Power-expected-posterior priors for variable selection in Gaussian linear models

DOI10.1214/14-BA887zbMath1335.62045arXiv1307.2442MaRDI QIDQ273575

Ioannis Ntzoufras, David Draper, Dimitris Fouskakis

Publication date: 22 April 2016

Published in: Bayesian Analysis (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1307.2442

zbMATH Keywords

consistencyBayes factorstraining samplesLASSO\(g\)-priorSCADBayesian variable selectionexpected-posterior priorsGaussian linear modelshyper-\(g\) priornon-local priorspower-priorprior compatibilityunit-information prior

Mathematics Subject Classification ID

Ridge regression; shrinkage estimators (Lasso) (62J07) Linear regression; mixed models (62J05) Bayesian inference (62F15)

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Cites Work

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• Computation for intrinsic variable selection in normal regression models via expected-posterior prior
• Compatibility of prior specifications across linear models
• Consistency of Bayesian procedures for variable selection
• Comparison of Bayesian objective procedures for variable selection in linear regression
• Estimating the dimension of a model
• Training samples in objective Bayesian model selection.
• Optimal predictive model selection.
• The Intrinsic Bayes Factor for Model Selection and Prediction
• Adaptive sampling for Bayesian variable selection
• Statistical challenges of high-dimensional data
• Mixtures of g Priors for Bayesian Variable Selection
• Estimating Optimal Transformations for Multiple Regression and Correlation
• Bayesian and Non-Bayesian Analysis of the Regression Model with Multivariate Student-t Error Terms
• Expected-posterior prior distributions for model selection
• Variable Selection via Nonconcave Penalized Likelihood and its Oracle Properties
• A Reference Bayesian Test for Nested Hypotheses and its Relationship to the Schwarz Criterion
• Bayesian Model Selection in High-Dimensional Settings
• Inference From Intrinsic Bayes’ Procedures Under Model Selection and Uncertainty
• Objective Testing Procedures in Linear Models: Calibration of the p‐values
• Objective Bayesian Variable Selection