A procedure for ranking parameter importance for estimation in predictive mechanistic models

We begin with a mechanistic model that is considered to be a reasonably good predictor of the real-life system with a set of parameters determined from prior biophysical studies and expert knowledge. For complex mechanistic growth models, it is usually advantageous to numerically estimate a subset of the ‘most important’ parameters (i.e., those that most influence dynamic model behavior) based on data and fix the others at their estimated a priori values. Determining a reduced-order parameter subset for end-user estimation can be challenging, often relying heavily on expert knowledge and trial-and-error. A straightforward but oversimplified method relies on one-at-a-time (OAT) sensitivity of model outputs to changes in individual parameters. However, this commonly used method fails to account for how simultaneous changes in multiple parameters can significantly impact model outputs in unpredictable ways due to model nonlinearities. Additionally, hidden relationships between parameters can prevent consistent identifiability of parameters from different initial estimates. Rather than analyzing the effect of individual parameter variation on the model outputs, we evaluate the importance of parameters to the curvature of the quadratic cost function (sum squared difference between reference and model output sequences). This analysis is carried out by calculating the matrix of second-order partial derivatives of the cost function (aka Hessian matrix) with respect to the model parameters. Calculating the cost function Hessian allows analysis of changes in multiple parameters simultaneously. The method is presented as an analytic, reproducible procedure for determining a ranking for parameter importance. The procedure is demonstrated on a limited version of the Yield-SAFE predictive agroforestry growth model. For the analysis, 12 model parameters are considered with their nominal values set to those given in a published implementation of Yield-SAFE. The Hessian was calculated at 212 ( = 4096) locations systematically selected in the neighborhood of the nominal parameter setting, each generating a parameter ranking determined by the relative contribution of each parameter to the cost function curvature. The top ranked 6 parameters were the same for 4091 of 4096 locations, suggesting that this procedure has potential to guide modelers in recommending the most important parameters for estimation given reasonably good initial parameter estimates and real data.