統計学輪講（第８回）

統計学輪講（第8回）
日時      2014年06月10日(火)    14時50分～16時30分
場所      経済学部新棟３階第３教室
講演者    Malay Ghosh (Professor, University of Florida)
演題      Bayesian Variable Selection and Estimation for Group Lasso

概要
The paper revisits Bayesian group lasso and uses spike and slab priors for variable selection. 
In the process, the connection of our model with penalized regression is demonstrated, and 
the role of posterior median for thresholding is pointed out. We show that the posterior median 
estimator has the oracle property for group variable selection and estimation under orthogonal 
design while the group lasso has suboptimal asymptotic estimation rate when variable selection 
consistency is achieved.
Next we consider Bayesian sparse group lasso again with spike and slab priors to select variables 
both at the group level and also within the group, and develop the necessary algorithm for 
its implementation. We demonstrate via simulation that the posterior median estimator of our 
spike and slab models has excellent performance in both variable selection and estimation.