Statistical Reasoning: Choosing and Checking the Ingredients, Inferences Based on a Measure of Statistical Evidence with Some Applications
Luai Al-Labadi, Zeynep Baskurt, Michael Evans

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.
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