Inferential framework for nonstationary dynamics. I. Theory.

A general Bayesian framework is introduced for the inference of time-varying parameters in nonstationary, nonlinear, stochastic dynamical systems. Its convergence is discussed. The performance of the method is analyzed in the context of detecting signaling in a system of neurons modeled as FitzHugh-Nagumo (FHN) oscillators. It is assumed that only fast action potentials for each oscillator mixed by an unknown measurement matrix can be detected. It is shown that the proposed approach is able to reconstruct unmeasured (hidden) variables of the FHN oscillators, to determine the model parameters, to detect stepwise changes of control parameters for each oscillator, and to follow continuous evolution of the control parameters in the adiabatic limit.