Tomi Peltola, Aki Havulinna, Veikko Salomaa, and Aki Vehtari write:
This paper describes an application of Bayesian linear survival regression . . . We compare the Gaussian, Laplace and horseshoe shrinkage priors, and find that the last has the best predictive performance and shrinks strong predictors less than the others. . . .
P.S. Here’s more horseshoe from PyStan developer Allen Riddell, who writes:
Betting that only a subset of the explanatory variables are useful for prediction is a bet on sparsity. A popular model making this bet is the Lasso or, less handily, L1-regularized regression. A Bayesian competitor to the Lasso makes use of the “Horseshoe prior” (which I’ll call “the Horseshoe” for symmetry). This prior captures the belief that regression coefficients are rather likely to be zero (the bet on sparsity). The following shows how to use the Horseshoe in Stan.
And the Horseshoe+ prior from Anindya Bhadra, Jyotishka Datta, Nicholas Polson, and Brandon Willard, who write:
The horseshoe+ prior is a natural extension of the horseshoe prior . . . concentrates at a rate faster than that of the horseshoe in the Kullback-Leibler (K-L) sense . . . lower mean squared error . . . In simulations, the horseshoe+ estimator demonstrates superior performance in a standard design setting against competing methods, including the horseshoe and Dirichlet-Laplace estimators. . . .
And they too have R and Stan code!