Sound and Relatively Complete Belief Hoare Logic for Statistical Hypothesis Testing Programs

TL;DR

This paper introduces a belief Hoare logic (BHL) for formally reasoning about the correctness of statistical hypothesis testing programs, emphasizing the role of prior beliefs and providing a sound, relatively complete framework.

Contribution

It presents the first formal logic for verifying statistical hypothesis testing programs, incorporating prior beliefs and ensuring soundness and relative completeness.

Findings

BHL is sound and relatively complete for hypothesis testing programs.

The framework clarifies the role of prior beliefs in statistical inference.

Demonstrates practical reasoning about hypothesis testing issues.

Abstract

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.