Duggento, A. and Luchinsky, D. G. and Smelyanskiy, V. N. and McCkintock, P. V. E. (2009) Inferential framework for non-stationary dynamics : theory and applications. Journal of Statistical Mechanics: Theory and Experiment, 2009 (1): P01025.
Abstract
An extended Bayesian inference framework is presented, aiming to infer time-varying parameters in non-stationary nonlinear stochastic dynamical systems. The convergence of the method is discussed. The performance of the technique is studied using, as an example, signal reconstruction for a system of neurons modeled by FitzHugh–Nagumo oscillators: it is applied to reconstruction of the model parameters and elements of the measurement matrix, as well as to inference of the time-varying parameters of the non stationary system. It is shown that the proposed approach is able to reconstruct unmeasured (hidden) variables of the system, to determine the model parameters, to detect stepwise changes of control parameters for each oscillator and to track the continuous evolution of the control parameters in the adiabatic limit.