Efficient structure-preserving numerical scheme applied to nonlinear stochastic filtering of a neural mass model
Sprache des Vortragstitels:
12th German Probability and Statistics Days 2016 - Bochumer Stochastik-Tage
Sprache des Tagungstitel:
Neural mass models provide a useful framework for modelling mesoscopic neural dynamics and in this talk we consider the Jansen and Rit Neural Mass Model (JR-NMM). This system of ODEs has been introduced as a model in the context of electroencephalography (EEG) rhythms and evoked potentials and has been proposed as an underlying model in various application settings, e.g. for detecting epileptic seizures. We formulate a stochastic version of the JR-NMM which arises by incorporating random input and has the structure of a nonlinear stochastic oscillator. We simulate the stochastic JR-NMM by an efficient numerical scheme based on a splitting approach which preserves the qualitative behaviour of the solution. The final goal is to use the stochastic JR-NMM as the underlying model in a nonlinear filtering framework in order to solve the inverse problem. In particular, we compute certain parameters of the model from simulated EEG-related data. Eventually, we take advantage of our efficient numerical method for various nonlinear stochastic filters.