Bayesian Modelling of the effects of nitrogen doses on the morphological characteristics of braquiaria grass

Abstract

The Bayesian approach in regression models has shown good results in parameter estimations, where it can increase accuracy and precision. The objective of the current study was to analyze the application of Bayesian statistics to the modeling yield for leaf dry matter (LM) and stem (SM), in kg ha-1, leaf ratio (LR), crude protein content for leaves (CPL) and stem (CPS) (%) of Brachiaria grass as a function of varying N doses (0; 100; 200 and 300 kg ha-1 yr-1). Simple and two degree polynomial linear regression models were analyzed. Information for a priori distributions was obtained from the literature. A posteriori distribution was generated using a Monte Carlo method via Markov chains. Parameters significance was assyed with HPD (Highest Posteriori Density) with a 95% interval. Model selections was performed using DIC (Deviance Information Criterion); and adjustment quality estimated with means and 95% HPD for Bayesian R2 distribution ranges. The models selected for the variables LM, SM and CPS were linear, while for LR and CPL, they were second level polynomial. The lowest doses that maximize response variables were: LM: 274 ha-1yr-1, SM: 280 ha-1yr-1, LR: 113 ha-1yr-1, CPL: 265 ha-1yr-1, CPS: 289 ha-1yr-1. The Bayesian approach allowed the inclusion of literatureverified a priori information, and the identification of evidence optimization range intervals.

Keywords

• Bayes factor. Regression models. A priori information. Optimization.