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This paper examines, from a historical and model-based Bayesian perspective, two inferential issues: (1) the relation between confidence coverage and credibility of interval statements about model parameters; (2) the prediction of new values of a random variable. Confidence and credible intervals have different properties. This worries some statisticians, who want them to have the same properties,...
Recent papers have discussed general procedures with complex models to obtain confidence interval statements for a parameter of interest in the presence of nuisance parameters. This paper discusses the role of the likelihood in these procedures, and points out the simplicity of the Bayesian credible interval approach to the same models.
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