Probabilities of Causation: Bounds from Incomplete and Subpopulation Data

Probabilities of causation (PoCs) play a central role in individual-level explanation and decision making. Tian and Pearl showed that PoCs are in general not point-identifiable and derived tight bounds for three fundamental PoCs using observational and experimental data. However, in real-world applications, such data are often incomplete; for instance, data may only be available for a subpopulation. In this paper, we show how informative bounds on fundamental PoCs can be obtained from incomplete data. We further investigate whether informative bounds on the PoCs of one subpopulation can be derived given data from another subpopulation; that is, we study the transportability of PoC bounds.