ABSTRACT Although teaching Bayes’ theorem is popular, the standard approach—targeting posterior distributions of parameters—may be improved. We advocate teaching Bayes’ theorem in a ratio form where the posterior beliefs relative to the prior beliefs equals the conditional probability of data relative to the marginal probability of data. This form leads to an interpretation that the strength of evidence is relative predictive accuracy. With this approach, students are encouraged to view Bayes’ theorem as an updating mechanism, to obtain a deeper appreciation of the role of the prior and of marginal data, and to view estimation and model comparison from a unified perspective.

中文翻译：

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教学贝叶斯定理：作为预测准确性的证据强度

摘要 虽然贝叶斯定理的教学很流行，但标准方法——针对参数的后验分布——可能会得到改进。我们主张以比率形式教授贝叶斯定理，其中相对于先验信念的后验信念等于数据相对于数据边际概率的条件概率。这种形式导致一种解释，即证据的强度是相对预测准确性。通过这种方法，鼓励学生将贝叶斯定理视为一种更新机制，以更深入地了解先验数据和边际数据的作用，并从统一的角度看待估计和模型比较。