Measuring and Controlling Bias for Some Bayesian Inferences and the Relation to Frequentist Criteria

TL;DR

This paper explores how to measure and control bias in Bayesian inferences, linking Bayesian and frequentist approaches to improve the objectivity and reliability of statistical conclusions.

Contribution

It introduces a method to quantify and manage bias in Bayesian inference, establishing optimality results and clarifying the relationship with frequentist criteria.

Findings

Bias can be measured and controlled using the principle of evidence.

Optimality results support the use of the principle of evidence.

A connection between Bayesian bias measurement and frequentist properties is demonstrated.

Abstract

A common concern with Bayesian methodology in scientific contexts is that inferences can be heavily influenced by subjective biases. As presented here, there are two types of bias for some quantity of interest: bias against and bias in favor. Based upon the principle of evidence, it is shown how to measure and control these biases for both hypothesis assessment and estimation problems. Optimality results are established for the principle of evidence as the basis of the approach to these problems. A close relationship is established between measuring bias in Bayesian inferences and frequentist properties that hold for any proper prior. This leads to a possible resolution to an apparent conflict between these approaches to statistical reasoning. Frequentism is seen as establishing a figure of merit for a statistical study, while Bayesianism plays the key role in determining inferences based upon statistical evidence.