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Measuring and Controlling Bias for Some Bayesian Inferences and the Relation to Frequentist Criteria
1Department of Statistical Sciences, University of Toronto, Toronto, ON M5G 1Z5, Canada.
Entropy (Basel, Switzerland)
|February 9, 2021
Summary
This study introduces a method to measure and control subjective biases in Bayesian inference, ensuring more objective scientific conclusions. It reconciles Bayesian and frequentist statistical approaches by highlighting their complementary roles in data analysis.
Area of Science:
- Statistics
- Scientific Methodology
Background:
- Bayesian methodology is susceptible to subjective biases in scientific inferences.
- Bias can manifest as bias against or bias in favor of a quantity of interest.
Purpose of the Study:
- To develop a principled approach for measuring and controlling biases in Bayesian hypothesis assessment and estimation.
- To establish optimality results for the principle of evidence in addressing these biases.
Main Methods:
- The principle of evidence is utilized to quantify and manage biases.
- The study establishes connections between Bayesian bias measures and frequentist properties.
Main Results:
- A framework is presented for measuring and controlling both bias against and bias in favor.
- Optimality is demonstrated for the principle of evidence-based approach.
- A link is found between Bayesian bias measurement and frequentist properties for any proper prior.
Conclusions:
- The principle of evidence offers a robust method to mitigate subjective biases in Bayesian statistics.
- This work resolves apparent conflicts between Bayesian and frequentist statistical reasoning.
- Bayesian inference is grounded in statistical evidence, complementing frequentist figures of merit.
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