From: Modeling brain connectivity dynamics in functional magnetic resonance imaging via particle filtering
Input the BOLD fMRI data series | \(\mathbf{x }_t\) |
Set the number of particles | N (\(=2000\) in our case) |
Set starting point for coefficients values | \(\mathbf{a }_{t=0}=0\) |
Start PF | for \(t=1:T\) |
updating step | generate N particles from previous coefficients’ values through \(a_{ij}(t)=a_{ij}(t-1)+\nu _{ij}(t)\) |
estimation step | predict the values of the observations at time t from values at time \(t-1\) with \(\mathbf{x }(t)=\mathbf{a }(t)\mathbf{x }(t-1)+{\varvec{\eta }}(t)\) compute the likelihood between predicted values and observed values with (6) normalize the weights and resample |
End PF | end for on t |