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基于贝叶斯法理学的案件分析
Case Analysis Based on Bayesian Legal Theory

1. 无罪推定与先验概率

Presumption of Innocence and Prior Probability

  • 中文：贝叶斯法理学强调，法律中的“无罪推定”可以理解为对无罪假设 (H_0) 赋予强先验概率。在没有充分证据之前，后验概率应保持接近无罪。

  • English: Bayesian legal theory emphasizes that the legal principle of “presumption of innocence” can be understood as assigning a strong prior probability to the innocence hypothesis (H_0). Without sufficient evidence, the posterior probability should remain close to innocence.

2. 证据与似然函数

Evidence and Likelihood Functions

  • 中文：检方必须提供证据来提升有罪假设 (H_1) 的后验概率。证据的作用是通过似然函数改变信念。然而在本案中，账号粉丝极少、互动几乎为零，缺乏任何客观数据证明“严重混乱”。因此似然比（Bayes factor）接近于 1，无法支持有罪结论。

  • English: The prosecution must provide evidence to increase the posterior probability of the guilt hypothesis (H_1). Evidence works through likelihood functions to update beliefs. In this case, the account had very few followers and almost zero engagement, with no objective data showing “serious disorder.” Thus, the Bayes factor is close to 1, offering no support for a guilty conclusion.

3. 身份与意图的推定

Identity and Presumed Intent

  • 中文：法院以被告的博士身份为由，推定其“必然知道信息是虚假”。这实际上是将身份当作先验概率的提升，而不是基于证据的似然更新。贝叶斯法理学认为，意图是潜在变量，必须通过行为证据来推断，而不是通过身份假设来直接设定。

  • English: The court presumed that because the defendant had a PhD, he “must have known” the information was false. This effectively inflates the prior probability of guilt based on identity rather than updating likelihoods with evidence. Bayesian jurisprudence holds that intent is a latent variable that must be inferred through behavioral evidence, not assumed from identity.

4. 类别错误与假设空间

Category Errors and Hypothesis Space

  • 中文：艺术作品、情感表达、学术观点与事实陈述在逻辑上属于不同类别。将它们全部归为“虚假信息”是错误的假设空间设定。贝叶斯分析要求对不同类别分别建模，否则似然函数无法正确比较。

  • English: Artistic works, emotional expressions, academic viewpoints, and factual statements belong to different logical categories. Lumping them all together as “false information” mis-specifies the hypothesis space. Bayesian analysis requires separate modeling of categories; otherwise, likelihood functions cannot be properly compared.

5. 决策理论与损失函数

Decision Theory and Loss Functions

  • 中文：在贝叶斯法理学中，错误定罪（假阳性）的社会成本远高于错误无罪（假阴性）。因此，在证据不足时，理性决策应选择无罪。这体现了法律中“疑罪从无”的原则。

  • English: In Bayesian legal theory, the social cost of false positives (wrongful convictions) is far greater than false negatives (letting someone go free). Therefore, when evidence is insufficient, rational decision-making should favor acquittal. This reflects the legal principle of “in dubio pro reo” (when in doubt, rule for the accused).

6. 结论

Conclusion

  • 中文：本案在贝叶斯法理学框架下存在三大问题：

    1. 先验被身份不当抬高；

    2. 似然证据缺失或与事实矛盾；

    3. 假设空间错误地混合了不同类别。
      因此，后验概率应仍然倾向于无罪，判决缺乏理性与科学依据。

  • English: Under the Bayesian jurisprudence framework, this case suffers from three major flaws:

    1. Priors were improperly inflated by identity;

    2. Likelihood evidence was missing or contradicted by facts;

    3. The hypothesis space was mis-specified by conflating categories.
      Therefore, the posterior probability should remain in favor of innocence, and the conviction lacks rational and scientific justification.