A model-based initial guess for estimating parameters in systems of ordinary differential equations

The inverse problem of parameter estimation from noisy observations is a major challenge in statistical inference for dynamical systems. Parameter estimation is usually carried out by optimizing some criterion function over the parameter space. Unless the optimization process starts with a good initial guess, the estimation may take an unreasonable amount of time, and may converge to local solutions, if at all. In this article, we introduce a novel technique for generating good initial guesses that can be used by any estimation method. We focus on the fairly general and often applied class of systems linear in the parameters. The new methodology bypasses numerical integration and can handle partially observed systems. We illustrate the performance of the method using simulations and apply it to real data.