Bayesian estimation of nonlinear models parameters in the description of growth coffee fruits

Abstract

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.