Group Inverse-Gamma Gamma Shrinkage for Sparse Linear Models with Block-Correlated Regressors Article Swipe
Jonathan Boss
,
Jyotishka Datta
,
Xin Wang
,
Sung Kyun Park
,
Jian Kang
,
Bhramar Mukherjee
·
YOU?
·
· 2023
· Open Access
·
· DOI: https://doi.org/10.1214/23-ba1371
YOU?
·
· 2023
· Open Access
·
· DOI: https://doi.org/10.1214/23-ba1371
Heavy-tailed continuous shrinkage priors, such as the horseshoe prior, are widely used for sparse estimation problems. However, there is limited work extending these priors to explicitly incorporate multivariate shrinkage for regressors with grouping structures. Of particular interest in this article, is regression coefficient estimation where pockets of high collinearity in the regressor space are contained within known regressor groupings. To assuage variance inflation due to multicollinearity we propose the group inverse-gamma gamma (GIGG) prior, a heavy-tailed prior that can trade-off between local and group shrinkage in a data adaptive fashion. A special case of the GIGG prior is the group horseshoe prior, whose shrinkage profile is dependent within-group such that the regression coefficients marginally have exact horseshoe regularization. We establish posterior consistency and posterior concentration results for regression coefficients in linear models and mean parameters in sparse normal means models. The full conditional distributions corresponding to GIGG regression can be derived in closed form, leading to straightforward posterior computation. We show that GIGG regression results in low mean-squared error across a wide range of correlation structures and within-group signal densities via simulation. We apply GIGG regression to data from the National Health and Nutrition Examination Survey for associating environmental exposures with liver functionality.
Related Topics
Concepts
Prior probability
Mathematics
Statistics
Variance inflation factor
Multicollinearity
Linear regression
Shrinkage estimator
Shrinkage
Regression
Mean squared error
Applied mathematics
Bayesian probability
Bias of an estimator
Minimum-variance unbiased estimator
Metadata
- Type
- article
- Language
- en
- Landing Page
- https://doi.org/10.1214/23-ba1371
- https://projecteuclid.org/journals/bayesian-analysis/advance-publication/Group-Inverse-Gamma-Gamma-Shrinkage-for-Sparse-Linear-Models-with/10.1214/23-BA1371.pdf
- OA Status
- diamond
- Cited By
- 8
- References
- 59
- Related Works
- 10
- OpenAlex ID
- https://openalex.org/W4321379965
All OpenAlex metadata
Raw OpenAlex JSON
- OpenAlex ID
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https://openalex.org/W4321379965Canonical identifier for this work in OpenAlex
- DOI
-
https://doi.org/10.1214/23-ba1371Digital Object Identifier
- Title
-
Group Inverse-Gamma Gamma Shrinkage for Sparse Linear Models with Block-Correlated RegressorsWork title
- Type
-
articleOpenAlex work type
- Language
-
enPrimary language
- Publication year
-
2023Year of publication
- Publication date
-
2023-02-20Full publication date if available
- Authors
-
Jonathan Boss, Jyotishka Datta, Xin Wang, Sung Kyun Park, Jian Kang, Bhramar MukherjeeList of authors in order
- Landing page
-
https://doi.org/10.1214/23-ba1371Publisher landing page
- PDF URL
-
https://projecteuclid.org/journals/bayesian-analysis/advance-publication/Group-Inverse-Gamma-Gamma-Shrinkage-for-Sparse-Linear-Models-with/10.1214/23-BA1371.pdfDirect link to full text PDF
- Open access
-
YesWhether a free full text is available
- OA status
-
diamondOpen access status per OpenAlex
- OA URL
-
https://projecteuclid.org/journals/bayesian-analysis/advance-publication/Group-Inverse-Gamma-Gamma-Shrinkage-for-Sparse-Linear-Models-with/10.1214/23-BA1371.pdfDirect OA link when available
- Concepts
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Prior probability, Mathematics, Statistics, Variance inflation factor, Multicollinearity, Linear regression, Shrinkage estimator, Shrinkage, Regression, Mean squared error, Applied mathematics, Bayesian probability, Bias of an estimator, Minimum-variance unbiased estimatorTop concepts (fields/topics) attached by OpenAlex
- Cited by
-
8Total citation count in OpenAlex
- Citations by year (recent)
-
2025: 7, 2024: 1Per-year citation counts (last 5 years)
- References (count)
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59Number of works referenced by this work
- Related works (count)
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10Other works algorithmically related by OpenAlex
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