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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Vydané v:	Journal of the American Statistical Association Ročník 103; číslo 482; s. 681 - 686
Hlavní autori:	Park, Trevor, Casella, George
Médium:	Journal Article
Jazyk:	English
Vydavateľské údaje:	Alexandria, VA Taylor & Francis 01.06.2008 American Statistical Association Taylor & Francis Ltd
Predmet:	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
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Popis
Shrnutí:	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.
Bibliografia:	ObjectType-Article-1 SourceType-Scholarly Journals-1 ObjectType-Feature-2 content type line 14 ObjectType-Feature-1 ObjectType-Article-2 content type line 23
ISSN:	0162-1459 1537-274X
DOI:	10.1198/016214508000000337