Optimal information deletion and Bayes' theorem
Fuente:
arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2026
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| _version_ | 1866914580008009728 |
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| author | Montcho, Hans Rue, Håvard |
| author_facet | Montcho, Hans Rue, Håvard |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2602_09061 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Optimal information deletion and Bayes' theorem Montcho, Hans Rue, Håvard Methodology Information Theory Statistics Theory 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. |
| title | Optimal information deletion and Bayes' theorem |
| topic | Methodology Information Theory Statistics Theory |
| url | https://arxiv.org/abs/2602.09061 |