AI 中文总结
本文以足球进球频率估算为例，运用戴维森的哲学理论批判贝叶斯统计的常见二元区分，提出统计实践需满足融贯性、慈善性与三角测量法三项约束以优化实践。
AI 中文摘要
贝叶斯统计基于几个常见区分：频率学派与贝叶斯学派、客观概率与主观概率、模型与拟合所用数据、先验与后验。本文运用唐纳德·戴维森的“经验论的第三教条”，从图式-内容二元论角度批判这些区分。以估算足球（soccer）球队进球频率的单一运行示例，论证信念本身具有客观性，模型与数据应被视为同一信念系统的组成部分而非不同类事物，贝叶斯定理描述该系统内部关系而非外部数据对模型的更新。关键在于信念系统如何构建、检验与重建。为此，运用戴维森的彻底解释建构纲领，提出信念系统不仅需具备融贯性（统计学家已有要求），还应具备慈善性与三角测量法，需对他人及共享世界负责。本文主张，这三项约束恰好是从先验 eliciting 到模型检验等优良统计实践已试图满足的要求，明确讨论这些约束可改进统计实践。
英文摘要
Bayesian statistics rests on a few familiar distinctions: frequentist vs. Bayesian, objective versus subjective probability, a model versus the data it is fitted to, a prior versus a posterior. Here, I use Donald Davidson's "third dogma of empiricism" to critique such distinctions in terms of scheme/content dualisms. With a single running example -- estimating how often a football (soccer) team scores -- I argue that a degree of belief is in itself objective, that model and data are better seen as parts of one belief system than as different kinds of things, and that Bayes' theorem describes relations within that system rather than data updating a model from outside. What matters instead is how belief systems are built, checked and rebuilt. To this end, I use Davidson's constructive programme of radical interpretation to suggest that a belief system should be not only coherent (as statisticians already require) but also charitable and triangulated, answerable to other people and to a shared world. I argue that these three constraints are exactly what good statistical practice -- from eliciting priors to checking models -- already tries to satisfy and talking about them explicitly could improve this practice.
