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Schumacher, Johannes
11 June 2015
(has links)
This 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.
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