Improving a Cross Entropy Approach to Parameter Estimation for ODEs and DDEs

We investigate and extend the cross entropy (CE) approach for parameter estimation for ODE and DDE models introduced in [27]. Software is developed to allow models to be easily specified for use with an existing package for working with DDEs. Our software implements CE and is used to explore potential improvements to the method. A 3-stage optimization procedure is presented. First, an inexpensive initial guess for some of the parameters is obtained to reduce the size of the search space. Second, a global search phase is performed to obtain an estimate for the parameters that is ‘close’ to the optimal values. Third, a local optimizer, that can converge super-linearly, is used to obtain the final estimates for the parameters. The performance of this 3-stage procedure is demonstrated by estimating parameters on several test problems from the literature. Additionally, we look at ways to reduce the computational cost of simulating the ODEs and DDEs during the estimation procedure.