Sparse Regression Modeling via the Map Bayesian Lasso

Abstract

Sparse regression procedures that are typified by the lasso enable us to perform variable selection and parameter estimation simultaneously. However, the lasso does not give the estimate of error variance, and also the tuning parameter selection still remains an important issue. On the other hand, although the Bayesian lasso can determine the estimate of error variance and the value of a tuning parameter as some Bayesian point estimates, it is difficult to derive sparse solution for the estimates of regression coefficients. To overcome these drawbacks, we propose a MAP Bayesian lasso by using the Monte Carlo integration for the posterior approximation. Monte Carlo simulations and real data examples are conducted to examine the efficiency of the proposed procedure.