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The Bayesian Inference of Pareto Models Based on Information Geometry

Bayesian methods have been rapidly developed due to the important role of explicable causality in practical problems. We develope geometric approaches to Bayesian inference of Pareto models, and give an application to the analysis of sea clutter. For Pareto two-parameter model, we show the non-exist...

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Detalles Bibliográficos
Autores principales: Sun, Fupeng, Cao, Yueqi, Zhang, Shiqiang, Sun, Huafei
Formato: Online Artículo Texto
Lenguaje:English
Publicado: MDPI 2020
Materias:
Acceso en línea:https://www.ncbi.nlm.nih.gov/pmc/articles/PMC7823987/
https://www.ncbi.nlm.nih.gov/pubmed/33396778
http://dx.doi.org/10.3390/e23010045
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author Sun, Fupeng
Cao, Yueqi
Zhang, Shiqiang
Sun, Huafei
author_facet Sun, Fupeng
Cao, Yueqi
Zhang, Shiqiang
Sun, Huafei
author_sort Sun, Fupeng
collection PubMed
description Bayesian methods have been rapidly developed due to the important role of explicable causality in practical problems. We develope geometric approaches to Bayesian inference of Pareto models, and give an application to the analysis of sea clutter. For Pareto two-parameter model, we show the non-existence of α-parallel prior in general, hence we adopt Jeffreys prior to deal with the Bayesian inference. Considering geodesic distance as the loss function, an estimation in the sense of minimal mean geodesic distance is obtained. Meanwhile, by involving Al-Bayyati’s loss function we gain a new class of Bayesian estimations. In the simulation, for sea clutter, we adopt Pareto model to acquire various types of parameter estimations and the posterior prediction results. Simulation results show the advantages of the Bayesian estimations proposed and the posterior prediction.
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spelling pubmed-78239872021-02-24 The Bayesian Inference of Pareto Models Based on Information Geometry Sun, Fupeng Cao, Yueqi Zhang, Shiqiang Sun, Huafei Entropy (Basel) Article Bayesian methods have been rapidly developed due to the important role of explicable causality in practical problems. We develope geometric approaches to Bayesian inference of Pareto models, and give an application to the analysis of sea clutter. For Pareto two-parameter model, we show the non-existence of α-parallel prior in general, hence we adopt Jeffreys prior to deal with the Bayesian inference. Considering geodesic distance as the loss function, an estimation in the sense of minimal mean geodesic distance is obtained. Meanwhile, by involving Al-Bayyati’s loss function we gain a new class of Bayesian estimations. In the simulation, for sea clutter, we adopt Pareto model to acquire various types of parameter estimations and the posterior prediction results. Simulation results show the advantages of the Bayesian estimations proposed and the posterior prediction. MDPI 2020-12-30 /pmc/articles/PMC7823987/ /pubmed/33396778 http://dx.doi.org/10.3390/e23010045 Text en © 2020 by the authors. 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 (http://creativecommons.org/licenses/by/4.0/).
spellingShingle Article
Sun, Fupeng
Cao, Yueqi
Zhang, Shiqiang
Sun, Huafei
The Bayesian Inference of Pareto Models Based on Information Geometry
title The Bayesian Inference of Pareto Models Based on Information Geometry
title_full The Bayesian Inference of Pareto Models Based on Information Geometry
title_fullStr The Bayesian Inference of Pareto Models Based on Information Geometry
title_full_unstemmed The Bayesian Inference of Pareto Models Based on Information Geometry
title_short The Bayesian Inference of Pareto Models Based on Information Geometry
title_sort bayesian inference of pareto models based on information geometry
topic Article
url https://www.ncbi.nlm.nih.gov/pmc/articles/PMC7823987/
https://www.ncbi.nlm.nih.gov/pubmed/33396778
http://dx.doi.org/10.3390/e23010045
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