Bayesian inferential framework for diagnosis of non-stationary systems

Smelyanskiy, Vadim N. and Luchinsky, Dmitry G. and Duggento, Andrea and McClintock, Peter V. E. (2007) Bayesian inferential framework for diagnosis of non-stationary systems. In: Noise and Fluctuations in Biological, Biophysical, and Biomedical Systems. PROCEEDINGS OF THE SOCIETY OF PHOTO-OPTICAL INSTRUMENTATION ENGINEERS (SPIE) . SPIE, Bellingham, Wash.. ISBN 9780819467393

Abstract

A Bayesian framework for parameter inference in non-stationary, nonlinear, stochastic, dynamical systems is introduced. It is applied to decode time variation of control parameters from time-series data modelling physiological signals. In this context a system of FitzHugh-Nagumo (FHN) oscillators is considered, for which synthetically generated signals are mixed via a measurement matrix. For each oscillator only one of the dynamical variables is assumed to be measured, while another variable remains hidden (unobservable). The control parameter for each FHN oscillator is varying in time. It is shown that the proposed approach allows one: (i) to reconstruct both unmeasured (hidden) variables of the FHN oscillators and the model parameters, (ii) to detect stepwise changes of control parameters for each oscillator, and (iii) to follow a continuous evolution of the control parameters in the quasi-adiabatic limit.