{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,12]],"date-time":"2025-10-12T03:30:56Z","timestamp":1760239856479,"version":"build-2065373602"},"reference-count":20,"publisher":"MDPI AG","issue":"1","license":[{"start":{"date-parts":[[2020,12,30]],"date-time":"2020-12-30T00:00:00Z","timestamp":1609286400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"National Key Research and Development Plan of China","award":["No. 2020YFC2006201"],"award-info":[{"award-number":["No. 2020YFC2006201"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Entropy"],"abstract":"<jats:p>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 \u03b1-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\u2019s 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.<\/jats:p>","DOI":"10.3390\/e23010045","type":"journal-article","created":{"date-parts":[[2020,12,30]],"date-time":"2020-12-30T09:35:23Z","timestamp":1609320923000},"page":"45","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":3,"title":["The Bayesian Inference of Pareto Models Based on Information Geometry"],"prefix":"10.3390","volume":"23","author":[{"given":"Fupeng","family":"Sun","sequence":"first","affiliation":[{"name":"School of Mathematics and Statistics, Beijing Institute of Technology, Beijing 100081, China"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-8856-2902","authenticated-orcid":false,"given":"Yueqi","family":"Cao","sequence":"additional","affiliation":[{"name":"School of Mathematics and Statistics, Beijing Institute of Technology, Beijing 100081, China"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-5473-8009","authenticated-orcid":false,"given":"Shiqiang","family":"Zhang","sequence":"additional","affiliation":[{"name":"School of Mathematics and Statistics, Beijing Institute of Technology, Beijing 100081, China"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-5871-9961","authenticated-orcid":false,"given":"Huafei","family":"Sun","sequence":"additional","affiliation":[{"name":"School of Mathematics and Statistics, Beijing Institute of Technology, Beijing 100081, China"}]}],"member":"1968","published-online":{"date-parts":[[2020,12,30]]},"reference":[{"key":"ref_1","first-page":"1013","article-title":"On the geometry of Bayesian inference","volume":"14","author":"Page","year":"2017","journal-title":"Bayesian Anal."},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"545","DOI":"10.1016\/0005-1098(90)90025-D","article-title":"Recursive nonlinear estimation: A geometric approach","volume":"26","author":"Kulhavy","year":"1990","journal-title":"Automatica"},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"836","DOI":"10.1214\/aoms\/1177703583","article-title":"Invariant prior distributions","volume":"35","author":"Hartigan","year":"1964","journal-title":"Ann. 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Model."}],"container-title":["Entropy"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/1099-4300\/23\/1\/45\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T10:47:58Z","timestamp":1760179678000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/1099-4300\/23\/1\/45"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2020,12,30]]},"references-count":20,"journal-issue":{"issue":"1","published-online":{"date-parts":[[2021,1]]}},"alternative-id":["e23010045"],"URL":"https:\/\/doi.org\/10.3390\/e23010045","relation":{},"ISSN":["1099-4300"],"issn-type":[{"type":"electronic","value":"1099-4300"}],"subject":[],"published":{"date-parts":[[2020,12,30]]}}}