Continuous Time Particle Filtering for fMRI

We construct a biologically motivated stochastic differential model of the neu- ral and hemodynamic activity underlying the observed Blood Oxygen Level De- pendent (BOLD) signal in Functional Magnetic Resonance Imaging (fMRI). The model poses a difficult parameter estimation problem, both theoretically due to the nonlinearity and divergence of the differential system, and computationally due to its time and space complexity. We adapt a particle filter and smoother to the task, and discuss some of the practical approaches used to tackle the difficulties, includ- ing use of sparse matrices and parallelisation. Results demonstrate the tractability of the approach in its application to an effective connectivity study.