Probabilities of Causation: Role of Observational Data
This work addresses a specific methodological gap in causal inference for decision-making, but it is incremental as it builds directly on prior bounds by Tian and Pearl.
The paper tackles the problem of bounding probabilities of causation when observational data is limited, by defining conditions under which such data improves bound quality, and applies this to unit selection, showing expected improvements under uniform distribution assumptions.
Probabilities of causation play a crucial role in modern decision-making. Pearl defined three binary probabilities of causation, the probability of necessity and sufficiency (PNS), the probability of sufficiency (PS), and the probability of necessity (PN). These probabilities were then bounded by Tian and Pearl using a combination of experimental and observational data. However, observational data are not always available in practice; in such a case, Tian and Pearl's Theorem provided valid but less effective bounds using pure experimental data. In this paper, we discuss the conditions that observational data are worth considering to improve the quality of the bounds. More specifically, we defined the expected improvement of the bounds by assuming the observational distributions are uniformly distributed on their feasible interval. We further applied the proposed theorems to the unit selection problem defined by Li and Pearl.