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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ftmdpi:oai:mdpi.com:/2227-7390/9/5/548/ 2023-08-20T04:10:09+02:00 Qualitative Properties of Randomized Maximum Entropy Estimates of Probability Density Functions Yuri S. Popkov 2021-03-05 application/pdf https://doi.org/10.3390/math9050548 EN eng Multidisciplinary Digital Publishing Institute Mathematics and Computer Science https://dx.doi.org/10.3390/math9050548 https://creativecommons.org/licenses/by/4.0/ Mathematics; Volume 9; Issue 5; Pages: 548 randomized maximum entropy estimation probability density functions Lagrange multipliers Lyapunov-type problems implicit function rotation of vector field asymptotic efficiency thermokarst lakes forecasting Text 2021 ftmdpi https://doi.org/10.3390/math9050548 2023-08-01T01:12:31Z 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. Text Thermokarst Siberia MDPI Open Access Publishing Lagrange ENVELOPE(-62.597,-62.597,-64.529,-64.529) Mathematics 9 5 548 |
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Open Polar |
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MDPI Open Access Publishing |
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ftmdpi |
language |
English |
topic |
randomized maximum entropy estimation probability density functions Lagrange multipliers Lyapunov-type problems implicit function rotation of vector field asymptotic efficiency thermokarst lakes forecasting |
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randomized maximum entropy estimation probability density functions Lagrange multipliers Lyapunov-type problems implicit function rotation of vector field asymptotic efficiency thermokarst lakes forecasting 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 asymptotic efficiency thermokarst lakes forecasting |
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 |
Text |
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 |
Multidisciplinary Digital Publishing Institute |
publishDate |
2021 |
url |
https://doi.org/10.3390/math9050548 |
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; Volume 9; Issue 5; Pages: 548 |
op_relation |
Mathematics and Computer Science https://dx.doi.org/10.3390/math9050548 |
op_rights |
https://creativecommons.org/licenses/by/4.0/ |
op_doi |
https://doi.org/10.3390/math9050548 |
container_title |
Mathematics |
container_volume |
9 |
container_issue |
5 |
container_start_page |
548 |
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1774724128333365248 |