File Download
There are no files associated with this item.
Links for fulltext
(May Require Subscription)
- Publisher Website: 10.1214/17-BA1076
- Scopus: eid_2-s2.0-85047822701
- WOS: WOS:000434021600007
- Find via
Supplementary
- Citations:
- Appears in Collections:
Article: Variable selection via penalized credible regions with Dirichlet-Laplace global-local shrinkage priors
Title | Variable selection via penalized credible regions with Dirichlet-Laplace global-local shrinkage priors |
---|---|
Authors | |
Keywords | Variable selection Posterior consistency Hyperparameter tuning Posterior credible region Global-local shrinkage prior Dirichlet-Laplace |
Issue Date | 2018 |
Citation | Bayesian Analysis, 2018, v. 13, n. 3, p. 823-844 How to Cite? |
Abstract | © 2018 International Society for Bayesian Analysis. The method of Bayesian variable selection via penalized credible regions separates model fitting and variable selection. The idea is to search for the sparsest solution within the joint posterior credible regions. Although the approach was successful, it depended on the use of conjugate normal priors. More recently, improvements in the use of global-local shrinkage priors have been made for highdimensional Bayesian variable selection. In this paper, we incorporate global-local priors into the credible region selection framework. The Dirichlet-Laplace (DL) prior is adapted to linear regression. Posterior consistency for the normal and DL priors are shown, along with variable selection consistency. We further introduce a new method to tune hyperparameters in prior distributions for linear regression. We propose to choose the hyperparameters to minimize a discrepancy between the induced distribution on R-square and a prespecified target distribution. Prior elicitation on R-square is more natural, particularly when there are a large number of predictor variables in which elicitation on that scale is not feasible. For a normal prior, these hyperparameters are available in closed form to minimize the Kullback-Leibler divergence between the distributions. |
Persistent Identifier | http://hdl.handle.net/10722/276595 |
ISSN | 2023 Impact Factor: 4.9 2023 SCImago Journal Rankings: 1.761 |
ISI Accession Number ID |
DC Field | Value | Language |
---|---|---|
dc.contributor.author | Zhang, Yan | - |
dc.contributor.author | Bondell, Howard D. | - |
dc.date.accessioned | 2019-09-18T08:34:05Z | - |
dc.date.available | 2019-09-18T08:34:05Z | - |
dc.date.issued | 2018 | - |
dc.identifier.citation | Bayesian Analysis, 2018, v. 13, n. 3, p. 823-844 | - |
dc.identifier.issn | 1936-0975 | - |
dc.identifier.uri | http://hdl.handle.net/10722/276595 | - |
dc.description.abstract | © 2018 International Society for Bayesian Analysis. The method of Bayesian variable selection via penalized credible regions separates model fitting and variable selection. The idea is to search for the sparsest solution within the joint posterior credible regions. Although the approach was successful, it depended on the use of conjugate normal priors. More recently, improvements in the use of global-local shrinkage priors have been made for highdimensional Bayesian variable selection. In this paper, we incorporate global-local priors into the credible region selection framework. The Dirichlet-Laplace (DL) prior is adapted to linear regression. Posterior consistency for the normal and DL priors are shown, along with variable selection consistency. We further introduce a new method to tune hyperparameters in prior distributions for linear regression. We propose to choose the hyperparameters to minimize a discrepancy between the induced distribution on R-square and a prespecified target distribution. Prior elicitation on R-square is more natural, particularly when there are a large number of predictor variables in which elicitation on that scale is not feasible. For a normal prior, these hyperparameters are available in closed form to minimize the Kullback-Leibler divergence between the distributions. | - |
dc.language | eng | - |
dc.relation.ispartof | Bayesian Analysis | - |
dc.subject | Variable selection | - |
dc.subject | Posterior consistency | - |
dc.subject | Hyperparameter tuning | - |
dc.subject | Posterior credible region | - |
dc.subject | Global-local shrinkage prior | - |
dc.subject | Dirichlet-Laplace | - |
dc.title | Variable selection via penalized credible regions with Dirichlet-Laplace global-local shrinkage priors | - |
dc.type | Article | - |
dc.description.nature | link_to_OA_fulltext | - |
dc.identifier.doi | 10.1214/17-BA1076 | - |
dc.identifier.scopus | eid_2-s2.0-85047822701 | - |
dc.identifier.volume | 13 | - |
dc.identifier.issue | 3 | - |
dc.identifier.spage | 823 | - |
dc.identifier.epage | 844 | - |
dc.identifier.eissn | 1931-6690 | - |
dc.identifier.isi | WOS:000434021600007 | - |
dc.identifier.issnl | 1931-6690 | - |