Bayesian Reference Analysis for the Generalized Normal Linear Regression Model

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...

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Bibliographic Details
Published in:Symmetry (Basel) 2021-05, Vol.13 (5), p.856
Main Authors: Tomazella, Vera Lucia Damasceno, Jesus, Sandra Rêgo, Gazon, Amanda Buosi, Louzada, Francisco, Nadarajah, Saralees, Nascimento, Diego Carvalho, Rodrigues, Francisco Aparecido, Ramos, Pedro Luiz
Format: Article
Language:English
Subjects:
Bayesian analysis
Bayesian inference
Eucalyptus
generalized normal linear regression model
Jeffreys prior
Kullback–Leibler divergence
Markov analysis
Markov chains
Normal distribution
normal linear regression model
Parameter estimation
Random variables
reference prior
Regression analysis
Regression models
Social exclusion
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Summary: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.
ISSN:2073-8994
2073-8994
DOI:10.3390/sym13050856