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Parameterization of the Stochastic Model for Evaluating Variable Small Data in the Shannon Entropy Basis

The article analytically summarizes the idea of applying Shannon’s principle of entropy maximization to sets that represent the results of observations of the “input” and “output” entities of the stochastic model for evaluating variable small data. To formalize this idea, a sequential transition fro...

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Autores principales: Bisikalo, Oleh, Kharchenko, Vyacheslav, Kovtun, Viacheslav, Krak, Iurii, Pavlov, Sergii
Formato: Online Artículo Texto
Lenguaje:English
Publicado: MDPI 2023
Materias:
Acceso en línea:https://www.ncbi.nlm.nih.gov/pmc/articles/PMC9954879/
https://www.ncbi.nlm.nih.gov/pubmed/36832553
http://dx.doi.org/10.3390/e25020184
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author Bisikalo, Oleh
Kharchenko, Vyacheslav
Kovtun, Viacheslav
Krak, Iurii
Pavlov, Sergii
author_facet Bisikalo, Oleh
Kharchenko, Vyacheslav
Kovtun, Viacheslav
Krak, Iurii
Pavlov, Sergii
author_sort Bisikalo, Oleh
collection PubMed
description The article analytically summarizes the idea of applying Shannon’s principle of entropy maximization to sets that represent the results of observations of the “input” and “output” entities of the stochastic model for evaluating variable small data. To formalize this idea, a sequential transition from the likelihood function to the likelihood functional and the Shannon entropy functional is analytically described. Shannon’s entropy characterizes the uncertainty caused not only by the probabilistic nature of the parameters of the stochastic data evaluation model but also by interferences that distort the results of the measurements of the values of these parameters. Accordingly, based on the Shannon entropy, it is possible to determine the best estimates of the values of these parameters for maximally uncertain (per entropy unit) distortions that cause measurement variability. This postulate is organically transferred to the statement that the estimates of the density of the probability distribution of the parameters of the stochastic model of small data obtained as a result of Shannon entropy maximization will also take into account the fact of the variability of the process of their measurements. In the article, this principle is developed into the information technology of the parametric and non-parametric evaluation on the basis of Shannon entropy of small data measured under the influence of interferences. The article analytically formalizes three key elements: -instances of the class of parameterized stochastic models for evaluating variable small data; -methods of estimating the probability density function of their parameters, represented by normalized or interval probabilities; -approaches to generating an ensemble of random vectors of initial parameters.
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spelling pubmed-99548792023-02-25 Parameterization of the Stochastic Model for Evaluating Variable Small Data in the Shannon Entropy Basis Bisikalo, Oleh Kharchenko, Vyacheslav Kovtun, Viacheslav Krak, Iurii Pavlov, Sergii Entropy (Basel) Article The article analytically summarizes the idea of applying Shannon’s principle of entropy maximization to sets that represent the results of observations of the “input” and “output” entities of the stochastic model for evaluating variable small data. To formalize this idea, a sequential transition from the likelihood function to the likelihood functional and the Shannon entropy functional is analytically described. Shannon’s entropy characterizes the uncertainty caused not only by the probabilistic nature of the parameters of the stochastic data evaluation model but also by interferences that distort the results of the measurements of the values of these parameters. Accordingly, based on the Shannon entropy, it is possible to determine the best estimates of the values of these parameters for maximally uncertain (per entropy unit) distortions that cause measurement variability. This postulate is organically transferred to the statement that the estimates of the density of the probability distribution of the parameters of the stochastic model of small data obtained as a result of Shannon entropy maximization will also take into account the fact of the variability of the process of their measurements. In the article, this principle is developed into the information technology of the parametric and non-parametric evaluation on the basis of Shannon entropy of small data measured under the influence of interferences. The article analytically formalizes three key elements: -instances of the class of parameterized stochastic models for evaluating variable small data; -methods of estimating the probability density function of their parameters, represented by normalized or interval probabilities; -approaches to generating an ensemble of random vectors of initial parameters. MDPI 2023-01-17 /pmc/articles/PMC9954879/ /pubmed/36832553 http://dx.doi.org/10.3390/e25020184 Text en © 2023 by the authors. https://creativecommons.org/licenses/by/4.0/Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https://creativecommons.org/licenses/by/4.0/).
spellingShingle Article
Bisikalo, Oleh
Kharchenko, Vyacheslav
Kovtun, Viacheslav
Krak, Iurii
Pavlov, Sergii
Parameterization of the Stochastic Model for Evaluating Variable Small Data in the Shannon Entropy Basis
title Parameterization of the Stochastic Model for Evaluating Variable Small Data in the Shannon Entropy Basis
title_full Parameterization of the Stochastic Model for Evaluating Variable Small Data in the Shannon Entropy Basis
title_fullStr Parameterization of the Stochastic Model for Evaluating Variable Small Data in the Shannon Entropy Basis
title_full_unstemmed Parameterization of the Stochastic Model for Evaluating Variable Small Data in the Shannon Entropy Basis
title_short Parameterization of the Stochastic Model for Evaluating Variable Small Data in the Shannon Entropy Basis
title_sort parameterization of the stochastic model for evaluating variable small data in the shannon entropy basis
topic Article
url https://www.ncbi.nlm.nih.gov/pmc/articles/PMC9954879/
https://www.ncbi.nlm.nih.gov/pubmed/36832553
http://dx.doi.org/10.3390/e25020184
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