Thanks for the suggestions, Rutvik!

Dealing with behavioral data is way much easier because you see those numbers right in front of you, and easily compare the consequences when removing/replacing potential outliers. With massive data in FMRI analysis, things are pretty complicated, and it'd be a little troubling if we simply remove/replace outliers blindfold. If it's one or a couple of subjects that uniformly have outliers across the whole brain, life is easy. But more likely we'll have some or all subjects with outliers here and there in the brain. It might be fine to remove/replace those voxels whose beta goes 2 standard deviations above the mean. How about those 2 standard deviations below the mean? Such a binary decision is also a little problematic: would a beta 1.9 SDs above the mean be OK to keep?

Instead of simple purging, I'm thinking along the line of modeling them, but this involves a lot theoretical work (and programming too), and I don't know if it's going to work or not at this point.

Gang