Bayesian elastic net based on empirical likelihood

Abstract

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.

Keywords:

• Bayesian empirical likelihood
• Hamiltonian Monte Carlo
• variable selection

Disclosure statement

No potential conflict of interest was reported by the author(s).

Data availability statement

All data used in simulation studies are generated randomly and the air pollution data are obtained from McDonald et al. [62]. The R code used to generate, import, and analyse the data used in this paper is publicly available at the URL: https://github.com/chulmoon/BEN-EL.