Nonlinear slight parameter changes detection: a forecasting approach

Abstract

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 forecasting 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

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