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

翻译：在同一期刊中，Arnold Zellner曾发表关于贝叶斯定理作为最优信息处理规则的奠基性论文。该成果催生了贝叶斯定理的变分表述，这构成了广义变分推断的核心思想。近四十年后，我们从信息删除的视角重新审视这些思想。我们研究了当部分数据被移除时，将后验分布更新为前数据分布的规则。在此语境下，不破坏或创造信息的规则被称为最优信息删除规则，我们证明该规则与传统贝叶斯定理的应用完全一致。