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Variable Selection Using Nonlocal Priors in High-Dimensional Generalized Linear Models With Application to fMRI Data

Xuan Cao1, Kyoungjae Lee2

  • 1Department of Mathematical Sciences, University of Cincinnati, Cincinnati, OH 45221, USA.

Entropy (Basel, Switzerland)
|December 8, 2020
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Summary

This study establishes strong model selection consistency for nonlocal priors in high-dimensional generalized linear models. The findings are crucial for accurate variable selection in complex statistical analyses.

Keywords:
high-dimensionalnonlocal priorstrong selection consistency

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Area of Science:

  • Statistics
  • Statistical modeling
  • Machine learning

Background:

  • High-dimensional variable selection is critical in modern statistics.
  • Nonlocal priors are well-studied for linear regression but not generalized linear models.
  • Model selection properties of nonlocal priors in high-dimensional generalized linear models remain underexplored.

Purpose of the Study:

  • To investigate the high-dimensional model selection properties of nonlocal priors in generalized linear models.
  • To establish theoretical guarantees for variable selection consistency.
  • To apply the developed methods to real-world neuroimaging data.

Main Methods:

  • Utilized a hierarchical generalized linear regression model.
  • Employed a product moment nonlocal prior over coefficients.
  • Established strong model selection consistency under standard regularity assumptions.
  • Implemented Laplace approximation for posterior probability computation.
  • Employed shotgun stochastic search for posterior space exploration.

Main Results:

  • Demonstrated strong model selection consistency in high-dimensional settings.
  • Showed that the number of covariates can grow sub-exponentially with sample size.
  • Validated the proposed method via simulation studies.
  • Illustrated the method's utility with a functional activity analysis in fMRI data for Parkinson's disease prediction.

Conclusions:

  • The proposed method provides a robust approach for variable selection in high-dimensional generalized linear models.
  • This research fills a critical gap in understanding nonlocal priors for complex statistical models.
  • The findings have implications for predictive modeling in various fields, including neuroscience.