Bayesian estimation of nonlinear models parameters in the description of growth coffee fruits
Conteúdo do artigo principal
Resumo
Coffee is one of the main products of Brazilian agriculture and the country is currently the largest producer and exporter in the world. The coffee fruit has a double sigmoidal growth pattern, however, as well
as in other fruits that also show such a growth pattern, the authors generally do not estimate parameters
of regression models to describe such curve. In the study of fruit growth curves, the sample size is generally small, so the estimation of the parameters should preferably be done by the Bayesian methodology,
since a priori information is incorporated, reducing the effects of having few observations. The Markov
Chain Monte Carlo algorithms are the most used computational tool in Bayesian statistics. However,
these generate dependent samples, can be complicated to implement and, mainly, to teach. There are also
other alternatives to the MCMC algorithms to obtain approximations of integrals of interest in Bayesian
inference, the main ones are based on the importance resampling techniques. The objective of this work
is to use Bayesian inference with the weighted importance resampling technique in the estimation of parameters of double sigmoidal nonlinear regression models to the description of coffee fruit growth. The
double nonlinear logistic model was used in the description of the accumulation of fresh weight in coffee
fruits. All prioris used have Beta distribution and were obtained by the called prior of specialist technique.
Bayesian methodology was efficient, since it provided parameters with practical interpretation to coffee
fruit growth, consistent with the reality. Thus, Bayesian inference by weighted importance resampling
was a good alternative for the parameters estimation of nonlinear double sigmoid regression models. The logistic model showed that the growth of coffee fruits is more intense in the first sigmoid (until 162 DAF) of the growth curve and stabilizes in its final weight after 262 daf.
Detalhes do artigo
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Referências
Allaman, I.B., Jeçihovschi, E.G. Estimation of the critical points of an epidemic by means of a Logistic growth model. Brazilian Journal of Biometrics. 40 (2), 223-241 (2022).
Blasco, A., Piles, M. & Varona, L. Bayesian analysis of the effect of selection for growth rate ongrowth curves in rabbits. Genetics Selection Evolution. 35, 21-41 (2003).
Cole, S.R., Chu. H, Greenland, S., Hamra, G., Richardson, D.B. Bayesian posterior distributions without markov chains. American Journal of Epidemiology. 175 (5), 368-375 (2012).
Cunha, A.R., Volpe, C.A. Curvas de crescimento do fruto de cafeeiro cv. Obatã IAC 1669-20 em diferentes alinhamentos de plantio. Semina: Ciencias Agrarias. 32 (1), 49-62 (2011).
Famiani, F., Casulli, V., Baldicchi, A., Battistelli, A., Moscatello, S., Walker, R.P. Developmentand metabolism of the fruit and seed of the Japanese plum Ozark premier (Rosaceae) .Journal of Plant Physiology.169 (6), 551-560 (2012).
Fernandes, F.A., Fernandes, T.J., Pereira, A.A., Meirelles, S.L.C., Costa, A.C. Growth curves of meat-producing mammals by von Bertalanffy’s model. Pesquisa Agropecuaria Brasileira. 54, e01162 (2019).
Fernandes, J.G., Silva, E.M., Ribeiro, T.D., Silva, E.M., Fernandes, T.J., Muniz, J.A. Description of the peach fruit growth curve by diphasic sigmoidal nonlinear models. Revista Brasileira de Fruticultura. 44 (3), e875 (2022).
Fernandes, T.J., Pereira, A.A., Muniz, J.A. Double sigmoidal models describing the growth of coffee berries. Ciencia Rural. 47 (08), e20160646 (2017).
Fruhalf, A.C.; Pereira, G.A.; Barbosa, A.C.M.C.; Fernandes, T.J.; Muniz, J.A. Nonlinear models in the study of the cedar diametric growth in a seasonally dry tropical forest. Revista Brasileira de Ciencias Agrarias. 15, e8558 (2020).
Garthwaite, P.H., Kadane, J.B., O’hagan, A. Statistical methods for eliciting probability distributions. Journal of the American Statistical Association. 100 (470), 680-701 (2005).
Liu, J.; Nordman, D.J., Meeker, W.Q. The Number of MCMC Draws Needed to Compute Bayesian Credible Bounds. The American Statistician. 70 (3), 275-284 (2016).
Lopes, H.F., Polson, N.G., Carvalho, C.M. Bayesian statistics with a smile: a resampling-sampling perspective. Brazilian Journal of Probability and Statistics. 26 (4), 358-371 (2012).
Martins Filho, S., Silva, F.F., Carneiro, A.P.S., Muniz, J.A. Bayesian approach in the growthcurves of two cultivars of common bean. Ciencia Rural. 38 (6), 1516-1521 (2008).
Mischan, M.M.; Passos, J.R.S.; Pinho, S.Z.; Carvalho, L.R. Inflection and stability points of diphasic logistic analysis of growth. Scientia Agricola. 72: 215-220 (2015).
Moala, F.A., Penha, D.L. Elicitation methods for Beta prior distribution. Revista Brasileira d eBiometria. 34 (1), 49-62 (2016).
Nava, A.D., Hernandes, V.A.G., Jaimes, M.N., Castro, E.H., Alvares, D.V., Villasenor, G.D.,Alberto, F.P., Lagunas, B.C. Growth kinetics of vegetative and reproductive organs of guava (Psidium guajava L.) in Iguala Guerrero, Mexico. Agricultural Sciences. 5, 1468-1475 (2014).
Nunes, F.L., Camargo, M.B.P., Fazuoli, L.C., Rolim, G.S., Pezzopane, J.R.M. Agrometeorological models to estimate the duration of flowering-maturation stage for three arabica coffeecultivars. Bragantia. 69(4), 1011-1018 (2010).
Oliveira, A.C.R, Cecon, P.R., Puiatti, G.A., Guimarães, M.E.S., Cruz, C.D., Finger, F.L.,Nascimento, M., Puiatti, M., Lacerda, M.S. Nonlinear models based on quantiles in the fitting of growth curves of pepper genotypes. Brazilian Journal of Biometrics. 39(3), 447-459 (2021).
Pensar, J., Xu, Y., Puranen, S., Pesonen, M., Kabashima, Y., Corander, J. High-dimensionalstructure learning of binary pairwise Markov networks: A comparative numerical study.Com-putational Statistics and Data Analysis.141, 62-76 (2020).
Pereira, A.A., Silva, E.M., Fernandes, T.J., Morais, A.R., Safadi, T., Muniz, J.A. Bayesian modeling of the coffee tree growth curve. Ciencia Rural. 52 (09), e20210275 (2022).
Peres, M.V.O., Oliveira, R.P., Achcar, J.A., Nunes, A.A. Case-fatality rate by Covid-19: a hierarchical bayesian analysis of countries in different regions of the word. Brazilian Journal ofBiometrics. 40 (2), 198-212 (2022).
Pinheiro, J., Bates, D., DebRoy, S., Sarkar, D.,NLME: Linear and Nonlinear Mixed EffectsModels. R package version3. 1-155, https://CRAN.R-project.org/package=nlme, (2022).
Plummer, M., Best, N., Cowles, K., Vines, K.,CODA: Convergence Diagnosis and Output Anal-ysis for MCMC, R News, vol6, 7-11, (2006).
R Core Team.R: A language and environment for statistical computing. R Foundation for Statistical Computing, Vienna, Austria. https://www.R-project.org/, (2022).
Salles, T.T.; Beijo, L.A.; Nogueira, D.A.; Almeida, G.C.; Martins, T.B.; Gomes, V.S. Modelling the growth curve of Santa Ines sheep using Bayesian approach. Livestock Science. 239: e104115 (2020).
Santos, M.A., Megguer, C.A., Costa, A.C., Lima, J.S. Growth and development of gabiroba Campomanesia adamantium (Cambess.) O. Berg fruits. African Journal of Agricultural Research. 10 (14), 1765-1772 (2015).
Silva, E.M., Fruhalf, A.C., Silva, E.M., Muniz, J.A., Fernandes, T.J., Silva, V.F. Evaluation ofthe critical points of the most adequate nonlinear model in adjusting growth data of “greendwarf ” coconut fruits. Revista Brasileira de Fruticultura., v.43(1), e-726 (2021).
Silva, E.M., Tadeu, M.H., Silva, V.F., Pio, R., Fernandes, T.J., Muniz, J.A. Description of blackberry fruit growth by nonlinear regression models. Revista Brasileira de Fruticultura. 42(2),e-177 (2020).
Smith, A.F.M., Gelfand, A.E. Bayesian statistics without tears: a sampling-resampling perspec-tive. The American Statistician. 46 (2), 84-88 (1992).
Straub, D., Papaioannou, I. Bayesian updating with structural reliability methods. Journal of Engineering Mechanics. 141 (3), 1-13 (2015).
Teixeira, G.L.; Fernandes, T.J.; Muniz, J.A., Souza, F.A.C., Moura, R.S., Melo, R.M.P.S. Growth curves of campolina horses using nonlinear models. Livestock Science. 251: e104631(2021).
VanDerwerken, D., Schmidler, S.C. Monitoring Joint Convergence of MCMC Samplers. Journal of Computational and Graphical Statistics. 26 (3), 558-568 (2017).
Voltolini, G.B.; Silva, L.C.; Alecrim, A.O.; Castanheira, D.T.; Resende, L.S.; Rezende, T.T.;Guimarães, R.J. Soil chemical attributes in coffee growing with diferent agronomic techniques. Coffee Science. 15: e151689 (2020).
Witmer, J. Bayes and MCMC for Undergraduates. The American Statistician.71 (3), 259-264 (2017).
Zheng, Y., Zhu, J. Markov chain Monte Carlo for a Spatial-Temporal Autologistic Regression Model. Journal of Computational and Graphical Statistics. 17 (1), 123-137 (2012).