Deciding with Judgment

Abstract

Non sample information is hidden in frequentist statistics in the choiceof the hypothesis to be tested and of the confidence level. Explicittreatment of these elements provides the connection between Bayesianand frequentist statistics. A frequentist decision maker starts from ajudgmental decision (the decision taken in the absence of data) andmoves to the closest boundary of the confidence interval of the first or-der conditions, for a given loss function. This statistical decision ruledoes not perform worse than the judgmental decision with a proba-bility equal to the confidence level. For any given prior, there is amapping from the sample realization to the confidence level whichmakes Bayesian and frequentist decision rules equivalent. Frequentistdecision rules can also be interpreted as decisions under ambiguity.

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