Home > fiducial inference, publications, simply explained > Confidence levels as degrees of belief

Confidence levels as degrees of belief

13 February 2013

D. R. Bickel, “A frequentist framework of inductive reasoning,” Sankhya A 74, 141-169 (2013). published version | 2009 version cda_displayimage| relationship to a working paper | simple explanation (added 17 July 2017)

A confidence measure is a parameter distribution that encodes all confidence intervals for a given data set, model, and pivot. This article establishes some properties of the confidence measure that commend it as a viable alternative to the Bayesian posterior distribution.

Confidence (correct frequentist coverage) and coherence (compliance with Ramsey-type restrictions on rational belief) are both presented as desirable properties. The only distributions on a scalar parameter space that have both properties are confidence measures.