Statistical Reasoning: Choosing and Checking the Ingredients, Inferences Based on a Measure of Statistical Evidence...

Area of Science:

• Statistical reasoning and inference
• Bayesian statistics
• Model checking and validation

Background:

• Traditional statistical methods face challenges in handling complex data and prior information.
• A need exists for a logically sound and practically applicable theory of statistical reasoning.
• Existing approaches may not adequately address prior-data conflict or model uncertainty.

Purpose of the Study:

• To discuss the features of a logically sound approach to statistical reasoning.
• To review a specific approach that meets these criteria.
• To demonstrate its utility in resolving anomalies and addressing practical problems.

Main Methods:

• Model selection and rigorous model checking.
• Elicitation of prior distributions with bias assessment.
• Checking for prior-data conflict.
• Inference using a measure of evidence for estimation and hypothesis assessment.

Main Results:

• A comprehensive approach to statistical inference is presented.
• A long-standing anomalous example in statistical reasoning is resolved.
• The approach is applied to a significant practical problem, including a novel elicitation algorithm.

Conclusions:

• The reviewed approach provides a logically sound framework for statistical reasoning.
• It effectively handles model checking, prior elicitation, and prior-data conflict.
• This methodology offers a robust solution for complex statistical inference problems and practical applications.