Bayesian Reference Analysis for the Generalized Normal Linear Regression Model

Symmetry

DiegoCarvalho Nascimento¹  AmandaBuosi Gazon²  VeraLucia Damasceno Tomazella²  Francisco Louzada³  FranciscoAparecido Rodrigues³  PedroLuiz Ramos³  SandraRêgo Jesus⁴  Saralees Nadarajah⁵ 

[1] Departamento de Matemática, Facultad de Ingeniería, Universidad de Atacama, Copiapó 1530000, Chile;Department of Statistics, Universidade Federal de São Carlos, São Paulo 13565-905, Brazil;Institute of Mathematical Science and Computing, University of São Paulo, São Carlos 13566-590, Brazil;Multidisciplinary Health Institute, Federal University of Bahia, Vitória da Conquista, Bahia 45029-094, Brazil;School of Mathematics, University of Manchester, Manchester M13 9PR, UK;

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

DOI  :  10.3390/sym13050856

来源: DOAJ

【 摘 要 】

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.

【 授权许可】

Unknown