Estimating statistics for detecting determinism using global dynamical models |
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| Affiliation: | 1. Institut für Theoretische Physik, Technische Universität Berlin, Hardenbergstraße 36, Berlin 10623, Germany;2. Complex Systems Lab, Discipline of Physics, Indian Institute of Technology Indore, Simrol, Indore, Madhya Pradesh 453552 India;1. Kotel''nikov''s Institute of Radio-Engineering and Electronics of RAS, Saratov Branch, Zelenaya 38, Saratov 410019, Russia;2. Saratov State University, Astrakhanskaya, 83 410012, Russia;3. Yuri Gagarin State Technical University of Saratov, Politehnicheskaya 77,Saratov 410054, Russia;4. St.Petersburg State University, Universitetskiy proezd, 28, Peterhof 198504, Russia;1. Saratov State University, Astrakhanskaya street 83, 410012 Saratov, Russia;2. Institut für Theoretische Physik, TU Berlin, Hardenbergstraße 36, 10623 Berlin, Germany;1. School of Mechanical and Aerospace Engineering, Oklahoma State University, Stillwater, Oklahoma 74078, USA;2. Department of Engineering Cybernetics, Norwegian University of Science and Technology, N-7465, Trondheim, Norway;3. CSE Group, Mathematics and Cybernetics, SINTEF Digital, 7034, Trondheim, Norway |
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| Abstract: | Classification of time series using a dynamical system ansatz is potentially powerful, however assessing performance for noisy experimental data is problematic. Here, we develop a rigorous statistical framework for calculating classification probabilities using global dynamical models, and analytically derive some asymptotic properties. We illustrate the method numerically by attempting to detect “determinism” in a noisy data set. |
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