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Prior sensitivity of null hypothesis Bayesian testing.

Herbert Hoijtink1

  • 1Department of Methodology and Statistics.

Psychological Methods
|September 27, 2021
PubMed
Summary
This summary is machine-generated.

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Bayes factor analysis for hypothesis evaluation shows null hypothesis Bayesian testing (NHBT) is sensitive to prior distribution scale parameters. Adjusting these parameters can improve the reliability of NHBT results.

Area of Science:

  • Statistics
  • Hypothesis Testing
  • Bayesian Inference

Background:

  • Bayes factors are increasingly utilized for hypothesis evaluation in research.
  • Two primary applications include null hypothesis Bayesian testing (NHBT) and informative hypothesis Bayesian testing (IHBT).
  • NHBT's sensitivity to prior distribution scale parameters presents challenges.

Purpose of the Study:

  • To investigate the sensitivity of NHBT to the specification of the scale parameter in prior distributions.
  • To evaluate the operating characteristics of different Bayes factors used in NHBT with default parameter values.
  • To propose a method for selecting the scaling parameter to ensure predictable Bayes factor behavior.

Main Methods:

  • Analysis of four different Bayes factors for NHBT.

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  • Evaluation of the impact of default scaling parameter values on Bayes factor bias.
  • Investigation of a specific scaling parameter choice (yielding a Bayes factor of 19) for zero observed effect size.

    • Main Results:

    • NHBT is sensitive to the scale parameter of the prior distribution, unlike IHBT.
    • Default scaling parameter values in NHBT often lead to unpredictable operating characteristics, biasing the Bayes factor.
    • Setting the scaling parameter to yield a Bayes factor of 19 (for zero effect size) results in clearly specified operating characteristics.

    Conclusions:

    • The choice of scaling parameter significantly impacts NHBT results.
    • A specific adjustment can improve the reliability of NHBT, but does not resolve all associated issues.
    • Further considerations include the multiverse of Bayes factors, calibration, and reporting practices in NHBT.