{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,6,17]],"date-time":"2026-06-17T17:19:13Z","timestamp":1781716753651,"version":"3.54.5"},"reference-count":39,"publisher":"MDPI AG","issue":"5","license":[{"start":{"date-parts":[[2021,5,12]],"date-time":"2021-05-12T00:00:00Z","timestamp":1620777600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Symmetry"],"abstract":"<jats:p>This article proposes the use of the Bayesian reference analysis to estimate the parameters of the generalized normal linear regression model. It is shown that the reference prior led to a proper posterior distribution, while the Jeffreys prior returned an improper one. The inferential purposes were obtained via Markov Chain Monte Carlo (MCMC). Furthermore, diagnostic techniques based on the Kullback\u2013Leibler divergence were used. The proposed method was illustrated using artificial data and real data on the height and diameter of Eucalyptus clones from Brazil.<\/jats:p>","DOI":"10.3390\/sym13050856","type":"journal-article","created":{"date-parts":[[2021,5,12]],"date-time":"2021-05-12T22:46:14Z","timestamp":1620859574000},"page":"856","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":7,"title":["Bayesian Reference Analysis for the Generalized Normal Linear Regression Model"],"prefix":"10.3390","volume":"13","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-6780-2089","authenticated-orcid":false,"given":"Vera Lucia Damasceno","family":"Tomazella","sequence":"first","affiliation":[{"name":"Department of Statistics, Universidade Federal de S\u00e3o Carlos, S\u00e3o Paulo 13565-905, Brazil"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Sandra R\u00eago","family":"Jesus","sequence":"additional","affiliation":[{"name":"Multidisciplinary Health Institute, Federal University of Bahia, Vit\u00f3ria da Conquista, Bahia 45029-094, Brazil"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-8140-5496","authenticated-orcid":false,"given":"Amanda Buosi","family":"Gazon","sequence":"additional","affiliation":[{"name":"Department of Statistics, Universidade Federal de S\u00e3o Carlos, S\u00e3o Paulo 13565-905, Brazil"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-7815-9554","authenticated-orcid":false,"given":"Francisco","family":"Louzada","sequence":"additional","affiliation":[{"name":"Institute of Mathematical Science and Computing, University of S\u00e3o Paulo, S\u00e3o Carlos 13566-590, Brazil"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Saralees","family":"Nadarajah","sequence":"additional","affiliation":[{"name":"School of Mathematics, University of Manchester, Manchester M13 9PR, UK"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-3406-4518","authenticated-orcid":false,"given":"Diego Carvalho","family":"Nascimento","sequence":"additional","affiliation":[{"name":"Departamento de Matem\u00e1tica, Facultad de Ingenier\u00eda, Universidad de Atacama, Copiap\u00f3 1530000, Chile"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Francisco Aparecido","family":"Rodrigues","sequence":"additional","affiliation":[{"name":"Institute of Mathematical Science and Computing, University of S\u00e3o Paulo, S\u00e3o Carlos 13566-590, Brazil"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-5387-2457","authenticated-orcid":false,"given":"Pedro Luiz","family":"Ramos","sequence":"additional","affiliation":[{"name":"Institute of Mathematical Science and Computing, University of S\u00e3o Paulo, S\u00e3o Carlos 13566-590, Brazil"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"1968","published-online":{"date-parts":[[2021,5,12]]},"reference":[{"key":"ref_1","first-page":"296","article-title":"On the law of frequency of errors","volume":"31","author":"Subbotin","year":"1923","journal-title":"Math. 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