The Bayesian Lasso

The Lasso estimate for linear regression parameters can be interpreted as a Bayesian posterior mode estimate when the regression parameters have independent Laplace (i.e., double-exponential) priors. Gibbs sampling from this posterior is possible using an expanded hierarchy with conjugate normal pri...

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Bibliographic Details
Published in:Journal of the American Statistical Association Vol. 103; no. 482; pp. 681 - 686
Main Authors: Park, Trevor, Casella, George
Format: Journal Article
Language:English
Published: Alexandria, VA Taylor & Francis 01.06.2008
American Statistical Association
Taylor & Francis Ltd
Subjects:
Algorithms
Analytical estimating
Applications
Bayes estimators
Bayesian analysis
Bayesian method
Diabetes
Empirical Bayes
Estimation methods
Exact sciences and technology
General topics
Gibbs sampler
Hierarchical model
Hierarchies
Inverse Gaussian
Least squares
Linear inference, regression
Linear models
Linear regression
Logic and foundations
Mathematical logic, foundations, set theory
Mathematics
Maximum likelihood estimation
Musical intervals
Normal distribution
Parameter estimation
Parameter modification
Penalized regression
Probability and statistics
Recursion theory
Regression
Regression analysis
Robustness (mathematics)
Sampling
Scale mixture of normals
Sciences and techniques of general use
Statistical analysis
Statistical discrepancies
Statistical median
Statistical methods
Statistics
Structural hierarchy
Theory and Methods
United States > US
Rank statistic
Conditional distribution
Gaussian distribution
Variance
Parametric method
Empirical Bayes
Distribution function
Penalized regression
Posterior distribution
Likelihood function
Variable selection
Bayes estimation
Covariance analysis
Prior distribution
Linear regression
Inverse Gaussian
Gibbs sampling
Variance analysis
Hierarchized structure
Statistical method
Statistical regression
Selection problem
Gibbs sampler
Hierarchical model
Scale mixture of normals
Inverse normal distribution
Application
ISSN:0162-1459, 1537-274X
Online Access:Get full text
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Description
Summary:The Lasso estimate for linear regression parameters can be interpreted as a Bayesian posterior mode estimate when the regression parameters have independent Laplace (i.e., double-exponential) priors. Gibbs sampling from this posterior is possible using an expanded hierarchy with conjugate normal priors for the regression parameters and independent exponential priors on their variances. A connection with the inverse-Gaussian distribution provides tractable full conditional distributions. The Bayesian Lasso provides interval estimates (Bayesian credible intervals) that can guide variable selection. Moreover, the structure of the hierarchical model provides both Bayesian and likelihood methods for selecting the Lasso parameter. Slight modifications lead to Bayesian versions of other Lasso-related estimation methods, including bridge regression and a robust variant.
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ISSN:0162-1459
1537-274X
DOI:10.1198/016214508000000337