Arnold Zellner published a seminal paper on Bayes' theorem as an optimal information processing rule, a result that led to the variational formulation of Bayes' theorem, and a central idea in generalized variational inference. Almost 40 years later, we revisit these ideas, but from the perspective of information deletion. We investigate rules that update a posterior distribution into an antedata distribution when a portion of data is removed. In such context, a rule that does not destroy or create nonexistent information is called the optimal information deletion rule and we prove that it coincides with the leave-data-out posterior from Bayes' theorem.

翻译：Arnold Zellner 发表了一篇关于贝叶斯定理作为最优信息处理规则的里程碑式论文，该结果引出了贝叶斯定理的变分形式，也成为广义变分推断的核心思想。时隔近40年，我们重新审视这些思想，但这次从信息删除的角度出发。我们研究当移除部分数据时，将后验分布更新为"前数据分布"的规则。在此背景下，不破坏或创造不存在信息的规则被称为最优信息删除规则，我们证明该规则恰好等同于贝叶斯定理中的留出数据后验分布。