先验概率
Lasso(编程语言)
贝叶斯线性回归
吉布斯抽样
数学
贝叶斯概率
共轭先验
统计
后验概率
贝叶斯分层建模
贝叶斯推理
计算机科学
万维网
作者
Trevor Park,George Casella
标识
DOI:10.1198/016214508000000337
摘要
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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