Qualitative Properties of Randomized Maximum Entropy Estimates of Probability Density Functions
The problem of randomized maximum entropy estimation for the probability density function of random model parameters with real data and measurement noises was formulated. This estimation procedure maximizes an information entropy functional on a set of integral equalities depending on the real data...
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ftdoajarticles:oai:doaj.org/article:555f4df5ad7e43869a20acb13498a4d2 2024-01-07T09:47:03+01:00 Qualitative Properties of Randomized Maximum Entropy Estimates of Probability Density Functions Yuri S. Popkov 2021-03-01T00:00:00Z https://doi.org/10.3390/math9050548 https://doaj.org/article/555f4df5ad7e43869a20acb13498a4d2 EN eng MDPI AG https://www.mdpi.com/2227-7390/9/5/548 https://doaj.org/toc/2227-7390 doi:10.3390/math9050548 2227-7390 https://doaj.org/article/555f4df5ad7e43869a20acb13498a4d2 Mathematics, Vol 9, Iss 5, p 548 (2021) randomized maximum entropy estimation probability density functions Lagrange multipliers Lyapunov-type problems implicit function rotation of vector field Mathematics QA1-939 article 2021 ftdoajarticles https://doi.org/10.3390/math9050548 2023-12-10T01:47:21Z The problem of randomized maximum entropy estimation for the probability density function of random model parameters with real data and measurement noises was formulated. This estimation procedure maximizes an information entropy functional on a set of integral equalities depending on the real data set. The technique of the Gâteaux derivatives is developed to solve this problem in analytical form. The probability density function estimates depend on Lagrange multipliers, which are obtained by balancing the model’s output with real data. A global theorem for the implicit dependence of these Lagrange multipliers on the data sample’s length is established using the rotation of homotopic vector fields. A theorem for the asymptotic efficiency of randomized maximum entropy estimate in terms of stationary Lagrange multipliers is formulated and proved. The proposed method is illustrated on the problem of forecasting of the evolution of the thermokarst lake area in Western Siberia. Article in Journal/Newspaper Thermokarst Siberia Directory of Open Access Journals: DOAJ Articles Lagrange ENVELOPE(-62.597,-62.597,-64.529,-64.529) Mathematics 9 5 548 |
institution |
Open Polar |
collection |
Directory of Open Access Journals: DOAJ Articles |
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ftdoajarticles |
language |
English |
topic |
randomized maximum entropy estimation probability density functions Lagrange multipliers Lyapunov-type problems implicit function rotation of vector field Mathematics QA1-939 |
spellingShingle |
randomized maximum entropy estimation probability density functions Lagrange multipliers Lyapunov-type problems implicit function rotation of vector field Mathematics QA1-939 Yuri S. Popkov Qualitative Properties of Randomized Maximum Entropy Estimates of Probability Density Functions |
topic_facet |
randomized maximum entropy estimation probability density functions Lagrange multipliers Lyapunov-type problems implicit function rotation of vector field Mathematics QA1-939 |
description |
The problem of randomized maximum entropy estimation for the probability density function of random model parameters with real data and measurement noises was formulated. This estimation procedure maximizes an information entropy functional on a set of integral equalities depending on the real data set. The technique of the Gâteaux derivatives is developed to solve this problem in analytical form. The probability density function estimates depend on Lagrange multipliers, which are obtained by balancing the model’s output with real data. A global theorem for the implicit dependence of these Lagrange multipliers on the data sample’s length is established using the rotation of homotopic vector fields. A theorem for the asymptotic efficiency of randomized maximum entropy estimate in terms of stationary Lagrange multipliers is formulated and proved. The proposed method is illustrated on the problem of forecasting of the evolution of the thermokarst lake area in Western Siberia. |
format |
Article in Journal/Newspaper |
author |
Yuri S. Popkov |
author_facet |
Yuri S. Popkov |
author_sort |
Yuri S. Popkov |
title |
Qualitative Properties of Randomized Maximum Entropy Estimates of Probability Density Functions |
title_short |
Qualitative Properties of Randomized Maximum Entropy Estimates of Probability Density Functions |
title_full |
Qualitative Properties of Randomized Maximum Entropy Estimates of Probability Density Functions |
title_fullStr |
Qualitative Properties of Randomized Maximum Entropy Estimates of Probability Density Functions |
title_full_unstemmed |
Qualitative Properties of Randomized Maximum Entropy Estimates of Probability Density Functions |
title_sort |
qualitative properties of randomized maximum entropy estimates of probability density functions |
publisher |
MDPI AG |
publishDate |
2021 |
url |
https://doi.org/10.3390/math9050548 https://doaj.org/article/555f4df5ad7e43869a20acb13498a4d2 |
long_lat |
ENVELOPE(-62.597,-62.597,-64.529,-64.529) |
geographic |
Lagrange |
geographic_facet |
Lagrange |
genre |
Thermokarst Siberia |
genre_facet |
Thermokarst Siberia |
op_source |
Mathematics, Vol 9, Iss 5, p 548 (2021) |
op_relation |
https://www.mdpi.com/2227-7390/9/5/548 https://doaj.org/toc/2227-7390 doi:10.3390/math9050548 2227-7390 https://doaj.org/article/555f4df5ad7e43869a20acb13498a4d2 |
op_doi |
https://doi.org/10.3390/math9050548 |
container_title |
Mathematics |
container_volume |
9 |
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5 |
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548 |
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1787429004870942720 |