My Statistics is Better than Yours (2412.10296v3)

Abstract: Statistical schools-such as Bayesianism and Frequentism-are often presented as competing frameworks, each claiming technical rigour and superiority. Frequentism emphasizes objective inferences through repeated sampling, while Bayesianism incorporates prior beliefs and updates them with new evidence. Despite their strengths, neither school proves universally applicable, and the pursuit of a single "correct" statistical framework is ultimately misguided. Instead, this essay advocates for a context-dependent approach to statistical norms, drawing on Douglas (2004)'s concept of "operational objectivity". The idea is that by aligning the context of the research question with the value judgments inherent to its field, a certain statistical paradigm is warranted. This essay explores the decision-theoretic foundations of Bayesianism, examines its descriptive limitations as highlighted by the Ellsberg paradox, and addresses the challenges of comparing different normative systems.