Efficient and structure-preserving numerical scheme applied to a continuous-time particle filter for a stochastic neural mass model
Sprache des Vortragstitels:
4th Austrian Stochastics Days
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 used for several applications, e.g. for detecting epileptic diseases. We propose 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. We take advantage of our efficient numerical method in order to solve the inverse problem by a continuous-time particle filter.