统计数据分析中的概率模型：用途、解释与频率主义即模型
Probability Models in Statistical Data Analysis: Uses, Interpretations, Frequentism-As-Model
AI总结：
本文重新解释频率主义概率，提出“频率主义即模型”观点，强调区分现实与模型理想化，以改进频率主义方法的使用与解释，并探讨其与贝叶斯推断的差异及模型假设的作用。
摘要：
注：现作为一章发表于《数学实践的历史与哲学手册》（Springer Nature，主编 B. Sriraman，https://doi.org/10.1007/978-3-030-19071-2_105-1）。数学概率论在统计学中的应用颇具争议。争议既涉及概率的解释，也涉及统计推断的方法。在概述主要方法之后，我将提出对频率主义概率的重新解释。大多数统计学家意识到，以频率主义方式解释的概率模型在客观现实中并非真实，而只是理想化。我认为，在实际应用频率主义方法并解释结果时，这一点常被忽视，而保持对现实与模型之间本质差异的警觉，可以促成对频率主义模型和方法的更恰当使用与解释，称为“频率主义即模型”。本文通过展示与现有工作的联系来详细阐述，重视独立同分布观测和领域知识所起的特殊作用，说明不真实的模型在何种条件下以及如何能够有用，对检验和置信区间给出详细解释，将其隐含的相容性逻辑与贝叶斯推断的逆概率逻辑相对照，重新解释模型假设的作用，重视稳健性，以及模型“解释等价性”的作用。认知概率也存在同样的问题，即其模型仅是理想化，因此也可以发展类似的“认知概率即模型”。
英文摘要：
Note: Published now as a chapter in "Handbook of the History and Philosophy of Mathematical Practice" (Springer Nature, editor B. Sriraman, https://doi.org/10.1007/978-3-030-19071-2_105-1). The application of mathematical probability theory in statistics is quite controversial. Controversies regard both the interpretation of probability, and approaches to statistical inference. After having given an overview of the main approaches, I will propose a re-interpretation of frequentist probability. Most statisticians are aware that probability models interpreted in a frequentist manner are not really true in objective reality, but only idealisations. I argue that this is often ignored when actually applying frequentist methods and interpreting the results, and that keeping up the awareness for the essential difference between reality and models can lead to a more appropriate use and interpretation of frequentist models and methods, called "frequentism-as-model". This is elaborated showing connections to existing work, appreciating the special role of independently and identically distributed observations and subject matter knowledge, giving an account of how and under what conditions models that are not true can be useful, giving detailed interpretations of tests and confidence intervals, confronting their implicit compatibility logic with the inverse probability logic of Bayesian inference, re-interpreting the role of model assumptions, appreciating robustness, and the role of "interpretative equivalence" of models. Epistemic probability shares the issue that its models are only idealisations, and an analogous "epistemic-probability-as-model" can also be developed.
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