Comparison of Statistical Approaches for Reconstructing Random Coefficients in the Problem of Stochastic Modeling of Air–Sea Heat Flux Increments
This paper compares two statistical methods for parameter reconstruction (random drift and diffusion coefficients of the Itô stochastic differential equation, SDE) in the problem of stochastic modeling of air–sea heat flux increment evolution. The first method relates to a nonparametric estimation o...
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MDPI AG
2024-01-01
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| Series: | Mathematics |
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| Online Access: | https://www.mdpi.com/2227-7390/12/2/288 |
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| author | Konstantin P. Belyaev Andrey K. Gorshenin Victor Yu. Korolev Anastasiia A. Osipova |
| author_facet | Konstantin P. Belyaev Andrey K. Gorshenin Victor Yu. Korolev Anastasiia A. Osipova |
| author_sort | Konstantin P. Belyaev |
| collection | DOAJ |
| description | This paper compares two statistical methods for parameter reconstruction (random drift and diffusion coefficients of the Itô stochastic differential equation, SDE) in the problem of stochastic modeling of air–sea heat flux increment evolution. The first method relates to a nonparametric estimation of the transition probabilities (wherein consistency is proven). The second approach is a semiparametric reconstruction based on the approximation of the SDE solution (in terms of distributions) by finite normal mixtures using the maximum likelihood estimates of the unknown parameters. This approach does not require any additional assumptions for the coefficients, with the exception of those guaranteeing the existence of the solution to the SDE itself. It is demonstrated that the corresponding conditions hold for the analyzed data. The comparison is carried out on the simulated samples, modeling the case where the SDE random coefficients are represented in trigonometric form, which is related to common climatic models, as well as on the ERA5 reanalysis data of the sensible and latent heat fluxes in the North Atlantic for 1979–2022. It is shown that the results of these two methods are close to each other in a quantitative sense, but differ somewhat in temporal variability and spatial localization. The differences during the observed period are analyzed, and their geophysical interpretations are presented. The semiparametric approach seems promising for physics-informed machine learning models. |
| first_indexed | 2024-03-08T10:42:21Z |
| format | Article |
| id | doaj.art-85970c384b514d70862e0f0e6ec015c5 |
| institution | Directory Open Access Journal |
| issn | 2227-7390 |
| language | English |
| last_indexed | 2024-03-08T10:42:21Z |
| publishDate | 2024-01-01 |
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| series | Mathematics |
| spelling | doaj.art-85970c384b514d70862e0f0e6ec015c52024-01-26T17:32:59ZengMDPI AGMathematics2227-73902024-01-0112228810.3390/math12020288Comparison of Statistical Approaches for Reconstructing Random Coefficients in the Problem of Stochastic Modeling of Air–Sea Heat Flux IncrementsKonstantin P. Belyaev0Andrey K. Gorshenin1Victor Yu. Korolev2Anastasiia A. Osipova3P.P. Shirshov Institute of Oceanology of Russian Academy of Sciences, 36 Nahimovskiy Pr., Moscow 117997, RussiaFederal Research Center «Computer Science and Control» of the Russian Academy of Sciences, 44-2 Vavilov. Str., Moscow 119333, RussiaFederal Research Center «Computer Science and Control» of the Russian Academy of Sciences, 44-2 Vavilov. Str., Moscow 119333, RussiaFederal Research Center «Computer Science and Control» of the Russian Academy of Sciences, 44-2 Vavilov. Str., Moscow 119333, RussiaThis paper compares two statistical methods for parameter reconstruction (random drift and diffusion coefficients of the Itô stochastic differential equation, SDE) in the problem of stochastic modeling of air–sea heat flux increment evolution. The first method relates to a nonparametric estimation of the transition probabilities (wherein consistency is proven). The second approach is a semiparametric reconstruction based on the approximation of the SDE solution (in terms of distributions) by finite normal mixtures using the maximum likelihood estimates of the unknown parameters. This approach does not require any additional assumptions for the coefficients, with the exception of those guaranteeing the existence of the solution to the SDE itself. It is demonstrated that the corresponding conditions hold for the analyzed data. The comparison is carried out on the simulated samples, modeling the case where the SDE random coefficients are represented in trigonometric form, which is related to common climatic models, as well as on the ERA5 reanalysis data of the sensible and latent heat fluxes in the North Atlantic for 1979–2022. It is shown that the results of these two methods are close to each other in a quantitative sense, but differ somewhat in temporal variability and spatial localization. The differences during the observed period are analyzed, and their geophysical interpretations are presented. The semiparametric approach seems promising for physics-informed machine learning models.https://www.mdpi.com/2227-7390/12/2/288stochastic modelstochastic differential equationparametric estimationnonparametric estimationsemiparametric approachfinite normal mixtures |
| spellingShingle | Konstantin P. Belyaev Andrey K. Gorshenin Victor Yu. Korolev Anastasiia A. Osipova Comparison of Statistical Approaches for Reconstructing Random Coefficients in the Problem of Stochastic Modeling of Air–Sea Heat Flux Increments Mathematics stochastic model stochastic differential equation parametric estimation nonparametric estimation semiparametric approach finite normal mixtures |
| title | Comparison of Statistical Approaches for Reconstructing Random Coefficients in the Problem of Stochastic Modeling of Air–Sea Heat Flux Increments |
| title_full | Comparison of Statistical Approaches for Reconstructing Random Coefficients in the Problem of Stochastic Modeling of Air–Sea Heat Flux Increments |
| title_fullStr | Comparison of Statistical Approaches for Reconstructing Random Coefficients in the Problem of Stochastic Modeling of Air–Sea Heat Flux Increments |
| title_full_unstemmed | Comparison of Statistical Approaches for Reconstructing Random Coefficients in the Problem of Stochastic Modeling of Air–Sea Heat Flux Increments |
| title_short | Comparison of Statistical Approaches for Reconstructing Random Coefficients in the Problem of Stochastic Modeling of Air–Sea Heat Flux Increments |
| title_sort | comparison of statistical approaches for reconstructing random coefficients in the problem of stochastic modeling of air sea heat flux increments |
| topic | stochastic model stochastic differential equation parametric estimation nonparametric estimation semiparametric approach finite normal mixtures |
| url | https://www.mdpi.com/2227-7390/12/2/288 |
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