Quantifying model uncertainty for the observed non-Gaussian data by the Hellinger distance
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 para...
Published in: | Communications in Nonlinear Science and Numerical Simulation |
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ftpotsdamik:oai:publications.pik-potsdam.de:item_25812 2023-10-29T02:35:54+01:00 Quantifying model uncertainty for the observed non-Gaussian data by the Hellinger distance Zheng, Y. Yang, F. Duan, J. Kurths, J. 2021-05-01 https://publications.pik-potsdam.de/pubman/item/item_25812 unknown info:eu-repo/semantics/altIdentifier/doi/10.1016/j.cnsns.2021.105720 https://publications.pik-potsdam.de/pubman/item/item_25812 Communications in Nonlinear Science and Numerical Simulation info:eu-repo/semantics/article 2021 ftpotsdamik https://doi.org/10.1016/j.cnsns.2021.105720 2023-09-30T17:59:54Z 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. Article in Journal/Newspaper Dansgaard-Oeschger events Publication Database PIK (Potsdam Institute for Climate Impact Research) Communications in Nonlinear Science and Numerical Simulation 96 105720 |
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Publication Database PIK (Potsdam Institute for Climate Impact Research) |
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ftpotsdamik |
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description |
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. |
format |
Article in Journal/Newspaper |
author |
Zheng, Y. Yang, F. Duan, J. Kurths, J. |
spellingShingle |
Zheng, Y. Yang, F. Duan, J. Kurths, J. Quantifying model uncertainty for the observed non-Gaussian data by the Hellinger distance |
author_facet |
Zheng, Y. Yang, F. Duan, J. Kurths, J. |
author_sort |
Zheng, Y. |
title |
Quantifying model uncertainty for the observed non-Gaussian data by the Hellinger distance |
title_short |
Quantifying model uncertainty for the observed non-Gaussian data by the Hellinger distance |
title_full |
Quantifying model uncertainty for the observed non-Gaussian data by the Hellinger distance |
title_fullStr |
Quantifying model uncertainty for the observed non-Gaussian data by the Hellinger distance |
title_full_unstemmed |
Quantifying model uncertainty for the observed non-Gaussian data by the Hellinger distance |
title_sort |
quantifying model uncertainty for the observed non-gaussian data by the hellinger distance |
publishDate |
2021 |
url |
https://publications.pik-potsdam.de/pubman/item/item_25812 |
genre |
Dansgaard-Oeschger events |
genre_facet |
Dansgaard-Oeschger events |
op_source |
Communications in Nonlinear Science and Numerical Simulation |
op_relation |
info:eu-repo/semantics/altIdentifier/doi/10.1016/j.cnsns.2021.105720 https://publications.pik-potsdam.de/pubman/item/item_25812 |
op_doi |
https://doi.org/10.1016/j.cnsns.2021.105720 |
container_title |
Communications in Nonlinear Science and Numerical Simulation |
container_volume |
96 |
container_start_page |
105720 |
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1781059382956523520 |