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Doctoral Thesis
DOI
10.11606/T.55.2011.tde-12052011-152309
Document
Author
Full name
Monica Fabiana Bento Moreira Thiersch
E-mail
Institute/School/College
Knowledge Area
Date of Defense
Published
São Carlos, 2011
Supervisor
Committee
Andrade Filho, Marinho Gomes de (President)
Assis, Adriana Leandra de
Cancho, Vicente Garibay
Malheiros, Euclides Braga
Noveli, Cibele Maria Russo
Title in Portuguese
Abordagem bayesiana dos modelos de regressão hipsométricos não lineares utilizados em biometria florestal
Keywords in Portuguese
MCMC
Método bayesiano
Modelos hipsométricos
Regressão não linear
Abstract in Portuguese
Neste trabalho está sendo proposto uma abordagem bayesiana para resolver o problema de inferência com restrição nos parâmetros para os modelos de Petterson, Prodan, Stofel e Curtis, utilizados para representar a relação hipsométrica em clones de Eucalyptus sp. Consideramos quatro diferentes densidades de probabilidade a priori, entre as quais, a densidade a priori não informativa de Jeffreys, a densidade a priori vaga normal flat, uma densidade a priori construída empiricamente e a densidade a priori potência. As estimativas bayesianas foram calculadas com a técnica de simulação de Monte Carlo em Cadeia de Markov (MCMC). Os métodos propostos foram aplicados em vários conjuntos de dados reais e os resultados foram comparados aos obtidos com os estimadores de máxima verossimilhança. Os resultados obtidos com as densidades a priori não informativa e vaga foram semelhantes aos resultados encontrados com os estimadores de máxima verossimilhança, porém, para vários conjuntos de dados, as estimativas não apresentaram coerência biológica. Por sua vez, as densidades a priori informativas empírica e a priori potência sempre produziram resultados coerentes biologicamente, independentemente do comportamento dos dados na parcela, destacando a superioridade desta abordagem
Title in English
Bayesian approach for the nonlinear regressian models used in forest biometrics
Keywords in English
Bayesian approach
Hypsometric models
MCMC
Nonlinear regressian
Abstract in English
In this work we propose a Bayesian approach to solve the inference problem with restriction on parameters for the models of Petterson, Prodan, Stofel and Curtis used to represent the hypsometric relationship in clones of Eucalyptus sp. We consider four different prior probability densities, the non informative Jeffreys prior, a vague prior with flat normal probability density, a prior constructed empirically and a power prior density. The Bayesian estimates were calculated using the Monte Carlo Markov Chain (MCMC) simulation technique. The proposed methods were applied to several real data sets and the results were compared to those obtained with the maximum likelihood estimators. The results obtained with a non informative prior and prior vague showed similar results to those found with the maximum likelihood estimators, but, for various data sets, the estimates did not show biological coherence. In turn, the methods a prior empirical informative and a prior power, always produce biologically consistent results, regardless of the behavior of the data in the plot, highlighting the superiority of this approach
 
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Publishing Date
2011-05-12
 
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