Time Window Determination for Inference of Time-Varying Dynamics: Application to Cardiorespiratory Interaction

Towards a Protocol for Adaptive Dynamical Bayesian Inference: Case of Limit-Cycle Oscillators

“…If a wide block of inference is used, only few points would be obtained and the time-variability of the parameters would be missed. For this reason, in the algorithm proposed in [20] the optimal time window is chosen as one eight of the period of the fastest changing parameter. In this way there will be 8 data points (8 inference blocks) describing one full oscillation of the fastest changing parameter.…”

“…The frequency of the fastest changing parameter is obtained by performing an initial inference with a fixed, reasonably large, propagation parameter and a time window as small as possible [20]. In this way, the best possible inference of the time variability is achieved, at the expense of greater noise.…”

“…At the same time, the propagation parameter should be greater than 1/tw,opt, in order not to enter the delayed inference regime. In order to test whether the proposed algorithm in [20] is valid for the case of coupled Poincarè oscillators, we investigated the difference between the inferred time varying parameters and their true values for different strengths of the noise and for different frequencies of the time varying parameters, corresponding to the frequency range of the cardiorespiratory interactions. We evaluated this difference by calculating the mean square error (MSE) between the time series of the inferred parameters with optimal time windows tw,opt and their true values at the corresponding times.…”

“…In the earlier applications of the method of dynamical Bayesian inference [8], [6], [24 -26] the time window and the propagation parameter were arbitrarily selected, based on the experience of the investigator. Recently we proposed a method for adaptive determination of these parameters [20]. The method is based on analysis of systems of two coupled oscillators in the presence of noise.…”

“…How much of the information is propagated from the previous to the next block of inference is determined by the so-called propagation parameter of the covariance matrix. In [20] we proposed a method for determining these two parameters within the dynamical Bayesian inference. In this paper we give further details on testing this method on a system of coupled limit cycle oscillators.…”