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Table 1 Schematic description of the PF algorithm

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