Bayesian optimal dynamic sampling procedures for on-farm field experimentation

For many decades, researchers have relied on small-scale agronomic experiments to provide input management recommendations to farmers. However, such experiments have most often provided production functions with large standard errors in addition to uncertainty about how well the estimates apply to different fields. To avoid such limitations, there has been a movement toward on-farm field experiments where experiments are conducted on the whole field. But questions remain as how best to conduct these on-farm field experiments and when it is most profitable to quit them. This study addressed these questions using a fully Bayesian decision-theoretic approach. Data were from Monte Carlo simulations assuming a linear response stochastic plateau production function from one field. Only uniform rate application was considered. The base model had corn and N prices of $0.116 kg−1 and $0.993 kg−1 and used 100 plots with an experimental design that allocated 10 plots to 0 kg of N, half of current optimal N (N*), and 150% of N*, with 70 using N*. With the base model, it was most profitable to quit such trials in year two. Sensitivity analysis suggested that the optimal strategy was to experiment on fewer plots, use levels of N closer to the optimum, and continue the experiment for longer than was done with the base model. These changes reduced losses from using nonoptimal levels of nitrogen. The assumptions used in the base model, however, might be more economical if plot sizes were small and so a smaller percentage of plots were used for experimentation.