Interpretation of non-parametric estimates of time-varying systems

There are numerous approaches to estimating the dynamics of time-varying systems. Ensemble approaches are especially suited for estimating time-varying biological systems as they require no assumptions about the time-varying behavior of the system being estimated. In this paper we evaluate the ability of non-parametric ensemble methods to estimate time-varying changes in the underlying parameters of a dynamic system. Using simulated data we determined that the estimated static gain of the system was filtered by the dynamics of the system. Furthermore, when the underlying parameters of the system changed in a step-wise fashion, the parameters estimated from the identified non-parametric impulse or frequency response functions did not match the simulated model parameters for a time corresponding to the transient response of the simulated system. These findings show that a system with time-varying parameters cannot be represented by a series of impulse or frequency responses characterized by parameters that match the values and time course of the underlying system. Thus, underlying system parameters cannot be inferred directly from non-parametric time-varying estimates, as they can be in a time-invariant case. These results have important implications for understanding the parametric variations associated with time-varying systems that are best studied using non-parametric approaches, such as many biological systems.