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Measuring statistical evidence using relative belief.

Michael Evans¹

¹Department of Statistics, University of Toronto.

Computational and Structural Biotechnology Journal

|March 1, 2016

Summary

This summary is machine-generated.

This study defines statistical evidence as the change in beliefs from prior to posterior. It proposes measuring evidence by quantifying this belief change, addressing objectivity concerns in statistical inference.

Keywords:

Checking for prior-data conflict Principle of empirical criticism Relative belief ratios Statistical evidence

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Area of Science:

Statistical Inference
Decision Theory

Background:

Measuring statistical evidence is a core challenge in statistical inference.
Existing characterizations of statistical evidence are often elusive.
Defining a quantitative measure for statistical evidence is crucial for robust analysis.

Purpose of the Study:

To provide a precise definition for measuring statistical evidence.
To propose a method for quantifying evidence based on belief change.
To address subjectivity and objectivity in statistical analyses.

Main Methods:

Defining statistical evidence as the change in beliefs from a priori to a posteriori.
Incorporating prior beliefs into the measurement of evidence.
Employing a falsifiability principle for statistical analysis components.

Main Results:

A proposed definition of statistical evidence based on belief transformation.
A framework for assessing prior-data conflict.
Methods for measuring a priori bias within prior beliefs.

Conclusions:

Statistical evidence can be quantitatively measured by the degree of belief change.
The proposed framework enhances objectivity in statistical inference.
The approach allows for the assessment of prior-data consistency.