从后验信念反推先验规范，为贝叶斯主义提供新基础
The Problem of the Priors, or Posteriors?
- 以未来后验信念为起点，逆向推导先验应遵循的规则
- 提出收敛主义贝叶斯主义，将后验趋近真理视为根本规范
- 适用于统计学与机器学习中奥卡姆剃刀的贝叶斯解释
先验问题广为人知：如何确定支配先验信念的规范。本文主张，解决该问题的关键在于关注我称为‘后验问题’的挑战——即直接确定支配后验信念的规范，这些规范通过时序条件化要求反向约束先验。这一前瞻式方法可概括为‘前瞻，倒推’。尽管此思想可追溯至Freedman（1963）、Carnap（1963）和Shimony（1970），但至今未受足够重视。本文系统辩护前瞻式贝叶斯主义，回应传统观点（主观与客观）的质疑，并提出一种具体路径：将后验信念向真理收敛视为根本而非派生规范。这种收敛主义贝叶斯主义，被论证对统计学与机器学习中奥卡姆剃刀的贝叶斯基础至关重要。
原文摘要 · Abstract (English)
The problem of the priors is well known: it concerns the challenge of identifying norms that govern one's prior credences. I argue that a key to addressing this problem lies in considering what I call the problem of the posteriors -- the challenge of identifying norms that directly govern one's posterior credences, which backward induce some norms on the priors via the diachronic requirement of conditionalization. This forward-looking approach can be summarized as: Think ahead, work backward. Although this idea can be traced to Freedman (1963), Carnap (1963), and Shimony (1970), I believe that it has not received enough attention. In this paper, I initiate a systematic defense of forward-looking Bayesianism, addressing potential objections from more traditional views (both subjectivist and objectivist). I also develop a specific approach to forward-looking Bayesianism -- one that values the convergence of posterior credences to the truth, and treats it as a fundamental rather than derived norm. This approach, called convergentist Bayesianism, is argued to be crucial for a Bayesian foundation of Ockham's razor in statistics and machine learning.
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