Fully Bayesian economically optimal design for a spatially varying coefficient linear stochastic plateau model over multiple years

On-farm experimentation to guide fertilizer recommendations is a potential precision agriculture tool. There is, however, no agreement on the optimal way to conduct on-farm experimentation, which motivated this paper. Optimal on-farm experimentation is addressed using fully Bayesian decision theory. Monte Carlo integration was used, assuming a linear stochastic plateau model with spatially correlated plateau parameters. The spatially varying coefficient model was used to guide the application of site-specific nitrogen. For the Monte Carlo simulation, the true economic optimal nitrogen value was held constant in each plot. Of the designs considered, experimenting on 15 out of 100 plots of a field with treatment levels that were wider than the true optimal levels and with fewer plots at the lowest nitrogen level maximized the farmers' profit over several years. The third year was the best time to quit experimenting. Much current work experiments on the whole field. With a spatially varying coefficient model, much information is gained without experimenting on every plot. The recommended approach is thus to experiment on a few plots scattered throughout the field.