  We propose a Bayesian elastic net that uses empirical likelihood and develop
an efficient tuning of Hamiltonian Monte Carlo for posterior sampling. The
proposed model relaxes the assumptions on the identity of the error
distribution, performs well when the variables are highly correlated, and
enables more straightforward inference by providing posterior distributions of
the regression coefficients. The Hamiltonian Monte Carlo method implemented in
Bayesian empirical likelihood overcomes the challenges that the posterior
distribution lacks a closed analytic form and its domain is nonconvex. We
develop the leapfrog parameter tuning algorithm for Bayesian empirical
likelihood. We also show that the posterior distributions of the regression
coefficients are asymptotically normal. Simulation studies and real data
analysis demonstrate the advantages of the proposed method in prediction
accuracy.
