发表机构
University of Maine（缅因大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
该研究针对自适应和AI介导场景中概率的两种角色分歧问题，综合多领域成果提出角色分离原则，开发统一稳定性框架并应用于AI输出校准等场景。
AI 中文摘要
概率在现代数据分析实践中扮演着两种截然不同的角色：(i) 作为一种内部相干、相对于滤子的语言，用于序贯预测，并结合给定的损失或效用进行决策；(ii) 作为经验性主张的基础，例如稳定性、校准性以及重复抽样的有效性。第一种角色相对于评估律$\boldsymbol{Q}$，而第二种角色则在支配律$\boldsymbol{P}$和已声明的重复机制下进行评估。在经典场景中，这些角色通常通过$\boldsymbol{P}$下的条件正确性、固定设计下的独立同分布（i.i.d.）或其他稳定律假设，或者通过可交换性实现对齐。在自适应和AI介导的场景中，这些角色可能会出现分歧，因为预测在反馈循环中运行，而可靠性则在潜在不同的律和机制下进行评估。我们综合了序贯预测、校准、鞅和博弈论有效性、自适应数据分析、保形预测以及长上下文AI可靠性的相关结果，形成了关于「角色分离」的正式论述。由此得出的「角色分离原则」将内部相干性与评估律下的条件均值正确性、以及针对目标的参考和稳定性条件区分开来。两个分离结果表明，极限频率分布的适当粗化不一定能识别支配律，且即使在该律下条件正确的预测也不一定伴随稳定性。随后，我们开发了一个统一的稳定性框架，涵盖基于滤子、基于偏移、策略-环境以及基于设计的机制，并通过一个机制条件审计清单将其付诸实施。应用示例阐明了校准主张、合成数据的有效性，以及与某些高置信度但无依据的AI输出相关的结构不匹配问题。
英文摘要
Probability plays two distinct roles in modern data-analytic practice: (i) as an internally coherent, filtration-relative language for sequential forecasting and, together with a stated loss or utility, decision making; and (ii) as a foundation for empirical claims such as stabilization, calibration, and repeated-sampling validity. The first role is relative to an assessment law $\mathbb Q$, whereas the second is evaluated under a governing law $\mathbb P$ and a declared repetition regime. In classical settings the roles are often aligned by conditional correctness under $\mathbb P$ together with i.i.d.\ or other stable-law assumptions under a fixed design, or by exchangeability. In adaptive and AI-mediated settings they can diverge because forecasts operate within feedback loops while reliability is evaluated under a potentially different law and regime. We synthesize relevant results from prequential forecasting, calibration, martingale and game-theoretic validity, adaptive data analysis, conformal prediction, and long-context AI reliability into a formal account of \emph{role separation}. The resulting \emph{Role Separation Principle} distinguishes internal coherence from conditional-mean correctness under the evaluation law and from target-specific reference and stability conditions. Two separation results show that a proper coarsening of the limiting-frequency distribution need not identify the governing law, and that even conditionally correct forecasts under that law need not accompany stabilization. We then develop a unified stabilization framework spanning filtration-based, shift-based, policy--environment, and design-based regimes and operationalize it through a regime-conditional audit checklist. Applied illustrations clarify calibration claims, synthetic-data validity, and structural mismatches relevant to some high-confidence unsupported AI outputs.
Comments50 pages, 2 figures
