.refereeProf. Dr. Frank Jäkel
dc.subject.bk31.73 - Mathematische Statistik
dc.subject.bk31.80 - Angewandte Mathematik
dc.subject.bk30.20 - Nichtlineare Dynamik
dc.subject.bk42.99 - Biologie: Sonstiges
dc.subject.zdmK70 - Statistical inference
dc.subject.msc62-07 - Data analysis
Enthalten in den Sammlungen:FB08 - E-Dissertationen

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