Hierarchical Bayesian Estimation of a Stochastic Plateau Response Function: Determining Optimal Levels of Nitrogen Fertilization

This article seeks to determine the optimal level of nitrogen to apply to winter wheat. The article makes two methodological contributions. One is to extend the estimation of a stochastic plateau function to the case where the plateau has a beta distribution instead of a normal distribution. The second is to adapt hierarchical Bayesian methods as an alternative to the frequentist approach to estimate wheat yield response to nitrogen fertilizer. The economically optimal rate of nitrogen varies between 64 and 169 kg/ha and is consistently higher with the Bayesian method and higher under most scenarios when nonnormality is assumed for the plateau parameter. Based on the likelihood odds ratio, the normal distribution is preferred with maximum likelihood estimation. But, based on the deviance information criterion, the beta model is preferred with the Bayesian estimation.