A set of Markov chain Monte Carlo algorithms that perform full Bayesian inference for the Bayesian elastic net, sampling the regression coefficients together with the penalty and error-variance parameters despite the intractable normalizing constant in the coefficient prior. A transformation of the parameter space renders the full conditional densities amenable to efficient rejection sampling, so every parameter is drawn directly with no Metropolis-within-Gibbs steps, avoiding proposal tuning and the resulting slow convergence and mixing.
This paper develops new Markov chain Monte Carlo algorithms for full Bayesian inference in the Bayesian elastic net, a regularized regression model whose coefficient prior encodes the elastic net (co…