Response surface approximation in Bayesian decision analysis using a multidimensional cubic spline: application to Lake Erie ecosystem management

In practical decision analysis, the "curse of dimensionality" entails making simplifying assumptions that can introduce errors into estimates of various indices that interest decision-makers. These indices include the expected performance of optimal and sub-optimal strategies; the benefit of explicitly considering uncertainty; and the benefit of additional information. This study quantifies the effects of simplifying assumptions on these indices of interest. To reduce errors arising form discretization of the decision space, we propose a multidimensional cubic spline for interpolating the performance of alternatives between a few simulated points. A case study analyzes decisions concerning phosphorous loading, fisheries management, and lower trophic research projects in Lake Erie under multiple objectives and ecological uncertainties. Results show that spline-based solutions often yield potentially superior decisions from those based on discretized-decision spaces.