A technique for the sensitivity analysis of functions in relation to decision-making objectives

Sensitivity analysis is usually focussed on parameters and is a relatively well-developed field compared with function sensitivity. But how sensitive are model conclusions to the choice of functions used in the right hand side of differential equation models? Most work in this area has been scenario-based where alternative functions are tested. In this paper, we examine the sensitivity of a model to changes in the shape of the functions. We do this in an automated way without the need to specify alternative functional forms. The question then is how much can we change a function that defines the dynamics of the system without producing a significant change in some performance measure? If the changes in functions need to be large in some sense, to cause significant changes in a performance measure, then there is less need to focus attention on getting the model functions correct. A method of approach to this type of analysis is presented and illustrated on an ecosystem model. Testing the proposed method on a simple model demonstrates that quite large changes can be made to functions before reaching a critical value in the decision criterion. This insight is as useful as the corresponding knowledge of the effect of uncertainty in parameter values. 1