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A default prior for regression coefficients.

Erik van Zwet1

  • 1Department of Biomedical Data Sciences, Leiden University Medical Center, Leiden, The Netherlands.

Statistical Methods in Medical Research
|December 14, 2018
PubMed
Summary
This summary is machine-generated.

The uniform prior is not ideal for regression coefficient inference in biomedical and social sciences. A normal prior with zero mean and standard deviation matching the M-estimator

Keywords:
Jeffreys priorObjective priorempirical Bayesnormal-normal modelobjective Bayesp-value debatetype M errortype S error

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Area of Science:

  • Statistics
  • Biostatistics
  • Econometrics

Background:

  • M-estimators for regression coefficients are approximately normal and unbiased for sufficient sample sizes.
  • Frequentist inference relies on normality-based confidence intervals and p-values.
  • Bayesian analysis with a uniform prior can yield results matching frequentist bounds, leading to its common use as an objective prior.

Purpose of the Study:

  • To argue against the suitability of the uniform prior for regression coefficient inference in biomedical and social sciences.
  • To propose a more appropriate default prior distribution for regression coefficients.
  • To provide justification for the proposed default prior based on informativeness and empirical evidence.

Main Methods:

  • The study evaluates the properties of the uniform prior in Bayesian inference for regression coefficients.
  • A normal prior distribution with mean zero and standard deviation equal to the M-estimator's standard error is proposed as a default.
  • The proposed prior's informativeness regarding the sign of the regression coefficient is analyzed.
  • The proposed prior's alignment with existing literature is assessed using a meta-analysis of MEDLINE articles.

Main Results:

  • The uniform prior is deemed unsuitable as a default prior for regression coefficient inference in specific scientific fields.
  • A normal prior (mean=0, sd=SE of M-estimator) is recommended as a more suitable default.
  • The recommended normal prior is shown to be non-informative for determining the sign of the regression coefficient.
  • The recommended prior demonstrates good agreement with findings from a meta-analysis of 50 MEDLINE articles.

Conclusions:

  • The uniform prior, despite its common use, is not recommended as a default for regression coefficient inference in biomedical and social sciences.
  • A normal prior distribution with specific parameters offers a more appropriate and informative default choice.
  • The proposed prior is justified by its non-informative nature regarding coefficient sign and its consistency with empirical evidence from scientific literature.