Why the Decision Theoretic Perspective Misrepresents Frequentist Inference: 'Nuts and Bolts' vs. Learning from Data

Abstract

The primary objective of this paper is to revisit a widely held view that decision theory provides a unifying framework for comparing the frequentist and Bayesian approaches by bringing into focus their common features and neutralizing their differences using a common terminology like decision rules, action spaces, loss and risk functions, admissibility, etc. The paper calls into question this viewpoint and argues that the decision theoretic perspective misrepresents the frequentist viewpoint primarily because the notions of expected loss and admissibility are inappropriate for frequentist inference; they do not represent legitimate error probabilities that calibrate the reliability of inference procedures. In a nutshell, the decision theoreric framing is applicable to what R. A. Fisher called "acceptance sampling", where the decisions revolve around a loss function originating in information `other than the data'. Frequentist inference is germane to scientific inference where the objective is to learn from data about the 'true' data generating mechanism.