Epsilon-Identifiability of Causal Quantities

Identifying the effects of causes and causes of effects is vital in virtually every scientific field. Often, however, the needed probabilities may not be fully identifiable from the data sources available. This paper shows how partial identifiability is still possible for several probabilities of causation. We term this epsilon-identifiability and demonstrate its usefulness in cases where the behavior of certain subpopulations can be restricted to within some narrow bounds. In particular, we show how unidentifiable causal effects and counterfactual probabilities can be narrowly bounded when such allowances are made. Often those allowances are easily measured and reasonably assumed. Finally, epsilon-identifiability is applied to the unit selection problem.