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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...
Autores principales: | , , , |
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Formato: | Online Artículo Texto |
Lenguaje: | English |
Publicado: |
MDPI
2020
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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. |
format | Online Article Text |
id | pubmed-7823987 |
institution | National Center for Biotechnology Information |
language | English |
publishDate | 2020 |
publisher | MDPI |
record_format | MEDLINE/PubMed |
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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