Deciding with Judgment

Non sample information is hidden in frequentist statistics in the choice of the hypothesis to be tested and of the confidence level. Explicit treatment of these elements provides the connection between Bayesian and frequentist statistics. A frequentist decision maker starts from a judgmental decision and moves to the closest boundary of the confidence interval of the first order conditions, for a given loss function. This statistical decision rule does not perform worse than the judgmental decision with a probability equal to the confidence level. For any given prior, there is a mapping from the sample realization to the confidence level which makes Bayesian and frequentist decision rules equivalent. Frequentist decision rules can be interpreted as decisions under ambiguity