Testing Partially-Identifiable Causal Queries Using Ternary Tests

2026-02-26

AI Summary

This study addresses the challenge that traditional binary hypothesis testing struggles to directly support causal inference in partially identifiable causal queries. To overcome this limitation, the paper introduces—for the first time—a systematic ternary (three-outcome) statistical testing framework. By establishing unified consistency and equivalence topological conditions, the authors provide principled guidance for constructing valid ternary tests and demonstrate that such tests can be fully implemented by appropriately combining existing binary testing tools. The proposed approach is successfully applied to scenarios including instrumental variable inequality testing and comparative treatment effect analysis, offering a reliable and operational inferential methodology for partially identifiable causal problems.

Technology Category

• Reasoning under Uncertainty: Causality
• Machine Learning: Causal Learning
• Constraint Satisfaction and Optimization: Satisfiability

Application Category

• Graph Algorithms and Modeling for the Web: Algorithms and analysis for incomplete, noisy, or partially observed Web-related graphs
• Search and Retrieval-Augmented AI: Web evaluation methodologies and metrics
• Security and Privacy: Large-scale security measurements

Abstract

We consider hypothesis testing of binary causal queries using observational data. Since the mapping of causal models to the observational distribution that they induce is not one-to-one, in general, causal queries are often only partially identifiable. When binary statistical tests are used for testing partially-identifiable causal queries, their results do not translate in a straightforward manner to the causal hypothesis testing problem. We propose using ternary (three-outcome) statistical tests to test partially-identifiable causal queries. We establish testability requirements that ternary tests must satisfy in terms of uniform consistency and present equivalent topological conditions on the hypotheses. To leverage the existing toolbox of binary tests, we prove that obtaining ternary tests by combining binary tests is complete. Finally, we demonstrate how topological conditions serve as a guide to construct ternary tests for two concrete causal hypothesis testing problems, namely testing the instrumental variable (IV) inequalities and comparing treatment efficacy.

Problem

• causal queries
• partial identifiability
• hypothesis testing
• observational data
• ternary tests

Innovation

• ternary tests
• partially-identifiable causal queries
• causal hypothesis testing
• uniform consistency
• topological conditions