Bayesian Reference Analysis for the Generalized Normal Linear Regression Model

Tomazella, Vera Lucia Damasceno; Jesus, Sandra Rêgo; Gazon, Amanda Buosi; Louzada, Francisco; Nadarajah, Saralees; Nascimento, Diego Carvalho; Rodrigues, Francisco Aparecido; Ramos, Pedro Luiz

doi:10.3390/sym13050856

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Bayesian Reference Analysis for the Generalized Normal Linear Regression Model

Vera Lucia Damasceno Tomazella

^1,*,†

^2,†,

^1,†

^3,†

^4,†,

Diego Carvalho Nascimento

^5,†

Francisco Aparecido Rodrigues

^3,† and

Pedro Luiz Ramos

^3,*,†

Department of Statistics, Universidade Federal de São Carlos, São Paulo 13565-905, Brazil

Multidisciplinary Health Institute, Federal University of Bahia, Vitória da Conquista, Bahia 45029-094, Brazil

Institute of Mathematical Science and Computing, University of São Paulo, São Carlos 13566-590, Brazil

⁴

School of Mathematics, University of Manchester, Manchester M13 9PR, UK

⁵

Departamento de Matemática, Facultad de Ingeniería, Universidad de Atacama, Copiapó 1530000, Chile

Authors to whom correspondence should be addressed.

^†

These authors contributed equally to this work.

Academic Editor: Christophe Chesneau

Symmetry 2021, 13(5), 856; https://doi.org/10.3390/sym13050856

Received: 9 April 2021 / Revised: 26 April 2021 / Accepted: 29 April 2021 / Published: 12 May 2021

(This article belongs to the Special Issue Symmetry in Statistics and Data Science)

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Abstract

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–Leibler divergence were used. The proposed method was illustrated using artificial data and real data on the height and diameter of Eucalyptus clones from Brazil. View Full-Text

Keywords: Bayesian inference; generalized normal linear regression model; normal linear regression model; reference prior; Jeffreys prior; Kullback–Leibler divergence

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MDPI and ACS Style

Tomazella, V.L.D.; Jesus, S.R.; Gazon, A.B.; Louzada, F.; Nadarajah, S.; Nascimento, D.C.; Rodrigues, F.A.; Ramos, P.L. Bayesian Reference Analysis for the Generalized Normal Linear Regression Model. Symmetry 2021, 13, 856. https://doi.org/10.3390/sym13050856

AMA Style

Tomazella VLD, Jesus SR, Gazon AB, Louzada F, Nadarajah S, Nascimento DC, Rodrigues FA, Ramos PL. Bayesian Reference Analysis for the Generalized Normal Linear Regression Model. Symmetry. 2021; 13(5):856. https://doi.org/10.3390/sym13050856

Chicago/Turabian Style

Tomazella, Vera L.D., Sandra R. Jesus, Amanda B. Gazon, Francisco Louzada, Saralees Nadarajah, Diego C. Nascimento, Francisco A. Rodrigues, and Pedro L. Ramos 2021. "Bayesian Reference Analysis for the Generalized Normal Linear Regression Model" Symmetry 13, no. 5: 856. https://doi.org/10.3390/sym13050856

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Bayesian Reference Analysis for the Generalized Normal Linear Regression Model

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