Bayesian reciprocal LASSO (BRL) is a recently proposed nonlocal regularization method for Bayesian linear regression models. This paper develops a modified version of BRL, accommodating faster posterior sampling than published methods, by bypassing the use of auxiliary latent variables. We present a slice-within-Gibbs algorithm based on the elliptical slice sampler that matches the predictive accuracy of previous BRL implementations. Simulation studies and real data analyses show that the new method (XBRL) outperforms its Bayesian cousin (BRL) in out-of-sample prediction across a wide range of scenarios while offering the advantage of faster posterior computation. We have implemented the XBRL algorithm as part of the R package BayesRecipe available at: https://github.com/himelmallick/BayesRecipe.
