Regensburg 2019 – wissenschaftliches Programm

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DY: Fachverband Dynamik und Statistische Physik

DY 63: Modeling and Data Analysis

DY 63.1: Vortrag

Freitag, 5. April 2019, 10:00–10:15, H20

Analyzing stochastic time serieses via Bayesian parameter estimation of Langevin models with correlated noise — Oliver Kamps and •Clemens Willers — Institut für Theoretische Physik, Westfälische Wilhelms-Universität Münster, Wilhelm-Klemm-Str. 9, 48149 Münster, Germany

Over the last years, the estimation of stochastic evolution equations of complex systems has been applied in many scientific fields ranging from physics to biology and finance. Especially, Langevin models with delta-correlated noise terms, which realize a Markovian dynamic, have been used successfully in this context [1]. However, many real world data sets exhibit correlated noise and a non-Markovian dynamic, for example data sets from turbulence [2].

To tackle this problem, we use Langevin models containing an added hidden component which realizes a driving correlated noise. We develop a method for the systematic estimation of the drift- and diffusion functions, parameterized through spline functions. The method is based on a likelihood function which is constructed by a short-time propagator for the measured values of the visible component. A Markov Chain Monte Carlo procedure makes it possible to get access to both the parameters and their reliability. The method is demonstrated using the example of turbulent real world data sets as the country-wide wind power production [3].

[1] Friedrich et al., Phys. Rep. 506, 87 (2011) [2] Friedrich and Peinke, Phys. Rev. Lett. 78, 863 (1997) [3] Kamps O., in Wind Energy-Impact of Turbulence, edited by Hölling M. et al. (Springer) 2014, p. 67.