Bayesian Elastic Net based on Empirical Likelihood

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. Simulation studies and case study on air pollution data are carried and show that the proposed method performs better than the existing methods.

Simulation Study

• Generating data
  • Run R files in ./simulation/data/ to generate data for simulation studies.
• Fitting models
  • For BEN-EL, the initial step size ($\epsilon$) and penalty parameters ($\lambda_1$ and $\lambda_2$) are estimated first and they are used to fit the model. For example, for simulation 1, the initial parameters are obtained by simulation1_BENEL_parameter.R and the BEN-EL model is conducted by simulation1_BENEL.R.
  • For the other methods (BEN, BL, EN, and LADL), run the corresponding R files. For example, for the BEN model of simulation 1, run simulation1_BEN.R.
  • For summary of results, run simulation1_result.R, simulation2_result.R, and simulation3_result.R.

Air Pollution Case Study

• Run pollution.R for applications and plots. pollution.Rdata is the data file from McDonald et al. ¹.

Footnotes

1. McDonald, G. C. and Schwing, R. C. (1973) Instabilities of regression estimates relating air pollution to mortality, Technometrics, 15, 463-482. ↩