Bayesian Inference of Time-Evolving Coupled Systems in the Presence of Noise

Abstract

A method is introduced for the analysis of interactions between time-dependent coupled oscillators, based on the signals they generate. It distinguishes unsynchronized dynamics from noise-induced phase slips, and enables the evolution of the coupling functions and other parameters to be followed. The technique is based on Bayesian inference of the time-evolving parameters, achieved by shaping the prior densities to incorporate knowledge of previous samples. The dynamics can be inferred from phase variables, in which case a finite number of Fourier base functions is used, or from state variables exploiting the model state base functions. The latter procedure is used for the detection of generalized synchronization. The method is tested numerically and applied to reveal and quantify the time-varying nature of synchronization, directionality and coupling functions from both cardiorespiratory and analogue electronic signals. It is found that, in contrast to many systems with time-invariant coupling functions, the functional relations for the interactions of an open (biological) system can in themselves be time-varying processes. The cardiorespiratory analysis demonstrated that not only the parameters, but also the functional relationships, can be time-varying, and the new technique can effectively follow their evolution.