Note: Accepted for publication as a chapter in "Handbook of the History and Philosophy of Mathematical Practice - Practical, Historical and Philosophical Instances of Probability" (Springer Nature, editor Egan Chernoff) 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.

翻译：注：本文已被接受作为章节收录于《数学实践的历史与哲学手册——概率的实践、历史与哲学实例》（Springer Nature出版，编辑Egan Chernoff）。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方式，也涉及统计推断的方法。在概述主要方法后，我将提出对频率主义概率的重新诠释。大多数统计学家意识到，以频率主义方式解释的概率模型并非客观现实中的真实存在，而仅是理想化模型。我认为，在实际应用频率主义方法并解释其结果时，这一认知常被忽略；而保持对现实与模型本质差异的警觉，可以导向更恰当地使用和诠释频率主义模型与方法，即"频率主义即模型"。本文通过关联现有研究来详细阐述这一观点：首先理解独立同分布观测与领域知识的特殊作用；其次说明非真实模型如何在特定条件下发挥效用；再次对检验和置信区间进行细致解读；接着将其隐含的兼容性逻辑与贝叶斯推断的逆概率逻辑进行对比；然后重新诠释模型假设的作用；最后探讨稳健性及模型的"解释等价性"。认知概率同样面临其模型仅为理想化的问题，因此可类比发展"认知概率即模型"的理念。