LASSO can be viewed as MAP of regression with Laplace prior. One can in turn put a prior on on the parameter of Laplace. By doing this one can have a meaningful bimodal posterior representing if the parameter is close to 0.
In this example we estimate the mean of a Gaussian with unknown variance. We put a Laplace prior on the mean and Gamma prior on the variance. We put a Gamma prior on the parameter of Laplace.
