  In the literature surrounding Bayesian penalized regression, the two primary
choices of prior distribution on the regression coefficients are zero-mean
Gaussian and Laplace. While both have been compared numerically and
theoretically, there remains little guidance on which to use in real-life
situations. We propose two viable solutions to this problem in the form of
prior distributions which combine and compromise between Laplace and Gaussian
priors, respectively. Through cross-validation the prior which optimizes
prediction performance is automatically selected. We then demonstrate the
improved performance of these new prior distributions relative to Laplace and
Gaussian priors in both a simulated and experimental environment.
