Coherent frequentism

The certainty distribution, a fiducial-like distribution of a scalar interest parameter, combines the logical consistency of Bayesian methods with the reliability of Neyman-Pearson methods. As a probability distribution over parameter space, the certainty distribution is coherent in the sense that it satisfies the axioms of the decision-theoretic and logic-theoretic systems typically cited in support of the Bayesian posterior distribution. Since the probabilities of a certainty distribution by definition are equal to the coverage rates of the corresponding confidence intervals, the resulting inferences are uniquely minimax to risk in a betting game designed to quantify inferential reliability.