I want to use a LASSO prior (Laplace prior) for a location parameter $\mu$

$$\pi(\mu \mid s) = \dfrac{1}{2s}\exp\left(-\frac{\vert \mu \vert}{s}\right).$$ However, I do not know to calibrate this prior.

This is, how can I select the hyperparameter $s$?

Are there any general Bayesian criteria to make this selection?


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