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.

翻译：我们提出了一种新的方法，用于形式化描述统计推断的需求，并检查程序是否恰当地使用了统计方法。具体而言，我们定义了信念霍尔逻辑（BHL），用于形式化并推理通过假设检验获得的统计信念。该程序逻辑相对于为假设检验构建的克里普克模型是可靠且相对完备的。我们通过示例展示了BHL在推理假设检验中实际问题方面的实用性。在我们的框架中，我们阐明了先验信念在通过假设检验获取统计信念中的重要性，并讨论了程序逻辑内部与外部统计推断合理性的整体图景。