Uncertainty quantification in high dimensional model selection and inference for regression
Abstract/Contents
- Abstract
- Recent advances in $ell_1$-regularization methods have proved to be very useful for high dimensional model selection and inference. In the high dimensional regression context, the lasso and its extensions have been successfully employed to identify parsimonious sets of predictors It is well known that the lasso has the advantage of performing model selection and estimation simultaneously. It is less well understood how much uncertainty the lasso estimates may have due to small sample sizes. To model this uncertainty, we present a method, called the "contour Bayesian lasso" for the purposes of constructing joint credible regions for regression parameters. The contour Bayesian lasso is an extension of a recent approach called the "Bayesian lasso" which in turn is based on the Bayesian interpretation of the lasso. The Bayesian lasso uses a Gibbs sampler to generate from the Bayesian lasso posterior and is thus a convenient approach for quantifying uncertainty of lasso estimates. We give theoretical results regarding the optimality of the contour approach, study posterior consistency and the convergence of the Gibbs sampler. We also analyze the frequentist properties of the Bayesian lasso approach. A theoretical analysis of how the convergence of the Gibbs sampler depends on the dimensionality and sample size is undertaken. Our methodology is also illustrated on simulated and real data. We demonstrate that our posterior credible method has good coverage, and thus yields more accurate sparse solutions when the sample size is small. Real life examples are given for the South African prostate cancer data and the diabetes data set.
Description
| Type of resource | text |
|---|---|
| Form | electronic; electronic resource; remote |
| Extent | 1 online resource. |
| Publication date | 2012 |
| Issuance | monographic |
| Language | English |
Creators/Contributors
| Associated with | Hu, Juegang |
|---|---|
| Associated with | Stanford University, Department of Statistics |
| Primary advisor | Rajaratnam, Balakanapathy |
| Thesis advisor | Rajaratnam, Balakanapathy |
| Thesis advisor | Efron, Bradley |
| Thesis advisor | Johnstone, Iain |
| Thesis advisor | Romano, Joseph P, 1960- |
| Advisor | Efron, Bradley |
| Advisor | Johnstone, Iain |
| Advisor | Romano, Joseph P, 1960- |
Subjects
| Genre | Theses |
|---|
Bibliographic information
| Statement of responsibility | Victor Hu. |
|---|---|
| Note | Submitted to the Department of Statistics. |
| Thesis | Thesis (Ph.D.)--Stanford University, 2012. |
| Location | electronic resource |
Access conditions
- Copyright
- © 2012 by Juegang Hu
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