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Biometrika Advance Access originally published online on September 24, 2009
Biometrika 2009 96(4):835-845; doi:10.1093/biomet/asp047
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© 2009 Biometrika Trust

Article

Bayesian lasso regression

Chris Hans

Department of Statistics, The Ohio State University, Columbus, Ohio 43210, U.S.A. hans{at}stat.osu.edu

Received for publication 1 July 2008. Revision received 1 March 2009.
  Abstract

The lasso estimate for linear regression corresponds to a posterior mode when independent, double-exponential prior distributions are placed on the regression coefficients. This paper introduces new aspects of the broader Bayesian treatment of lasso regression. A direct characterization of the regression coefficients’ posterior distribution is provided, and computation and inference under this characterization is shown to be straightforward. Emphasis is placed on point estimation using the posterior mean, which facilitates prediction of future observations via the posterior predictive distribution. It is shown that the standard lasso prediction method does not necessarily agree with model-based, Bayesian predictions. A new Gibbs sampler for Bayesian lasso regression is introduced.

Key Words: Double-exponential distribution • Gibbs sampler • L1 penalty • Laplace distribution • Markov chain Monte Carlo • Posterior predictive distribution • Regularization


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