Hierarchical Models and Bayesian Analysis for Field Experiments.

,Although Bayesian Statistics is very logical and intuitive and has a wide range of applications in agriculture, its use among agronomists is still very low. The major obstacle for wider adoption of Bayesian methodologies include the amount of computer time required to generate results and some in-depth theoretical and practical knowledge to conduct analyses. This presentation will show examples of one type of hierarchical model with Bayesian Analysis for several different on-farm experiments. Since hierarchical models are extensions of mixed effects linear models where multiple sources of variation are modeled at different scales, Bayesian statistics is a very convenient way to estimate model parameters where priors are derived from the data. The emphasis of this presentation will be on estimating parameters of posterior predictive distributions of yield responses to different treatments, which enable probabilistic inferences for situations in similar or future conditions given the observed data and prior distributions. The benefits of these analyses are in better utilization of unbalanced, messy or limited data, and better estimation of the effect of covariates observed at different scales. Bayesian probabilistic inferences are especially versatile for developing decision support and risk assessment tools, which are ideally suited for on-farm situations.