Bayesian Elastic Net based on Empirical Likelihood

TL;DR

This paper introduces a Bayesian elastic net model that incorporates empirical likelihood and employs a tuned Hamiltonian Monte Carlo method for efficient posterior sampling, improving inference and prediction in correlated variable settings.

Contribution

It presents a novel Bayesian elastic net framework based on empirical likelihood with an optimized HMC sampling technique, relaxing error distribution assumptions.

Findings

Performs well with highly correlated variables

Provides asymptotically normal posterior distributions

Enhances prediction accuracy in simulations and real data

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.