Sound and Relatively Complete Belief Hoare Logic for Statistical Hypothesis Testing Programs
| Autor: | Kawamoto, Yusuke, Sato, Tetsuya, Suenaga, Kohei |
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| Rok vydání: | 2022 |
| Předmět: | |
| Zdroj: | Artificial Intelligence, Vol.326, 104045, Elsevier, 2024 |
| Druh dokumentu: | Working Paper |
| DOI: | 10.1016/j.artint.2023.104045 |
| Popis: | We propose a new approach to formally describing the requirement for statistical inference and checking whether a program uses the statistical method appropriately. Specifically, we define belief Hoare logic (BHL) for formalizing and reasoning about the statistical beliefs acquired via hypothesis testing. This program logic is sound and relatively complete with respect to a Kripke model for hypothesis tests. We demonstrate by examples that BHL is useful for reasoning about practical issues in hypothesis testing. In our framework, we clarify the importance of prior beliefs in acquiring statistical beliefs through hypothesis testing, and discuss the whole picture of the justification of statistical inference inside and outside the program logic. Comment: Accepted to the journal Artificial Intelligence (AI); an extended version of the KR'21 conference paper https://proceedings.kr.org/2021/39/ |
| Databáze: | arXiv |
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