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 $α$-stable Lévy process is still lacking. Here, we propose an approach to infer all the uncertain non-Gaussian p...
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ftdatacite:10.48550/arxiv.2011.11170 2023-05-15T16:00:01+02:00 Quantifying model uncertainty for the observed non-Gaussian data by the Hellinger distance Zheng, Yayun Yang, Fang Duan, Jinqiao Kurths, Jürgen 2020 https://dx.doi.org/10.48550/arxiv.2011.11170 https://arxiv.org/abs/2011.11170 unknown arXiv https://dx.doi.org/10.1016/j.cnsns.2021.105720 Creative Commons Attribution 4.0 International https://creativecommons.org/licenses/by/4.0/legalcode cc-by-4.0 CC-BY Dynamical Systems math.DS FOS Mathematics article-journal Article ScholarlyArticle Text 2020 ftdatacite https://doi.org/10.48550/arxiv.2011.11170 https://doi.org/10.1016/j.cnsns.2021.105720 2022-03-10T15:18:57Z Mathematical models for complex systems under random fluctuations often certain uncertain parameters. However, quantifying model uncertainty for a stochastic differential equation with an $α$-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 DataCite Metadata Store (German National Library of Science and Technology) |
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topic |
Dynamical Systems math.DS FOS Mathematics |
spellingShingle |
Dynamical Systems math.DS FOS Mathematics Zheng, Yayun Yang, Fang Duan, Jinqiao Kurths, Jürgen Quantifying model uncertainty for the observed non-Gaussian data by the Hellinger distance |
topic_facet |
Dynamical Systems math.DS FOS Mathematics |
description |
Mathematical models for complex systems under random fluctuations often certain uncertain parameters. However, quantifying model uncertainty for a stochastic differential equation with an $α$-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, Yayun Yang, Fang Duan, Jinqiao Kurths, Jürgen |
author_facet |
Zheng, Yayun Yang, Fang Duan, Jinqiao Kurths, Jürgen |
author_sort |
Zheng, Yayun |
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 |
publisher |
arXiv |
publishDate |
2020 |
url |
https://dx.doi.org/10.48550/arxiv.2011.11170 https://arxiv.org/abs/2011.11170 |
genre |
Dansgaard-Oeschger events |
genre_facet |
Dansgaard-Oeschger events |
op_relation |
https://dx.doi.org/10.1016/j.cnsns.2021.105720 |
op_rights |
Creative Commons Attribution 4.0 International https://creativecommons.org/licenses/by/4.0/legalcode cc-by-4.0 |
op_rightsnorm |
CC-BY |
op_doi |
https://doi.org/10.48550/arxiv.2011.11170 https://doi.org/10.1016/j.cnsns.2021.105720 |
_version_ |
1766395893958836224 |