论文标题
统计数据分析中的概率模型：用途，解释，频繁主义与模型
Probability Models in Statistical Data Analysis: Uses, Interpretations, Frequentism-As-Model
论文作者
论文摘要
注意：现在以“数学实践历史和哲学手册”的章节发表（Springer Nature，编辑B. Sriraman，https://doi.org/10.1007/978-3-3-030-19071-2_105-1）。 数学概率理论在统计数据中的应用是有争议的。有争议的概率解释和统计推断的方法。在概述了主要方法之后，我将提出对频繁概率的重新解释。大多数统计学家都知道，以常见方式解释的概率模型在客观现实中并不是真正的，而是理想化。我认为，当实际应用频繁的方法并解释结果时，通常会忽略这一点，并且保持对现实和模型之间本质差异的认识可能会导致更适当的使用和解释频繁的模型和方法，称为“频繁主义 - 是模样”。这是对现有工作的联系，欣赏独立和相同分布的观察和主题知识的特殊作用的详尽，并说明了如何和在不正确的条件模型下如何和下方的模型可以有用，对测试和置信区间的详细解释，与他们的隐式逻辑相吻合，并与模型的不利性逻辑相抗性，并与模型的不利性逻辑相吻合，并与模型的依赖性相抗性，并与模型的作用相关，并将其置于模型中的作用，并将其构成依据，以构成模型，并与之相遇，并符合模型的作用，并与之相遇，并符合依据的作用。模型的“解释性对等”。认识论的概率共有一个问题，即它的模型仅是理想化的，并且也可以开发出类似的“认知概率 - 模型”。
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.
