A New Bayesian Lasso

• Activity Number: 352
• Type: Contributed
• Date/Time: Tuesday, July 31, 2012 : 10:30 AM to 12:20 PM
• Sponsor: Section on Bayesian Statistical Science
• Author(s): Himel Mallick*+ and Nengjun Yi
• Companies: The University of Alabama at Birmingham and The University of Alabama at Birmingham
• Keywords: LASSO ; Bayesian LASSO ; Hierarchical Model ; Penalized Regression

Abstract

The LASSO of Tibshirani (1996) has enjoyed a great deal of applicability in recent years. The LASSO estimate corresponds to the posterior mode when independent Laplace priors are assigned on the regression parameters. Park and Casella (2008) provided the Bayesian LASSO using scale mixtures of normal priors for the parameters and independent exponential priors on their variances. We propose a new hierarchical representation of Bayesian LASSO, based on the characterization of a Laplace distribution as a scale mixture of uniform and gamma. We consider a fully Bayesian treatment which leads to a new efficient Gibbs sampler in the MCMC estimation with tractable full conditional distributions. Furthermore, we develop an ECM algorithm to estimate the posterior mode of the parameters. Finally, we show how our approach can be extended to generalized linear models. We compare the performance of our method to the existing one as well as to its frequentist counterpart using simulations and real data.