  This paper develops a slice sampler for Bayesian linear regression models
with arbitrary priors. The new sampler has two advantages over current
approaches. One, it is faster than many custom implementations that rely on
auxiliary latent variables, if the number of regressors is large. Two, it can
be used with any prior with a density function that can be evaluated up to a
normalizing constant, making it ideal for investigating the properties of new
shrinkage priors without having to develop custom sampling algorithms. The new
sampler takes advantage of the special structure of the linear regression
likelihood, allowing it to produce better effective sample size per second than
common alternative approaches.
