It is thereby clear that there is far more mass centered at zero for the Laplacian prior, given an equal standard deviation. It is worth noting that given Laplacian prior our objective is not differentiable at zero, and so any gradient descent approaches have to be applied with care. This is only mentioned in passing, as again we aren't pursuing an optimisation/point-estimate model.

Given some parametisation of our prior weight distribution we can then begin to formulate our approach.