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.

我们提出了一种新方法来正式描述统计推断的要求并检查程序是否适当地使用了统计方法。具体来说，我们定义信念霍尔逻辑（BHL），用于对通过假设检验获得的统计信念进行形式化和推理。该程序逻辑相对于假设检验的 Kripke 模型来说是合理且相对完整的。我们通过例子证明 BHL 对于推理假设检验中的实际问题非常有用。在我们的框架中，我们阐明了先验信念在通过假设检验获得统计信念方面的重要性，并讨论了程序逻辑内部和外部统计推断合理性的全貌。