Inferential framework for nonstationary dynamics. I. Theory

Dmitri G. Luchinsky, Vadim N. Smelyanskiy, Andrea Duggento, and Peter V. E. McClintock
Phys. Rev. E 77, 061105 – Published 4 June 2008

Abstract

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.

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  • Received 30 January 2008

DOI:https://doi.org/10.1103/PhysRevE.77.061105

©2008 American Physical Society

Authors & Affiliations

Dmitri G. Luchinsky1,2, Vadim N. Smelyanskiy1, Andrea Duggento2, and Peter V. E. McClintock2

  • 1NASA Ames Research Center, Mail Stop 269-2, Moffett Field, California 94035, USA
  • 2Department of Physics, Lancaster University, Lancaster LA1 4YB, United Kingdom

See Also

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

Andrea Duggento, Dmitri G. Luchinsky, Vadim N. Smelyanskiy, Igor Khovanov, and Peter V. E. McClintock
Phys. Rev. E 77, 061106 (2008)

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Vol. 77, Iss. 6 — June 2008

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