Sound and Relatively Complete Belief Hoare Logic for Statistical Hypothesis Testing Programs
This work addresses the need for formal verification in statistical programming, though it appears incremental as it builds on existing Hoare logic and statistical frameworks.
The authors tackled the problem of formally verifying the appropriate use of statistical methods in programs by proposing belief Hoare logic (BHL), which is sound and relatively complete for reasoning about statistical beliefs from hypothesis testing.
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.