Sound and relatively complete belief Hoare logic for statistical hypothesis testing programs

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.

Automated summary

This paper proposes a new approach for formally describing the requirement for statistical inference and checking the appropriate use of statistical methods in programs. The authors define a belief Hoare logic (BHL) for formalizing and reasoning about statistical beliefs acquired through hypothesis testing. Examples demonstrate the usefulness of BHL in reasoning about practical issues in hypothesis testing, while also discussing the importance of prior beliefs in acquiring statistical beliefs.