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Adaptive prior weighting in generalized regression.

Leonhard Held1, Rafael Sauter1

  • 1Department of Biostatistics, Epidemiology, Biostatistics and Prevention Institute, University of Zurich, Hirschengraben 84, 8001 Zurich, Switzerland.

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Summary
This summary is machine-generated.

This study introduces adaptive prior weighting for Bayesian regression models to handle conflicts between prior information and observed data. The method improves model performance when prior specifications are incorrect.

Keywords:
Generalized regressionHyper-g priorINLAPrior weightPrior-data conflictg-prior

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Area of Science:

  • Statistics
  • Bayesian Inference
  • Regression Modeling

Background:

  • Prior distributions are crucial in Bayesian inference.
  • Prior-data conflict can arise from conflicting information sources.
  • Lack of clear guidance exists for handling prior-data conflict in generalized regression.

Purpose of the Study:

  • To propose adaptive weighting for multivariate normal prior distributions in regression.
  • To address the deficiency in handling prior-data conflict in generalized regression models.
  • To provide a Bayesian framework for managing prior-data conflict.

Main Methods:

  • Adaptive weighting of prespecified multivariate normal prior distributions.
  • Relating empirical Bayes estimates of prior weight to Box's p-value.
  • Implementing methods using Integrated Nested Laplace Approximations (INLA).
  • Applying to Bayesian logistic regression and Bayesian generalized linear mixed models.

Main Results:

  • Demonstrated applicability using logistic regression for cross-sectional data.
  • Simulation studies showed excellent performance in root mean squared error and coverage under prior misspecification.
  • Supplementary materials detail software implementation and application to longitudinal data.

Conclusions:

  • The proposed adaptive prior weighting method effectively manages prior-data conflict in Bayesian regression.
  • The methodology is implementable and performs well, even with misspecified priors.
  • Offers a robust approach for generalized regression models in various study designs.