What is it about?
Q. What is a confidence distribution? A. A parameter probability distribution that encodes all confidence intervals for a given data set, model, and pivot. This article establishes some properties of the confidence distribution that may commend it as a viable alternative to the Bayesian posterior distribution.
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Why is it important?
This paper presents a framework based on both confidence (correct frequentist coverage) and coherence (compliance with minimal restrictions on rational decisions) as desirable properties. It demonstrates that only distributions on a scalar parameter space that have both properties are confidence distributions.
Perspectives
In this paper, I address the old Bayesian criticism that frequentist methods are not coherent, that they can lead to bizarre inferences when confidence is interpreted as a level of belief that the true value of the parameter lies within the confidence interval. Since this paper does not have any fiducial distributions that are not also confidence distributions, it is less controversial from a frequentist viewpoint than papers on coherent fiducial inference.
David R. Bickel
University of North Carolina at Greensboro
Read the Original
This page is a summary of: A frequentist framework of inductive reasoning, Sankhya A, August 2012, Springer Science + Business Media, DOI: 10.1007/s13171-012-0020-x.
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