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Choosing informative priors in Bayesian regression models: a simulation study and tutorial using Stan and R.

Daniel Lüdecke1, Anna C Makowski1, Jens Klein1

  • 1Institute of Medical Sociology, University Medical Center Hamburg-Eppendorf, Hamburg, Germany.

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Summary

Choosing informative priors in Bayesian regression models is crucial for stable and credible results, especially with small sample sizes. This study guides researchers on selecting and justifying priors to improve statistical inference.

Keywords:
Bayesian statisticsinformative priorsprior elicitationsimulation studysmall sample size

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Area of Science:

  • Statistics
  • Biostatistics
  • Psychometrics

Background:

  • Bayesian regression models offer robust analysis for complex data, particularly with small sample sizes common in psychology and medical research.
  • Specifying appropriate prior distributions to regularize model parameters is a significant challenge, potentially leading to unstable or implausible estimates.
  • This study addresses the need for practical guidance on selecting and justifying informative priors to enhance Bayesian model stability and credibility.

Purpose of the Study:

  • To demonstrate the impact of different prior distributions on Bayesian regression models.
  • To provide a practical guide for choosing and justifying informative priors.
  • To produce more stable and credible statistical results.

Main Methods:

  • A simulation study systematically assessed the sensitivity of Bayesian linear regression models to prior specification by varying sample size, prior location, and scale.
  • A case-control study (N=526) applied Bayesian logistic regression to analyze dementia and fall incidence, comparing "believer," "agnostic," and "skeptical" priors.
  • Real-world patient data were used to demonstrate the practical application of informative prior selection.

Main Results:

  • Strongly informative priors significantly influenced posterior estimates in simulations, especially with small sample sizes; larger sample sizes led to estimates converging toward the true effect.
  • Frequentist logistic regression yielded an unstable odds ratio (8.87, CI: 1.66-165.19) for dementia and falls due to data sparsity.
  • A Bayesian model with a "believer" prior produced a more stable odds ratio (4.01, CrI: 1.99-8.78), demonstrating the benefit of justified priors.

Conclusions:

  • Transparent specification of informative priors is critical in Bayesian analysis, particularly for sparse data.
  • Evidence-based priors regularize models, preventing implausible outcomes and enhancing result stability and interpretability.
  • This approach strengthens statistical inference in research fields challenged by small sample sizes.