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Quantifying model uncertainty for the observed non-Gaussian data by the Hellinger distance

Authors

Zheng,  Yayun
External Organizations;

Yang,  Fang
External Organizations;

Duan,  Jinqiao
External Organizations;

/persons/resource/Juergen.Kurths

Kurths,  Jürgen
Potsdam Institute for Climate Impact Research;

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Citation

Zheng, Y., Yang, F., Duan, J., Kurths, J. (2021): Quantifying model uncertainty for the observed non-Gaussian data by the Hellinger distance. - Communications in Nonlinear Science and Numerical Simulation, 96, 105720.
https://doi.org/10.1016/j.cnsns.2021.105720


Cite as: https://publications.pik-potsdam.de/pubman/item/item_25812
Abstract
Mathematical models for complex systems under random fluctuations often certain uncertain parameters. However, quantifying model uncertainty for a stochastic differential equation with an -stable Lévy process is still lacking. Here, we propose an approach to infer all the uncertain non-Gaussian parameters and other system parameters by minimizing the Hellinger distance over the parameter space. The Hellinger distance measures the similarity between an empirical probability density of non-Gaussian observations and a solution (as a probability density) of the associated nonlocal Fokker-Planck equation. Numerical experiments verify that our method is feasible for estimating single and multiple parameters. Meanwhile, we find an optimal estimation interval of the estimated parameters. This method is beneficial for extracting governing dynamical system models under non-Gaussian fluctuations, as in the study of abrupt climate changes in the Dansgaard-Oeschger events.