Optimal design and directional leverage with applications in differential equation models

We consider the problem of estimating input parameters for a differential equation model, given experimental observations of the output. As time and cost limit both the number and quality of observations, the design is critical. A generalized notion of leverage is derived and, with this, we define directional leverage. Effective designs are argued to be those that sample in regions of high directional leverage. We present an algorithm for finding optimal designs and then establish relationships to existing design optimality criteria. Numerical examples demonstrating the performance of the algorithm are presented.