Bayesian Estimation with Informative Priors is Indistinguishable from Data Falsification.

Area of Science:

• Statistics
• Research Methodology

Background:

• Growing criticism of null hypothesis significance testing (NHST) and frequentist statistics has led to increased advocacy for Bayesian analyses.
• Bayesian approaches, particularly with informative priors, are often promoted for enabling strong inference in scientific research.

Purpose of the Study:

• To demonstrate the formal equivalence between Bayesian analysis using informative priors and data falsification.
• To establish the necessity of non-informative priors for maintaining research integrity in Bayesian statistics.
• To compare outcomes of Bayesian and frequentist methods under different prior assumptions.

Main Methods:

• Formal analysis showing that the information in informative priors can be represented as fabricated data.
• Comparison of point and interval estimates from Bayesian analyses with uniform priors against frequentist methods.
• Qualitative assessment of the interpretability of Bayesian and frequentist results when uniform priors are employed.

Main Results:

• Bayesian analysis with informative priors is formally equivalent to falsifying data, as prior information can be expressed as added fabricated observations.
• Only non-informative, uniform priors align with research integrity standards in all Bayesian analyses.
• Bayesian estimation using uniform priors produces point and interval estimates nearly identical to frequentist methods.

Conclusions:

• The use of informative priors in Bayesian analysis compromises research integrity due to its equivalence to data falsification.
• Non-informative, uniform priors are essential for credible Bayesian research, leading to results interchangeable with frequentist approaches.
• While statistically interchangeable with uniform priors, Bayesian interpretations necessitate careful consideration of assumptions about population parameters or acknowledge the posterior as representing researcher beliefs.