A Bayesian Decision-Theoretic Framework for Optimally Managing Asymmetric Error Costs in Hypothesis Testing

Abstract

The classical Neyman–Pearson paradigm of hypothesis testing mandates control of the Type I error rate (α) while maximizing power (1 − β), but this foundational approach has been widely criticized for its rigidity, reliance on arbitrary significance thresholds, and inability to formally incorporate the relative costs of different errors. This paper presents a Bayesian decision-theoretic framework as a principled alternative for optimizing the trade-off between Type I and Type II errors. By combining prior information with observed data to form a posterior distribution and minimizing a loss function that explicitly quantifies the consequences of decisions, the optimal decision rule emerges naturally and balances posterior evidence against asymmetric error costs. A detailed case study in medical diagnostics illustrates the practical advantages of this approach, demonstrating how optimal decisions change when the severity of errors is explicitly taken into account. The paper argues that the Bayesian framework provides a more coherent, flexible, and context-sensitive methodology for statistical decision-making, moving beyond the limitations imposed by a fixed α.