Confidence is epistemic probability for empirical science

In its orthodoxy standard frequentist statistics deals only with aleatory probability, suppressing the intuitive epistemic probability representing inferential uncertainty. Confidence distributions, which are posterior distributions not based on any Bayesian priors, are discussed in nontechnical terms, with emphasis on the confidence curve. The correspondence between confidence curves and likelihoods allows independent confidence curves and confidence intervals to be integrated. Confidence and (serious) p-values are interpreted as epistemic probabilities, which do not fully follow ordinary probability calculus. Dimension reduction and other operations might be done on the likelihood related to the confidence curve. Confidence distributions and objective Bayes have much in common.