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Bayesian variable selection using an adaptive powered correlation prior.

Arun Krishna1, Howard D Bondell, Sujit K Ghosh

  • 1Department of Statistics, North Carolina State University, Raleigh, NC 27695-8203, USA.

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This study introduces a new power parameter for Zellner's g-prior in Bayesian linear models. This parameter adaptively controls predictor correlations, improving model selection and handling collinearity effectively.

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Area of Science:

  • Statistics
  • Bayesian Inference
  • Linear Models

Background:

  • Subset selection in linear models is a significant challenge.
  • Zellner's g-prior, based on the empirical covariance matrix, is a common Bayesian approach.
  • Existing methods may struggle with highly correlated predictors.

Purpose of the Study:

  • To propose an extension of Zellner's g-prior incorporating a power parameter.
  • To enhance the control over predictor smoothing and model selection in the presence of collinearity.
  • To develop a data-adaptive prior selection method.

Main Methods:

  • Introduced a power parameter applied to the empirical covariance matrix of predictors.
  • Utilized the empirical covariance matrix to derive priors over model space.
  • Employed an empirical Bayes method for data-adaptive selection of the power parameter.

Main Results:

  • The power parameter effectively controls the smoothing of correlated predictors.
  • The proposed method adaptively determines the preference for or avoidance of models with collinear predictors.
  • Simulation studies and a real data example demonstrate the parameter's effectiveness.

Conclusions:

  • The modified g-prior with a power parameter offers improved performance over standard Zellner's prior and intrinsic priors.
  • The power parameter provides a flexible and data-driven approach to handling predictor correlations in Bayesian model selection.