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Entropy 2018, 20(4), 289; https://doi.org/10.3390/e20040289

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

1
Department of Mathematics, University of Sharjah, P.O. Box 27272 Sharjah, United Arab Emirates
2
Genetics and Genome Biology, Hospital for Sick Children, Toronto, ON M5G 1X8, Canada
3
Department of Statistical Sciences, University of Toronto, Toronto, ON M5S 3G3, Canada
*
Author to whom correspondence should be addressed.
Received: 17 February 2018 / Revised: 5 April 2018 / Accepted: 11 April 2018 / Published: 16 April 2018
(This article belongs to the Special Issue Foundations of Statistics)
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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. View Full-Text
Keywords: statistical reasoning; model checking; elicitation of priors; checking priors; measuring statistical evidence; relative belief inferences statistical reasoning; model checking; elicitation of priors; checking priors; measuring statistical evidence; relative belief inferences
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Al-Labadi, L.; Baskurt, Z.; Evans, M. Statistical Reasoning: Choosing and Checking the Ingredients, Inferences Based on a Measure of Statistical Evidence with Some Applications. Entropy 2018, 20, 289.

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