Análise bayesiana de modelos não lineares no estudo da cinética de herbicidas

Abstract

The agricultural sector requires attention due to its susceptibility to various interfering factors, among which weeds stand out. These plants compete with crops for water, nutrients, light, and space, in addition to serving as hosts for pathogens. One of the methods used for their control is the application of herbicides, whose dose–response relationship can be described using nonlinear models. In this thesis, three articles were developed with the objective of analyzing the dose–response relationship of the herbicides trifloxysulfuron-sodium and S-metolachlor applied to weeds of the genus Amaranthus, evaluating the susceptibility of these plants to each herbicide, and identifying the most appropriate model to represent the data. To this end, the parameters of nonlinear models were estimated from a Bayesian inference perspective, adopting maximum entropy prior distributions. To obtain the posterior distributions, the Markov Chain Monte Carlo (MCMC) method was employed, using the Gibbs sampling and Metropolis– Hastings algorithms. Model selection was performed based on the Deviance Information Criterion (DIC), as well as the Conditional Predictive Ordinate (CPO) and the Log Pseudo- Marginal Likelihood (LPML) criteria. In the first article, the nonlinear models of Groot, Weibull, and logistic were fitted. In the second article, it was considered that the assumption of normality does not always reflect the actual behavior of the data, which often lack symmetry. Thus, the Streibig logistic model was fitted under four specifications for the likelihood function — normal, Weibull, gamma, and exponential. In the third article, the Streibig logistic model was applied again, comparing the likelihood functions under the normal and Student’s t distributions. The results of this thesis indicate that the Bayesian approach, combined with maximum entropy prior distributions and different specifications for the data distribution, constitutes a consistent methodological alternative for the analysis of herbicide dose–response data, expanding the possibilities for applying this approach in the field. The comparison among the models revealed differences in the susceptibility of species of the genus Amaranthus. Furthermore, the consideration of distributions alternative to the normal proved useful for data modeling. Keywords: dose–response; Bayesian inference; maximum entropy; MCMC; likelihood.