Nonlinear slight parameter changes detection

Abstract

In many biological systems it is crucial to detect changes, as accurate as possible, in the parameters that govern their dynamics. In this work we propose a new method to perform an online automatic detection of such changes, making use of a well known nonlinear fore- casting algorithm. The approach takes advantage of the characterization of an interval of a signal by the reconstruction of its phase space through time-delay embedding. To this end, the optimal delay and embedding dimension are estimated, and a method is proposed for determining the forecasting parameters, after which it is possible to predict future values of the studied signal. In this novel approach the method is used as a way of detecting changes in the dynamics of a system, given that the forecast is performed using a template of the signal where its parameters remain constant. At this point, the measure of the prediction error is used to detect a change in the dynamics of the system. We also propose a second estimator of this change, namely prediction failure, which is a stronger binary estimator of change in the dynamics. The results are analyzed by a cumulative sum algorithm (CUSUM ) to obtain a detection point. In order to test their behavior, both methods are applied to deterministic discrete and continuos synthesized data, and to a simulated biological model.