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

TL;DR

This paper discusses a logically sound approach to statistical reasoning involving model selection, checking, prior elicitation, and evidence-based inference, demonstrated through resolving anomalies and practical applications.

Contribution

It introduces a comprehensive framework for statistical inference based on measures of evidence, including novel algorithms for prior elicitation and model checking.

Findings

Resolved a long-standing anomalous example using the proposed approach.

Developed a new elicitation algorithm for priors.

Applied the method to a significant practical problem.

Abstract

The features of a logically sound approach to a theory of statistical reasoning are discussed. A particular approach that satisfies these criteria is reviewed. This is seen to involve selection of a model, model checking, elicitation of a prior, checking the prior for bias, checking for prior-data conflict and estimation and hypothesis assessment inferences based on a measure of evidence. A long-standing anomalous example is resolved by this approach to inference and an application is made to a practical problem of considerable importance which, among other novel aspects of the analysis, involves the development of a relevant elicitation algorithm.