Bayesian Elastic Net based on Empirical Likelihood
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Empirical likelihood is a popular nonparametric method for inference and estimation. In this article, we propose a Bayesian elastic net model that is based on empirical likelihood for variable selection. The proposed method incorporates interpretability and robustness from Bayesian empirical likelihood approach. We derive asymptotic distributions of coefficients for credible intervals. The posterior distribution of Bayesian empirical likelihood does not have a closed-form analytic expression and has nonconvex domain, which causes implementation of MCMC challenging. To solve this problem, we implement the Hamiltonian Monte Carlo approach. Simulation studies and real data analysis demonstrate the advantages of the proposed method in variable selection and prediction accuracy.
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