【摘要】 本文针对既选择组水平变量又选择组内单个变量这两种情况下的变量选择惩罚方法,从贝叶斯的角度进行分析,指出其能被表示为一个最大后验估计.之后,给出贝叶斯框架下的两种群组变量选择惩罚方法的层次模型表达形式,并给出参数估计适于Gibbs抽样的满条件分布.最后,通过模拟比较得出结论:分别用BGL、BSGL模型进行组变量选择和双层变量选择是可行的,但得到的模型在验证集上的预测误差较大.更多还原

【Abstract】 Variable selection is of great importance in statistical modeling.Actually,there exist group structures among the predictors in applications.From the point view of Bayesian analysis,this paper revealed that penalized group variable selection methods of group level selection and bi-level selection could be interpreted as a Bayesian posterior mode estimate.Next,we gave the expression form of the hierarchical model in the Bayesian framework,and gave the Gibbs sampling of parameters.Finally,the simulation results showed that the BGL and BSGL models were feasible when selecting group variable and bi-level variable,but the mean square errors was larger in the validation set.更多还原