Calibrated Bayes: a Bayes/frequentist roadmap

The lack of an agreed inferential basis for statistics makes life “interesting” for academic statisticians, but at the price of negative implications for the status of statistics in industry, science, and government. The practice of our discipline will mature only when we can come to a basic agreement about how to apply statistics to real problems. Simple and more general illustrations are given of the negative consequences of the existing schism between frequentists and Bayesians. An assessment of strengths and weaknesses of the frequentist and Bayes systems of inference suggests that calibrated Bayes–a compromise based on the works of Box, Rubin, and others–captures the strengths of both approaches and provides a roadmap for future advances. The approach asserts that inferences under a particular model should be Bayesian, but model assessment can and should involve frequentist ideas. This article also discusses some implications of this proposed compromise for the teaching and practice of statistics. KEY WORDS: Bayesian statistics; Frequentist statistics; Likelihood principle; Model checking; Statistical inference.