Two-Stage Least Squares or Gradient Matching

Abstract

This chapter presents indirect methods of fitting parameters to ordinary differential equation models. Rather than solving the ODE, we instead obtain non-parametric estimates of the state trajectory and its derivative. This allows the right hand side of the ODE to be fit to the estimated derivatives, which is often numerically easier than the trajectory matching described in Chap. 7. We discuss the ways in which this approach allows us to diagnose model mis-specification, and develop confidence intervals for parameters. We also examine the related approach of fitting the trajectory to the integral of the right hand side function.