Inferential framework for nonstationary dynamics. II. Application to a model of physiological signaling.

The problem of how to reconstruct the parameters of a stochastic nonlinear dynamical system when they are time-varying is considered in the context of online decoding of physiological information from neuron signaling activity. To model the spiking of neurons, a set of FitzHugh-Nagumo (FHN) oscillators is used. It is assumed that only a fast dynamical variable can be detected for each neuron, and that the monitored signals are mixed by an unknown measurement matrix. The Bayesian framework introduced in paper I (immediately preceding this paper) is applied both for reconstruction of the model parameters and elements of the measurement matrix, and for inference of the time-varying parameters in the nonstationary system. It is shown that the proposed approach is able to reconstruct unmeasured (hidden) slow variables of the FHN oscillators, to learn to model each individual neuron, and to track continuous, random, and stepwise variations of the control parameter for each neuron in real time.